# Instruments and Equipment > Builders and Repair >  What is the function of the body?

## billhay4

I've been mulling this over in the quiet moments before I fall asleep.
It occurred to me that a harp doesn't have a sound board or sound box, yet it still makes beautiful music. So, what exactly are the functions of a sound board and sound box? Do they focus the sound, add certain qualities to it, amplify it, or something else?
That being asked, I'm led to a bigger question: what exactly is sound? I assume it's vibrations that are at a frequency the human ear detects and converts to certain signals to the brain. But is it just vibrations of the air? or of something else (the ether? disturbances in the space/time continuum? what?) I know sound travels through other mediums besides air, so what exactly has to vibrate to create sound? I'm being a bit silly here but I would like a concise definition of sound from someone who understands this better than I do.
For now, however, I am going on the assumption that my definition of sound is more or less correct which leads me back to my original question: how does the mandolin shape, size, construction, composition produce the particular sounds we associate with the instrument? Can they be produced another way?
Papers due at 12:00. No cheating.
Bill

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## murrmac

> It occurred to me that a harp doesn't have a sound board or sound box, yet it still makes beautiful music.


All the harps I have ever seen had a soundboard and a soundbox ...

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## billhay4

Concert harps?
Bill

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## billhay4

Seems like they might. So, then is a sound box or sound board necessary for an instrument to produce it's tone?
Bill

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## murrmac

I dig what you are saying ... Alan Carruth would be the man to answer your questions, but I don't know if he posts on here ...

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## bassthumper

best that I can tell the vibration is "formed" inside the sound chamber...

different tone woods influence the sound when used in various components....

instrument construction be it flat/arched tops..varied thickness in tap tuned tops/backs tend toward desired sound in the finished product

I suspect the size of concert harps they bounce the vibrations off surroundings...while I have no experience with harps maybe someone in the know could chime in...I suspect the placement in a room, size of rom etc. causes difference in tone

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## Mark Gunter

> I would like a concise definition of sound from someone who understands this better than I do.


Dang, Bill, I wish I knew more about this stuff myself. Unfortunately, I'm not that person who knows more about it than you do. I learned some things in my younger days, some of which may have been dis-proven since. Also, I have made public my own understanding on some related issues that kinda got me into hot water here before. Because of that, I hesitate to air my own thoughts again, but since you brought this up, I may as well have a go.

Sound is processed by humans primarily by vibrations of the eardrums and a biological chain of events that follows. The meaningful vibrations of the eardrum are caused by fluctuations in air pressure, due to waves we might call sound waves which are transmitted by air.

Now, when a man taps a tree, he hears a sound. When a man taps a hollow tree or log he hears a sound of a different quality. When he taps a hollow log with his ear near a hole in the tree he hears a different quality of sound from within the chamber of the hollow log at a clearer, increased volume. There is a resonance to the sound from a hollow log that is not present in the sound from a solid log when tapping. I assume that the origination of drums and of instruments with strings attached to a hollow chamber came about as a result of this type of primitive knowledge, but I can't prove it.

As to the importance of sound holes in an instrument: I got into trouble here over that before. Since that time, I made a quick experiment. I borrowed my bass player's bass fiddle for a few minutes, and plucked the strings placing my ear near different portions of the back, sides ad soundboard. I found that undeniably there was a great volume of sound issuing (presumably) from the sound holes that dwarfed the volume and clarity of sound from any other area! I write "presumably" because as you know, on a bass fiddle, the _bridge_ is situated right there between the sound holes. One might argue that the sound has greater volume and clarity in that area because that is where the string vibration is first transferred to the sound board through the bridge.

Although I'm no expert, I strongly believe that the sound holes serve an important function of directing the resonance from within an instrument outwards. I do not agree with those who post here that no sound comes from the sound hole of an instrument. I have read no scientific papers that convince me that that is the case.

Also, I read a post recently that claimed that the box or body of instrument was not for increasing the volume of projected sound. I also believe that that is a false statement. The _volume_ as well as the _quality_ is enhanced by tapping or vibrating a hollow box, and I believe especially one with a hole in it. Solid body electric guitars have little volume without electronic amplification, while hollow body instruments have great volume which, roughly speaking increases with the size of the chamber (jumbo vs parlor, other things being equal).

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## Mark Gunter

I'm going to add to what I wrote above, that my musings are general observations and when we look at specific frequencies, we might find that very high frequencies are better transmitted with lesser chambers, think xylophone as opposed to guitar or piano.

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## Marty Jacobson

A sound chamber isn't strictly necessary... (muhahaha)

https://vimeo.com/110633932

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billhay4, 

JEStanek, 

Mark Gunter

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## Mark Gunter

> A sound chamber isn't strictly necessary... (muhahaha)
> 
> https://vimeo.com/110633932


Now that's cool  :Cool:

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## pops1

If you relate the sound to a speaker cabinet a closed back cabinet will take more power to achieve a level of sound than say a ported cabinet. The sound hole, like markscarts I believe, allows air flow so the top is more free to move which in turn creates more volume. I believe if you made a mandolin without a sound hole it would be much quieter as the top would not be able to vibrate as freely due to it pushing and pulling a sealed chamber. That's where I'll stop and let someone more knowledgeable deny or confirm my statements and tell us what really is going on.

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CJFizzix

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## billhay4

Yeah, many percussion instruments don't have sound chambers as such. Triangles, etc.
I'll take exception to the statement above that vibrations are carried by air. Put your ear on a train track when a train is far away. Or listen underwater.
So, what does have to vibrate? 
I can understand that sound boxes affect vibrations but can anyone explain how (in 40 words or less).
Bill

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## Bill McCall

On mandolins I would suggest its to support the strings and allow a greater volume of air to be set in motion than a string on a plank. Cymbals don't have that problem.

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Mark Gunter

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## Tom Wright

Not sure about fitting into 40 words. 

Musical instruments need a resonater as a start, and some also have a vibrating radiating surface that is not the resonator. Wind instruments are resonators mainly, the vibration remaining airborne. String instruments have a resonating air volume for some lower frequencies, the top handles mid-range notes, and the higher harmonics mainly radiate from the bridge in the case of violin family. Guitars and mandolins (and banjos) radiate highest frequencies pretty much directly from the string.

This is my understanding of the mechanics, and the important item is the resonator. The reason a trumpet (whose input power is blowing a raspberry with your lips) is generating so much sound is that the input is almost entirely dumped into a narrow range of resonance. The tube keeps all the sound inside, but mainly it transforms a spread of frequencies (buzz) into a note with almost no harmonics. So all that energy is now at one pitch. There is no added energy, unlike electronic amplification. But in that narrow resonant range a trumpet is capable of such power that its wave hits over two atmospheres pressure. This means the bottom of the wave stops at a vacuum, and is why trumpets sounds brassy when loud---the air is being overdriven and is clipping the waveform.

Stringed instruments are less loud because they are less concentrating in the translation from input to resonance. The low notes are supported by the air volume, which is delivered via the ports, whose role is identical to those in speaker cabinets--they add extra resonance at a narrow pitch range at the expense of broader but weaker low response. So you would hear low bass notes there, mainly, and basses and mandolins are indeed miked to pick up some of that. The top is delivering harmonics for those same notes, but more weakly, and distributed across the top, so at any one point it is much weaker and less obvious to the ear. (F-holes also affect the kind of flexibility the top has, being more piston-like than the drum-like movement of an x-braced round-hole top.)

As in the vimeo, much percussion lacks a soundbox---drums may or may not have one. A piano also does not have a soundbox as such, mainly the radiating surface of the soundboard.

All harps do have a soundbox, but they don't have the obvious bass ports. I think this is to spread the response more smoothly across the range in the case of orchestral harps. But they are not quiet---there is lots of area on the soundbox top. I know what it's like to sit next to a strong player. Surface area matters.

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billhay4, 

hank, 

Mark Gunter

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## billhay4

Thanks, Tom,
This clarifies things for me a bit. Could you explain the difference between a resonator and a "vibrating radiating surface" a bit?
Bill

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## Tom Wright

A speaker cone is a radiating surface, so is the top of a guitar. It wiggles and moves air.

A resonator is a system that has a preferred vibration mode, that "wants" to vibrate at a particular pitch. This can be a tuning fork or a bottle you blow over. The string is a resonator, but without being mechanically coupled to something that can move air it is only heard in the tinkly high harmonics.

The soundbox/body is a secondary resonator that has a note, although it is kind of diffuse. The top has resonances also, and they are also a bit spread out, although some are well defined and you can hear one note kind of jump out when you play it. Instruments with "character" tend to have a bunch of sharply defined resonances that make one note sound a little different than the next, making it have a "color". The reason those violin bridge pickups and under-saddle guitar pickups sound "colorless" is this lack of particular resonances adding interest and definition.

This issue involves questions of efficiency and coupling strength. The vibrating string couples weakly to the top---that is why it keeps on ringing. A banjo string couples strongly, so its energy gets taken by the head and the string does not ring long at volume. The difference is the top, of course. Air won't get pushed by a string at lower frequencies, although faster movement does push it a little, so you can hear the twang even on an electric guitar not plugged in.

A trumpet both couples strongly--all the energy is captured---and is efficient in concentrating it into the very narrow pitch range of the basic scale notes.

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billhay4, 

red7flag

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## Mark Gunter

> I'll take exception to the statement above that vibrations are carried by air. Put your ear on a train track when a train is far away. Or listen underwater.
> So, what does have to vibrate?


40 words or less? Dunno 'bout that, but: Vibrations are indeed carried by air, and what has to vibrate is the ear drum. The eardrum can be made to vibrate perhaps by any number of means, but it is specially suited to vibrate to sound waves carried by air. That is not to say that vibrations are not also carried by other means. When you connect two tin cans by a length of string and add tension, sound going into one can vibrates the metal can which sends vibrations in waves through the string, vibrating the second can. With your ear near the second can you will hear the sound due to the second can's disturbing the air in your outer ear canal. Likewise, when you hear a sound from the rails of a railroad track, in order to hear it, the rails cause vibration via the air in your ear canal. That is the _primary_ means of hearing sound.

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## sblock

*What is sound?*  In less than 100 words:

"Sound" is simply a shorthand for describing *mechanical vibrations* (often vibrations in air, but also vibrations in other fluid media, like water, and in flexible solids, like strings, flat surfaces, and so on) *whose frequencies fall into the range where our ears can hear things* -- the so-called "acoustic range".  Roughly speaking, that's from about 20 Hz up to  about 20,000 Hz.  Below that range, and we usually call it "infrasound." Elephants can hear infrasound. Above that range, and we call it "ultrasound."  Bats can hear ultrasound.  But it's all *periodic, mechanical vibrations*. Nothing more or less.

*Why have a soundbox?*  In about 150 words:

Acoustic stringed instruments have a problem because the mechanical energy in their vibrating strings couples VERY poorly to the surrounding air, resulting in fairly weak sound propagation up to your ears. The solution to this problem is to do something called "impedance matching" (here, acoustic impedance, which is analogous to electrical impedance.)  A soundbox, or soundboard, in an acoustic instrument will accept the vibrating string energy as an input, and couple it _much more effectively_ to the surrounding air as an output.  It serves not just as a resonator, but also as an acoustic coupler. Another (similar) way to match acoustic impedance is through a horn or speaker, like in the old gramophone horns, which coupled a vibrating phonograph needle to the air, back in the days before electrical amplification. Dobros and banjos act in many ways like a speaker. And nearly all acoustic instruments have some kind of soundboard or soundbox, including harps.

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billhay4

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## Mark Gunter

One of the great things about the cafe is its educational value, and it's great to be able to hear from experts, and to dialog with experts on a wide variety of subjects. This is one that fascinates most of us because of our love for the stringed musical instrument. Obviously, there is more than one way to make an instrument with volume, sound boxes are not necessary for sound to occur, for pleasing sound to occur, or for loud sound to occur. But the question before us here is "What is the function of the body?" - the soundbox - of a mandolin, and by extension of other stringed instruments that have soundboxes. The explanations given are very good and informative, if a bit technical. Would I be correct, in non-technical terms, in answering that one of the functions of the body (soundbox) is to amplify and radiate the sound vibration of the strings? And of course, in the case before us, the sound is transmitted to the eardrum via the air?

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## Dave Cohen

I've answered this question and similar questions on this forum too many times to count.  Imo, I haven't done a very good job..  People have seemed appreciative, but after all is said and done, many still don't understand.

When it comes to how musical instruments make sound, everyone thinks they are physicists, except they aren't.  However, Tom Rossing _is_ a physicist, and is one who has devoted a lot of his energy to physics education.  Tom gave a lecture at the 1988 GAL convention.  That lecture became three articles in _American Lutherie_, and those articles ultimately became two articles in "The Big Red Book of American Lutherie, Volume Two".  The first is "An Introduction to Guitar Acoustics", pp 124-134.  The second is "Sound Radiation from Guitars", pp 144-152.  Questions like "What is the function of the body?" are sufficiently basic, and sufficiently broad, that a forum like this is not the most efficient way to get an answer.  Tom Rossing's articles, however, are more efficient.  And they are sitting there on paper, waiting for you, so they don't suffer from the limitations of iconic memory or echoic memory.

Al Carruth was mentioned in an earlier post.  There are three articles in "The Big Red Book of American Lutherie, Volume One" that Al particularly likes.  The first is "Basics of Air Resonances", by W.D. Allen, pp 8-12.  The second is "Radiation from Lower Guitar Modes" by Graham Caldersmith, pp 68-72.  The third is "Our Great Spherical Friend" by Frederick C. Lyman, Jr., pp 196-201.  Spend some time with the five articles I have referenced here, and you will have an idea of what an instrument body does.  The articles were all written over 25 yrs ago, and with the exception of perhaps Caldersmith's article, all were written for a lay audience.  If you want something mandolin-specific, you have to resort to my papers and to my chapter in the Rossing book, "The Science of String Instruments".  But there is really no substitute for going back to the more basic articles in the Big Red Books.

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jhowell, 

Rob Zamites

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## Mark Gunter

Dr. Cohen, my understanding then is that my last two questions can't be simply answered. Your best advice is that the OP or I should not entertain such questions on an internet forum, but rather read the articles referenced in $90.00 worth of books. Also, it seems that you feel the need to denigrate everyone here by suggesting that "everyone believes they are physicists when in fact they are not." Misconceptions such as, "I'll take exception to the statement above that vibrations are carried by air" cannot be addressed, because it is more important to belittle the non-physicists that contribute to the discussion.

I would very much love to read the articles you referenced, and perhaps some day I shall. In the meantime, let me make some uneducated observations.

I can skin a calf, make a thong from a piece of the hide, and string it under tension between the ends of a stick, making a crude bow. When I pluck the thong, it makes a sound that I like. I pluck it in time to my brother's blowing on a jug. All is well, but I discover that when I turn a washtub over and firmly plant one end of the bow on the bottom of the tub, the resulting sound is louder and of a different character; I like it. I much prefer the volume and tone. While physics has everything to do with what's going on with sound, I am not required to have a degree in physics to know that my purpose in adding the washtub is to increase the volume and color the sound I'm getting from my bow.

I submit that illustrates the most basic form of most portable stringed instruments - a stick, a string and a resonator, usually hollow: A gourd, a hollow log, a washtub. Why is the resonating chamber there? One reason is to increase the volume. Therefore, I disagree not with any of the experts here, but with folk who post that the soundbox of a mandolin does not serve to amplify the sound, as I read in a recent thread. Likewise, those who post that _no sound_ comes from soundholes are in error, and those who do not seem to understand that sound waves travel through the air are in error. That's no shame to them, but it seems a bit shameful to me that these things can't be addressed except by referring us to scholarly articles.

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Mandoplumb

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## Bertram Henze

> It occurred to me that a harp doesn't have a sound board or sound box


Have a look into a harp luthiers shop...
I recommend trying a real harp if you have the opportunity, it's a stirring experience. Not only do they have a soundbox and a top, they have holes on the backside, too (which come in handy for threading the strings through those holes in the top).

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Mark Gunter

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## Bertram Henze

> A sound chamber isn't strictly necessary... (muhahaha)
> 
> https://vimeo.com/110633932


Strictly speaking, there is kind of a sound chamber (two, in fact), only it's filled with coiled metal instead of air.

Sound chambers serve a double purpose:
1 - make a controlled balance of output between the extremes of big sustain and little volume (electric guitar) and little sustain and big volume (banjo).
2 - concentrate that output into a limited frequency range to acommodate the human ear, i.e. create the output where it can really be heard and not waste energy on inaudible vibrations; this is done by centering volume around a resonance frequency given by shape and size of body and holes.

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Mark Gunter

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## s1m0n

The strings vibrate the soundboard, which vibrates air, which is sound. The back of the soundbox bounces that vibrating air back to the soundboard, making a positive feedback loop that sustains and reinforces the initial note. 

It's not essential but it makes the operation more efficient, creating a louder output from a lower energy input (the force you apply to the string).

If you've ever plucked a taut guy wire or steel cable, you know that you can get a note from a vibrating string alone. It's not very loud, tho. If you add a soundboard, you get more noise from the same pluck because there's more vibrating surface to push the air. Add a resonating cavity behind the board and you'll get more noise still.

Incidentally, the laser gun sound effect for the initial Star Wars movie(s) came when a sound tech struck a huge, taut steel cable with a wrench and recorded the noise he made.

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## G7MOF

To me sound boxes just amplify better. For instance, a mandolin with a sound box against a solid bodies mandolin!

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## Dave Cohen

> Dr. Cohen, my understanding then is that my last two questions can't be simply answered. Your best advice is that the OP or I should not entertain such questions on an internet forum, but rather read the articles referenced in $90.00 worth of books. Also, it seems that you feel the need to denigrate everyone here by suggesting that "everyone believes they are physicists when in fact they are not." Misconceptions such as, "I'll take exception to the statement above that vibrations are carried by air" cannot be addressed, because it is more important to belittle the non-physicists that contribute to the discussion.
> 
> I would very much love to read the articles you referenced, and perhaps some day I shall. In the meantime, let me make some uneducated observations.
> 
> I can skin a calf, make a thong from a piece of the hide, and string it under tension between the ends of a stick, making a crude bow. When I pluck the thong, it makes a sound that I like. I pluck it in time to my brother's blowing on a jug. All is well, but I discover that when I turn a washtub over and firmly plant one end of the bow on the bottom of the tub, the resulting sound is louder and of a different character; I like it. I much prefer the volume and tone. While physics has everything to do with what's going on with sound, I am not required to have a degree in physics to know that my purpose in adding the washtub is to increase the volume and color the sound I'm getting from my bow.
> 
> I submit that illustrates the most basic form of most portable stringed instruments - a stick, a string and a resonator, usually hollow: A gourd, a hollow log, a washtub. Why is the resonating chamber there? One reason is to increase the volume. Therefore, I disagree not with any of the experts here, but with folk who post that the soundbox of a mandolin does not serve to amplify the sound, as I read in a recent thread. Likewise, those who post that _no sound_ comes from soundholes are in error, and those who do not seem to understand that sound waves travel through the air are in error. That's no shame to them, but it seems a bit shameful to me that these things can't be addressed except by referring us to scholarly articles.


I did not say, or even imply, that one should not seek an answer to the question of the thread in the thread itself.  I did say that  a much better answer could be obtained in a longer format, and one that could be returned to over time.  Nor did I say or suggest that non-physicists should bother to seek an answer to such questions.  I _have_ gotten tired of people making up non-physical answers to physical questions without even bothering to find out what is already known.  Nor did I reference only "scholarly articles".  As I said, all of the referenced articles were intended for lay audiences, and are in fact _not_ published in scholarly publications.  As for spending $90 for the two volumes of the Big Red Books, (i) they are available in some libraries, and (ii) you spend over $100 for a plumber or other tradesperson to come to your house for an hour's work or less.  Yet you don't put a comparable value on the either GAL's publications or the scholarly publications that can answer your questions.

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## Bertram Henze

> Your best advice is that the OP or I should not entertain such questions on an internet forum, but rather read the articles referenced in $90.00 worth of books. Also, it seems that you feel the need to denigrate everyone here by suggesting that "everyone believes they are physicists when in fact they are not." Misconceptions such as, "I'll take exception to the statement above that vibrations are carried by air" cannot be addressed, because it is more important to belittle the non-physicists that contribute to the discussion.


There are two phenomena that we physicists often encounter, but which take an enlightened philosopher to deal with: 
1 - the same question asked repeatedly, even after we have answered it elsewhere; but an answer is only understood (or even considered) after one has asked the question - it's hard to keep other answers "in store" in case the right question comes around. So answering to one person passes another person unnoticed. We must have the patience to work the communication field every time, because the question may be the same but the person is not. BUT, of course, the one who asks must equally have patience to hear a lengthy answer - a rebuff ("can't you say it as simple as it is?") turns all of us away.

2 - talking of "simple"... some folks like to make up their own answers which please them for their simplicity but either wouldn't neccessarily stand experimental test or do not explain anything (my favourite: "why does a stone fall down?" "because it is heavy"). These are frequently found in product commercials and even in popular science shows - and on forums. Both persons, asking and answering, perceive the question as a pain to get rid of quick rather than a chance to learn. I am not advocating patience with these. Nobody can have patience with the impatient.

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## Mark Gunter

In my own case, I am not impatiently requiring a simple answer to anything, nor am I unwilling to learn. I added a couple of questions of my own that should not require lengthy answers. One of the questions is meant to pin down a small part of the OP's original question. I asked, "Would I be correct, in non-technical terms, in answering that one of the functions of the body (soundbox) is to amplify and radiate the sound vibration of the strings?" In that question, I am not seeking understanding of the physics or mechanics of anything, I'm simply asking whether one might be justified in stating that "_one_ of the functions of the body is to amplify and radiate the sound of the strings?" *Is it too much to ask for a general consensus on that point?*

The second question is much different, it has to do with an understanding of a physical principle, and while I'm asking for a simple confirmation of the statement, I'm happy to hear any amount of exposition as well as recommendations for reading material, if someone is uncomfortable with providing a simple answer. In the meantime, I'm making no claim to be a physicist, nor do I require a physicist to answer the second question, which is this: "And of course, in the case before us, the sound is transmitted to the eardrum via the air?" Is it possible to come to a consensus that in the normal case of hearing the sound of a musical instrument, the sound is transmitted to the eardrum via the air?

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Tom Haywood

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## GarY Nava

> A sound chamber isn't strictly necessary... (muhahaha)
> 
> https://vimeo.com/110633932


Isn't the room the sound chamber?
Cheers Gary

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G7MOF

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## GarY Nava

To my mind, it’s all about energy conversion, the 1st law of thermodynamics. That converting  the kinetic energy of the string (or the player’s hand) as efficiently as possible into sound energy.
A couple of posts mention the word amplify. To amplify there would have to be additional energy input which there isn't.
In my opinion the soundboard and body facilitate this conversion.

I wrote this piece on mandolin design a while ago, you might find it of interest.-

Some thoughts on mandolin design

For most of the mandolin players, that I come into contact with, the sound that an instrument produces is paramount. As a professional luthier, I always try to build the best constructed and most aesthetically pleasing instrument that I can, but that all counts for very little unless the tone is there too.

We know from the law of conservation of energy, that energy cannot be created or destroyed but is transformed from one type to another. Essentially a mandolin (or any other acoustic instrument for that matter) has to transform the kinetic energy of the musician’s hand into sound energy. That transformation has to be done as efficiently as possible to get the maximum sound out of the instrument.

So you pluck the string, it vibrates (kinetic energy) and you want the maximum amount of this energy transferred into the soundboard. 

The job of the bridge is to hold the strings in the correct position relative to the rest of the instrument (for string spacing, action, intonation) and to make the soundboard vibrate. 

A bridge needs to be as light as possible, so that the minimum amount of energy is used in moving the bridge itself. However, it has to be strong enough to support the strings and wide enough at its base to be stable. I make my bridges without any metal height adjusters; I feel that any mechanism that cuts the bridge into two parts must interfere with the bridge’s efficiency. Admittedly, I use a removable bone saddle to aid the adjustment of the action, but that saddle is firmly embedded within a deep slot and the bone saddle helps with acoustic impedance matching- metal to bone to ebony to spruce.

My bridge actually looks like a bridge! It makes contact with the soundboard only at the two ends- the central portion is removed; this reduces mass and lessens any restriction of the soundboard’s vibrations. However, by reducing the area of contact, you increase the pressure at the points of contact with the soundboard, which in my opinion, allows the transfer of energy to be more efficient. The feet of the bridge are not in some random position- they rest on the bracing which is designed to support the downward force and to help transmit energy across the soundboard.
The break angle at the bridge is also critical- the greater the angle the greater the downward force. However, if the bridge is pressing down too much on the soundboard, it will choke it- you know yourself, if you press down on the soundboard you will dampen the instrument (a good argument for armrests). The break angle is governed by the angle of the neck relative to the soundboard and is not just a function of the bridge.

The tailpiece should be a rigid anchor for the strings, so that energy is not absorbed by it; my theory is that any of the available energy will follow the path of least resistance and that path should be into the soundboard via the bridge.
The tailpiece must be a minimum length. If the length of the string between the bridge and the tailpiece is too great, you get this part of the string vibrating in sympathy and that’s wasting our precious input energy. You’ll notice that on some mandolins that have the anchor point of the strings close to the tail block, they will have harmonic suppressors fitted to the strings, behind the bridge.
I like to think that the body of the mandolin is like a loud speaker; the soundboard is the equivalent to the paper cone and that the back and sides are the metal chassis. Therefore, the back and sides should be rigid so that they don’t absorb energy from the soundboard. I also like the inner surfaces to be extremely smooth so they act as a reflector.
Having stated some of my design ideas; you should appreciate why I use French polish as my finish of choice. French polish is a very light surface coating and as such will have a minimal damping effect on the soundboard.

Well there’s is my two pennies worth!
Cheers Gary

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## Mark Gunter

> To amplifier there would have to be additional energy input which there isn't.


It seems that Dr. Cohen may be correct that these subjects become too complex because they are too broad to discuss in a internet forum. If amplification refers to the output which are waves of sound in the air, then we are discussing the amplitude of the wave. Isn't the amplitude of the wave increased when the vibration is transferred to the soundboard, resulting in greater volume in the perception of the listener? It seems to be a matter of efficiency in the mode of transferring vibrations to the air, rather than an increased input of energy. No matter, if we cannot even agree that an increase in volume is one function of the soundbox.

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## Bertram Henze

> No matter, if we cannot even agree that an increase in volume is one function of the soundbox.


That's why physicists' explanations are often tedious to read: they try to avoid misconceptions created through easy use of imprecise wording.
We can all agree that
- the sound box makes the instrument louder (instrument output)
- the sound from the instrument reaches the ear by air (ear input)

However, the instrument does not only have output, it has also input: the pick stroke. The soundbox lifts the instrument output, but not higher than the instrument input - it's rather an optimization than amplification. Amplification only comes into play when instrument output exceeds instrument input, with the help of extra power from elsewhere (the mains, mostly).

So - every amplification is an increase of output, but not every increase of output is an amplification.

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Mark Gunter

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## Mark Gunter

> That's why physicists' explanations are often tedious to read: they try to avoid misconceptions created through easy use of imprecise wording.
> We can all agree that
> - the sound box makes the instrument louder (instrument output)
> - the sound from the instrument reaches the ear by air (ear input)
> 
> However, the instrument does not only have output, it has also input: the pick stroke. The soundbox lifts the instrument output, but not higher than the instrument input - it's rather an optimization than amplification. Amplification only comes into play when instrument output exceeds instrument input, with the help of extra power from elsewhere (the mains, mostly).
> 
> So - every amplification is an increase of output, but not every increase of output is an amplification.


Thank you Bertram! As regards amplification, it seems to me that you have addressed that in reference to amplification of a signal prior to its transfer to the air, as accomplished by means of an electron tube or silicon chip. Am I wrong to use that term in reference to the amplitude of the wave that reaches the eardrums? In one case, with no sound chamber, the waves that reach the ear have lesser amplitude. Once the sound chamber is added, the waves that reach the ear have greater amplitude. There is presumably a loss of some frequencies and sustain that pay for the gain. And I mused that the gain in the amplitude of the output is due to an increased efficiency in transference of the energy to the air rather than an additional input of energy.

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## Bertram Henze

> Once the sound chamber is added, the waves that reach the ear have greater amplitude. There is presumably a loss of some frequencies and sustain that pay for the gain. And I mused that the gain in the amplitude of the output is due to an increased efficiency in transference of the energy to the air rather than an additional input of energy.


That's correctly put, as far as I can see. Efficiency is the word I didn't find when I needed it.
But the word amplification really points to that process of a small signal controlling a big signal, not only in music (other example: laser - Light Amplification by Stimulated Emission of Radiation).

----------

Mark Gunter

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## Mark Gunter

> That's correctly put, as far as I can see. Efficiency is the word I didn't find when I needed it.
> But the word amplification really points to that process of a small signal controlling a big signal, not only in music (other example: laser - Light Amplification by Stimulated Emission of Radiation).


I was not aware that the term had such a narrow use. In my youth I studied electron theory, vacuum tube theory and solid state theory, and I'm familiar with the effects of the little signal you mentioned. I only assumed that the word amplification would apply in comparing the amplitude of output waves from a device receiving  (roughly) the same input signals when a modification results in significantly increased amplitude of the output. Seems I always get in trouble thinking out loud here, (sigh).

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## Larry Simonson

Hang in there  Mark, this is an interesting thread.  There were some things mentioned that caught my attention like the need to remember the law of conservation of energy and the conjecture that the conversion of mechanical energy into sound is associated with some impedance matching element, likely the bridge.   I had first heard this suggested in a seminar given by Michael Kasha about 50 years ago and I think it may be true based on how minor variations in the bridge can have significant affect an instrument's performance.   

On the lighter side, though I love physicists and wish I was smart enough to be one, I am reminded of an old story where a physicist was asked to calculate the maximum velocity of a given race horse and said that the first step in that calculation was to assume the horse was a small uniform sphere.   :Smile:

----------

jhowell, 

Mark Gunter

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## Dave Cohen

> It seems that Dr. Cohen may be correct that these subjects become too complex because they are too broad to discuss in a internet forum. If amplification refers to the output which are waves of sound in the air, then we are discussing the amplitude of the wave. Isn't the amplitude of the wave increased when the vibration is transferred to the soundboard, resulting in greater volume in the perception of the listener? It seems to be a matter of efficiency in the mode of transferring vibrations to the air, rather than an increased input of energy. No matter, if we cannot even agree that an increase in volume is one function of the soundbox.


The subject is _not_ too broad to be discussed on an internet forum, but it is _inefficient_ to discuss it there.  As Bertram said, scientists like to give qualified answers, and those require the long posts, and people tire quickly of the long posts.  Also, it usually takes a lot of back-and-forth to finally answer a question satisfactorily.  That is where the inefficiency comes in.  What is your time worth?  If you put a value your time, you will probably find that it is cheaper to buy the Big Red Books than to go back and forth on the internet fora.

Another detail.  Explanation of scientific concepts is often done best with the addition of sketches, diagrams, graphs, etc.  The visual aspect of those things is important and simplifying.  Posting existing visuals on internet fora takes time; posting visuals that have to be made anew for the particular discussion takes even more time.  When those visuals so often exist already in, e.g., GAL articles, that ends up taking you a lot less time.  It especially ends up taking me a lot less time.

----------

Mark Gunter

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## Bertram Henze

Hey, getting in trouble is the purpose of thinking out loud - that's the way we learn. Embrace it. Another example for that is playing a break in a jam or leading a set in an Irish session: we walk out on a limb and learn from success or failure. Welcome to the rollercoaster called life.

----------

Mark Gunter

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## Graham McDonald

I would remind folks that Dave Cohen has for many years been politely and patiently explaining the complex acoustic systems that make stringed instruments so fascinating. Put his name into the search box and read back through years of posts where he has described, usually in the most accessible way, what are sometimes very complex ideas. Only occasionally has he snarled at some self-proclaimed expert whose pomposity exceeded his or her understanding and even then he has been kind about it. Anyone interested in these little instruments of ours owes Dave a great debt of gratitude for his generosity in the sharing of his knowledge.

Cheers

----------

Bob Clark, 

Dale Ludewig, 

fatt-dad, 

jhowell, 

Jimmy Kittle, 

ptritz

----------


## Seattle

I'll give my understanding (as a non-physicist) who has read some of these more scientific works on the subject of sound and musical instruments. I don't pretend to be 100% correct.

I'm posting just to give my simplifying conclusions after reading these works.

I'm not going to address how sounds works other than to say you have to have some medium and therefore it can't be in a vacuum.

 Sound comes from the strings vibrating and the cross section of the strings hitting the air. That's not very much surface to move the air so it isn't very loud.

A soundboard is much larger and when it vibrates it moves much more air and is therefore louder.

The bridge transfers the vibrations from the strings to the soundboard. You don't want the bridge to be too efficient or the resulting sound would be more like a sudden clap.

The hole in a guitar (mandolin) is more or less like an air pump. The soundboard vibrates, the air in the body cavity compresses, the back moves a bit as well and the whole thing serves as an air pump.

Most of the higher frequencies come from close to the top of the soundboard. Most of the lower frequencies come from inside the body cavity. An explanation of what is going on around the sound hole is described as the Helmholtz effect (as I recall) so you can look that you if interested.

You can cover the soundhole on a guitar (mandolin) and the decrease in the volume is much greater when you are hitting let's say the "a" string on a guitar or the "d" string on a mandolin than when you are hitting the "e" string.

This just shows that more of the higher frequency sound is coming from on top of the soundboard and the lower frequency sound from inside the body cavity.

I think this explanation is fairly correct and fairly simply laid out.

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David Lewis

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## fscotte

I can think of no better purpose of the body than to show off that gorgeous curly maple.


And that reminds me... What do you call a banjo with the back resonator removed?  A good start.

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## peter.coombe

> And that reminds me... What do you call a banjo with the back resonator removed? A good start.


A less efficient banjo.

I am not a physicist so have been trying to stay out of this, but some of the posts have made me groan and cringe.  There is NO amplification involved, the amount of energy remains the same.  In basic laymans terms, a soundbox makes the conversion of the kinetic energy in a vibrating string into sound energy more efficient.  Instead of most of the kinetic energy in the vibrating string going to heat energy, more of it goes to sound energy (which then ultimately ends up as heat energy).  How that happens gets complicated and you should read the papers cited by Dave if you want to understand it in more detail.  I have read most of them, but it was a long time ago and I have forgotten just about all of it.   The end result is it sounds louder, but the efficiency gain is not the same for different frequencies so is non linear.  Hence different instruments sound different.

Hopefully that does not get me into trouble, that is enough physics for me for one day.

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## fscotte

And what do you call a "less efficient" banjo?  A good start.

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## theCOOP

http://youtu.be/MenTEcA4jVk

Program How It's Made: harps

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## Tom Haywood

Part of the difficulty in this discussion is that the word "amplify" has a common meaning which is "to increase or augment". That meaning and usage dates back more than 600 years to the French word "amplifier" in the 1300's, some 300 years or more before the beginning of our modern scientific approach to understanding sound, and it is still in common use today. Most everyone knows that a non-powered megaphone increases the loudness of a voice at a distance and in a particular direction. The common description is that the megaphone amplifies the voice, and that would be correct given the long-standing meaning of this word. Our physics and science-minded friends have given the word a special meaning dating back about 100 years to the use of electricity to add energy to the sound source and thereby make it louder by increasing the amplitude of the sound waves. This more limited meaning is a term of art which is understood by those trained in its use, and which appears to others to be consistent with the normal meaning. Confusion arises when folks using the limited meaning tell the rest of us that our use of the word is wrong, that no amplification is taking place because no energy is added. Impedance coupling is a more accurate description from the standpoint of the discipline called Physics. The megaphone and the mandolin body may be impedance coupling devices, but in common parlance and experience they increase or amplify the volume of the initial sound source - the voice or the strings. Choosing to use a more limited definition of a common word does not of itself make wrong the common usage.

----------

billhay4, 

Jess L., 

Mark Gunter

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## bassthumper

my Martin B1 "pushes more air" than my mandolins do...great tone but not enough volume to be heard in a BG jam...

my Englehart "pushes enough air" to easily be heard..AND FELT...even when played gently....

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## Mark Gunter

> the use of electricity to add energy to the sound source and thereby make it louder by increasing the amplitude of the sound waves.


Increased amplitude of sound waves = amplified, in the way I used the term. I can tell by what you've written that you understand that. In the interest of clarity, the sentence above needs to be explained: The basic use of electronics for amplification in audio devices uses electricity to strengthen a signal, which is delivered to an output device like a speaker. The moving cone of the speaker then disturbs the air creating sound waves. The distinction is that the sound is represented within such an amplifier (e.g., transistor tube or solid state transistor) by pulses of electronic current (weak signal) that is used to modify a strong current, which is then used to drive the speaker. In the case of such an audio device using electronic amplification, the "sound wave" is what actually goes into the air; the part that is affected by electrical energy is a "signal" that represents the sound wave. 

@peter.coombe, Cringe and groan away at what I write. I'm not impersonating a physicist, claiming infallibility or even claiming to be able to express these ideas as a scholar in the particular field, I'm expressing my opinion here and trying to learn. Sorry if I don't fit in the right box for y'all. I have plenty of respect for the experts here, but can't say I take everything they write as gospel, and really consider myself no more pompous than the establishment is. In fact, I'm a pretty good guy once you get to know me, pomposity and all.  :Smile:

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## Jess L.

> Part of the difficulty in this discussion is that the word "amplify" has a common meaning which is "to increase or augment". That meaning and usage dates back more than 600 years to the French word "amplifier" in the 1300's, some 300 years or more before the beginning of our modern scientific approach to understanding sound, and it is still in common use today. Most everyone knows that a non-powered megaphone increases the loudness of a voice at a distance and in a particular direction. The common description is that the megaphone amplifies the voice, and that would be correct given the long-standing meaning of this word. Our physics and science-minded friends have given the word a special meaning dating back about 100 years to the use of electricity to add energy to the sound source and thereby make it louder by increasing the amplitude of the sound waves. This more limited meaning is a term of art which is understood by those trained in its use, and which appears to others to be consistent with the normal meaning. Confusion arises when folks using the limited meaning tell the rest of us that our use of the word is wrong, that no amplification is taking place because no energy is added. Impedance coupling is a more accurate description from the standpoint of the discipline called Physics. The megaphone and the mandolin body may be impedance coupling devices, but in common parlance and experience they increase or amplify the volume of the initial sound source - the voice or the strings. Choosing to use a more limited definition of a common word does not of itself make wrong the common usage.


Well stated. Thank you.  :Smile:

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## Bertram Henze

> Choosing to use a more limited definition of a common word does not of itself make wrong the common usage.


Not wrong, but easier to misunderstand (amplification is not the only example for a common word reduced to a meaning by physics - force, energy, momentum, power are others). 

OTOH, if usage of the limited definitions is in danger of being taken for common language, we physicists can always resort to mathematical equations  :Wink:

----------

jhowell

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## billhay4

Sorry not to contribute, but I've been away from the computer over the weekend.
I posed this question precisely in hopes of a "messy" discussion like this one. I agree with Dave Cohen that such discussions are inefficient. However, learning (in my case, anyway) is quite inefficient, a lengthy process of misunderstanding and clarification.
I thank all of you for participating in this process.
I understand the distinction between amplification and impedance coupling now (whether I will forget this is up in the air). I have a flawed understanding of the function of the sound box and soundboard. I am still not sure that air is required for sound to be made (I think not but some medium is). I do not think anyone has come up with a unified theory of mandolins yet, but they are working on it. As soon as it is completed, others will rush to challenge it.
Finally, I would like all the scientists among you to recall the each individual learns differently and incompletely (even you). Some learn by reading Red Books (I have read these articles), others by listening, some by making fools of themselves (my way), and some simply by being superior human beings. All of these methods are valuable IF expansion of the mind ensues.
Bill

----------

Jess L., 

Mark Gunter

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## Seattle

Some medium is required and since air is what we have around us that particular question probably results in arguments where the distinction is without a difference. :Smile:  The simple answer is that the sound box provides the bass.  :Smile:  The top of the sound box provides the treble.

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## Mark Gunter

> I am still not sure that air is required for sound to be made (I think not but some medium is).


Bill, I think you may be missing the point about air. Air is not "required for sound to be made"; that is, vibrations which produce sound do not have to originate in air. Air is generally required for sound to _travel_ to the eardrums. The eardrums could be vibrated by other means, for instance hydraulically (for example, if you are underwater and your outer ear canal is filled with water with no air captured within it) - but the primary most efficient means of exciting the eardrum is pneumatically (via the air). So, whether we are discussing strings on a plank with no soundboard, or a mandolin that has a sound chamber, it is the effect of the string or the soundboard vibrating against air that enables you to _hear_ the resulting sound. So I'm not sure what you mean about air not being part of the equation. 

Concerning the air in a soundbox as of a guitar or mandolin, that enclosed air does have an effect on the sound that is produced. According to T. D. Rossing in his introduction to _The Science of Stringed Instruments_, 



> Guitar researchers have paid considerable attention to the resonances of the
> guitar body, and how the low-frequency resonances can be regarded as being due to
> the coupled vibrations of the top plate, back plate, and enclosed air. Luthiers have
> experimented with different bracing patterns, especially in the top plate. Unlike the
> violin, which has changed very little for many decades, the guitar is still evolving.


It would be good if you could explain what you mean exactly when you say that you are not sure that air is required for sound to be made.

As a side note, I observe that most people can play air guitar or mandolin much better than they can play the real thing. I include myself in that group.  :Grin:

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## Mark Gunter

An addendum, rather than an edit: The human ear has been created (or evolved, take your pick) to specifically process sound carried by air. A simple experiment will teach the young child that he or she can process sound vibrations with their head in open air and no breeze much better than with their head under water. Sound waves can travel through steel rails, water, string, virtually anything that can vibrate within frequencies conducive to human hearing, but such vibrations are normally transferred to and travel through the air before you hear them with your ears.

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## billhay4

Mark,
I understand all of that and have from the first post. However, it is not technically accurate to insist that vibrations have to be carrier by air to be heard. I understand how sound is normally made and how it is normally heard by humans, but it can also occur elsewise as I have stated.
I can understand how, in the context of mandolins, people would insist that we consider air as the medium and I agree. But what if I were designing a mandolin to be played under water, or in space?
I'm not but that doesn't mean I won't try. My first exolin is almost ready to be shown. Here's a hint:

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## sblock

> Increased amplitude of sound waves = amplified, in the way I used the term. I can tell by what you've written that you understand that. In the interest of clarity, the sentence above needs to be explained: The basic use of electronics for amplification in audio devices uses electricity to strengthen a signal, which is delivered to an output device like a speaker. The moving cone of the speaker then disturbs the air creating sound waves. The distinction is that the sound is represented within such an amplifier (e.g., transistor tube or solid state transistor) by pulses of electronic current (weak signal) that is used to modify a strong current, which is then used to drive the speaker. In the case of such an audio device using electronic amplification, the "sound wave" is what actually goes into the air; the part that is affected by electrical energy is a "signal" that represents the sound wave. 
> 
> @peter.coombe, Cringe and groan away at what I write. I'm not impersonating a physicist, claiming infallibility or even claiming to be able to express these ideas as a scholar in the particular field, I'm expressing my opinion here and trying to learn. Sorry if I don't fit in the right box for y'all. I have plenty of respect for the experts here, but can't say I take everything they write as gospel, and really consider myself no more pompous than the establishment is. In fact, I'm a pretty good guy once you get to know me, pomposity and all.


Mark, as several folks have pointed out, physicists and engineers tend use the word "amplify" in a subtley different way than you tend to do.  By "amplify", they mean that *energy in the radiated sound has been increased*.  And they reserve the word for an energetic increase, not an apparent loudness increase (and this makes a big difference, it turns out). "Amplification" is what an electronic amplifier does to the sound signal in, say, a phonograph needle moving over a record, or in a radio signal obtained from a broadcast over the air.  But with an acoustic instrument like a mandolin, once you've plucked the string to sound a note, that's ALL the energy that particular note will ever get! Put differently, there's no way for an acoustic mandolin to amplify it:  there is no additional source of energy beyond what you put into it when you plucked it.  But that does not mean that you can't make the string sound louder to someone's ear on the other side of the room.  Someone else pointed out a great analogy, here:  the old-fashioned megaphone.  Singing or speaking into such a megaphone _will not amplify_ your voice; it's just a passive device.  But using the megaphone WILL direct the vibrations of your voice into a narrower cone in the forward direction. So less sound energy escapes to the back and sides, and more heads straight out toward a listener in front of you.  Put another way, it changes the sound radiation field and focuses more energy towards the front. So your voice is louder to the folks in front of you (and softer to those behind you; energy is conserved!) The resonator on the back of a 5-string bluegrass banjo (not an older open-back model) plays a similar role.  And that's also one role (of several) played by the soundboxes and soundholes found on guitars, violins, mandolins, etc.  There have been LOTS of discussions here on the MC about how different mandolin soundhole shapes (ff-holes, oval holes, and even side ports)  affect the radiated sound field.  It comes down to a matter of *efficiency* (what you do with limited energy) and not to a matter of amplification.  And, as you probably know, designing a mandolin to be louder for a listener sitting in front does not often make it louder for the player sitting behind the instrument. On the contrary: there is only so much sonic energy to go around.

The other point that's been raised in this thread, and it's a vitally important one, is the role played by the soundboard or soundbox as an _acoustic coupler_.  The energy in a vibrating string couples very poorly to the surrounding air, and it moves little air.  The body of an acoustic instrument is designed to couple the vibrational energy from the string better into sound waves, in addition to focusing those waves in the radiated acoustic field (a "megaphone effect," if you will). With good coupling, less of the string energy is dissipated as heat (this is acoustic damping), or even as infrasound or ultrasound, and _more of the string energy appears as sound_ you hear, with frequencies and overtones in the range that we can best sense (20 Hz to 20,000 Hz).  So it's not just where the sound goes, but what goes into making up the sound!  And here is exactly where things like acoustic _resonances_ play a big role.  When the fundamental frequency of a vibrating string, or one of its stronger overtones, happens to match one of these resonances, the acoustic coupling becomes much stronger between the string and the instrument, and the energy tends to be transferred more quickly.  The _timbre_ of a note (mostly, its overtone series) is hugely affected by the frequencies and physical properties of all these resonances.

Of course, the vibrating string energy should not just go into making the instrument body or its air cavity vibrate!  It then needs to get coupled into the air surrounding the instrument, and get radiated efficiently towards the listener. One good way to do this is with a wooden soundboard over an air cavity, and have sound hole(s) -- like a mandolin, violin, acoustic guitar, etc. A time-tested approach!  But there are other ways, like the Stroh violin (Google it), which uses not a conventional body, but a horn instead -- much like a megaphone or an old gramaphone. See here:



Or the Dobro, which uses a speaker-cone scheme (and the open-back banjo is not so different)

Anyway, this is a vast and complex subject.  The Stroh violin makes it clear that the roles of (1) shaping the radiated sound field, and (2) efficiently coupling the vibrating string energy into sound in the surrounding air, do not _have to_ be played by a conventional instrument body.  But _SOMETHING_ has to serve these twin roles!  So when you inquire, "what is the function of the body?" that's my attempt at a simplified answer.  It turns out that it's not about amplification at all; it's all about acoustic efficiency in coupling the limited available energy into sound that will reach the listener's ear.

I hope these words have been helpful.  I am sure you're a good guy.   :Smile:

----------

billhay4

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## Bruiser

It should be said that not all vibrations are equal.  

An object can oscillate side to side, like the pendulum of a clock or the tines of tuning fork.  Call that a transverse wave or vibration.

Or an object can oscillate along its length, like repeatedly pulling on the end of a long spring (like a Slinky toy), so the motion of one end is transmitted along the length of of the spring.  Call that longitudinal wave, or a compressional wave, because the spring is being compressed and expanded by the motion of your hand.  

Sound travels through air by compressional waves, by repeated compression and rarefaction of the air molecules, with the molecules vibrating back and forth along the direction of sound travel.  Sound can travel through any medium that carries vibration, but our ears and brain usually process compressional waves in air, so that is how sound is usually described.

Plucking a mandolin string causes the string to vibrate from side-to-side, in a direction perpendicular to the length of the string.  That is a tranverse motion.  It does cause compressional waves in the air, but they don't sound loud to us because  a string has a small surface area; it doesn't move much air.

However, when the string's vibration is coupled to the soundboard via the bridge, the board has a much larger area and can set up more and larger compressional waves in the air, so it sounds lounder to our ears.

The ear functions by sensing compression waves in air (or water, whatever).  "Sound" can come from any vibration source which causes the air around it to move, but we only call it sound when compressional waves impinge on our ear drums and the auditory nerves tell the brain "Hey, we hear something."

That's not a physicist's explanation; that's the explanation of a guy who took a few quarters of physics 30+ years ago, but I think it's generally correct.  

Ed

----------

billhay4, 

Jess L., 

Mark Gunter

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## Mark Gunter

sblock, I'm sure that is a helpful post; it has told me nothing I didn't already know; if you'll read my posts you'll see that I well understood from the start the difference between electronic amplification and the volume increase that is gained when a soundboard/soundbox is used, the problem is that I was using the word "amplify" to describe the increase in the volume of the soundwave - the actual output that reaches the ear. I also understand that this increase in volume which I referred to as amplification is due to the efficiency of transferring the vibrations to a soundbox and soundboard. I readily nod to the fact that the experts are using the word amplify in a much narrower sense than I was. I have pointed out numerous times that I used the word in reference to the amplitude of the actual sound wave reaching the ear _as compared to_ that of the corollary sound wave that might be produced by the same action on a similar instrument _without the soundbox_. I don't know how much more clear I can be on that. I will happily refrain from using the word "amplify" in the future in that manner in order to avoid confusion. I'm not suggesting that we should use that particular term in the way I used it. The point I was making about the function of the body still stands, in that one function of the body of the instrument is to make the instrument sound louder. My interest in this discussion is the reason for a soundbox on a stringed instrument, an invention that _predates_ modern science and even the historical record. The first instruments must have been crude, but when a soundbox of some fashion was used there was an increase in volume that was desirable. As these instruments have developed through history, they have been refined through experimentation and of course there has been study and experimentation that continues today in order to understand the complexities involved. It remains that the soundbox increases the volume and affects the tonal qualities. This increase in volume, which is somewhat directional, is one of the main reasons that soundboxes exist on musical instruments.

As to the other note I've been sounding here: Sound waves travel through air . . . I have been beating that horse because I do not understand Bill's point, or his anxiety, about it. I have not insisted that sound waves must be carried by air to be heard, but I've pointed out that that is the normal mode of hearing. I've not heard of a musical instrument that is not meant to be heard by the human ear via the motion of air in the outer ear canal, yet that is not to say that some do not exist. We have sonic devices designed specifically for transmitting very low frequency waves through water; sea creatures may communicate via sound in the water; perhaps someone has made musical instruments intended to be felt rather than heard - in other words, I am not spouting absolutes on that point, but if we are discussing common sound boxes of stringed instruments it would not be easy to discuss how they make sound and music without reference to sound waves in the air, so I'm a bit confused still about what Bill is getting at there.

By the way Bill, interesting shape to that body, can't wait to see the finished product.

----------


## Dave Cohen

> I posed this question precisely in hopes of a "messy" discussion like this one.
> 
> Finally, I would like all the scientists among you to recall the each individual learns differently and incompletely (even you). Some learn by reading Red Books (I have read these articles), others by listening, some by making fools of themselves (my way), and some simply by being superior human beings. All of these methods are valuable IF expansion of the mind ensues.
> Bill


Bill, I was a professor for 34 yrs before retiring.  I am well aware that everyone learns differently.  The problem for me with the "messy discussions" on these fora is that you are asking the scientists here to essentially give you an IEP (individualized educational plan) at their expense.  In academia, we are paid salaries to do that sort of thing.  The goal of higher education is ultimately to teach the learner how to learn for him/herself.  Once we get past secondary education, there are limits on how much time we have per student.  While we provide as much guidance as possible, at some point, the student has to take some responsibility and do the homework.  Without that, no amount of support we can provide will ultimately do any good.

Scientists (at least physical scientists) tend to be visual thinkers, because the problems to be solved need to be visualized.  One of the first things we teach students about problem solving is - draw a picture or sketch of the system before doing anything else.  The students find that once they are able to draw a sketch of the system, the problem is just about solved.  That is why I referenced the articles in the Big Red Books; they have pictures, sketches, diagrams, and graphs.  With that in mind, if you go back to the pictures, & etc. in the articles, then look in the text for the descriptions associated with the pictures, you will doubtless still have questions.  The difference is that those questions will be narrower and more specific.  _Then_, if you bring those specific questions to someone who can help you, you will get the specific answers, one by one.  Science is reductionist.  We do not get the big picture by looking for the big picture; we only get it by reducing the big picture to its' component problems that are manageable, solving those problems, then putting them together for the big picture.  And unfortunately for some learning styles, learning science is also reductionist.

What was the pint of all that?  Learning the function of the (instrument) body is likewise reductionist.  You learn what the strings do, what the plates do, how they do what they do together, what the air does,......, then you put all those pieces together, and only then do you begin to have an understanding of "What is the function of the body?"

----------

Bob Clark

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## fscotte

Now, how would you build a mandoln differently if it were meant to be played in outer space...

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## Jess L.

I think a lot of being able to find an answer (to any question/subject) on one's own, is *already* knowing enough about it to ask the 'right' question. That's hard to do, and is subject to misinterpretation. 

Ever went to Google to look something up, and been bewildered by thousands of search results because the question you posed wasn't specific enough? Or too specific? 

I learned something important from my dad, one of his favorite sayings: 




> *"An entire book full of answers won't do you any good if you don't know what all the questions are."*


This is where a person might find difficulty simply being referred to a large technical manual to seek an answer, because some of that stuff might not even make sense without someone to explain what it all applies to. This is where I would be, anyway. 

I guess, generally speaking, part of the task of the more-knowledgeable persons in humankind, is to figure out what it is that someone is *really* asking and distill it down enough to get some usable info, without getting side-tracked with technical disagreements. For instance... 

Computer tech support is a prime example.  :Disbelief:  Casual computer users routinely get their facts mixed up due to their lack of familiarity with the exact meaning of some of the modern technical terms, for instance one of the classics is that they constantly confuse *RAM* with *hard-disk space* as if it was all one and the same thing ("But isn't it all just memory?") etc. It's hard to answer their questions when you're not entirely sure the nature of the question, this is where experience comes in handy, after a while you can kind of guess what they are *really* wanting to know. And explain it to them in a way that gives them enough practical info to solve whatever problem they're having. (I'm the family's tech-support/IT person, I have to deal with this stuff all the time.) 

I guess my point is, *we are all ignorant in different topics*. I wonder, *did Einstein know how to set valve lash by ear* on the internal-combustion engines of his time, or how to maintain a safe optimal boiler pressure in a steam locomotive? Or the correct procedures to shoe a horse? Would he even be bothered with wanting to know? It (presumably) wasn't his area of specialty. He was smart, but I'd be willing to bet that there were topics that he didn't know enough about to even formulate a proper question to ask about it. No one knows *everything*. 

Anyway, all that aside... I patently refuse to discontinue my use of the word "amplified"  :Cool:  in its hundreds-years-old *tried-and-true* meaning of *"now it's louder than it was before"*. As others have pointed out here, and I've already commented on, the word "amplify" existed centuries prior to humans harnessing electricity, whereupon specialists and technicians and physicists etc gave the word a new narrowly-defined technical meaning. The original and *commonly-used* by the masses version of "amplify" means *"make it louder"*, regardless of how that is accomplished, whether via electricity or just a megaphone. The *method* of amplification is a mere trivial technical detail in that context, generally speaking the average person doesn't want to know how/why it's louder (whether purely mechanical, or electrical), they just know it's louder and that it's a good thing. 

Not sure of the logic in applying an *electronics* word to an *acoustic* instrument anyway, acoustic mandolins existed long before humans were using electricity and devising specialized forms of old words such as "amplify". 

Speaking of *megaphones* that others have mentioned, weren't the early *record-players non-electrical*? Here's a human-powered gramophone, you can see the person winding it up from about 0:07 to 0:20, and it looks like the big flared thing serves as a 'megaphone' which, according to our friendly physicists here  :Smile:  doesn't "amplify" the sound in the modern scientific sense of the word, but according to the rest of us folk it's "amplified" alright 'cause it's louder than it was before.  :Smile:   :Cool:  

So... This next bit has already been mentioned by others, but not sure everyone has read it, so I'll reinforce the info a little now... 

Note: While I realize that dictionaries aren't authoritative, rather they just report on how real-life people are using words in everyday life, nevertheless (for better or worse) it's real-life that most of us have to deal with,  :Whistling:  here are some definitions: 




> *Amplify*
> to make larger, greater, or stronger; enlarge; extend.to expand in stating or describing, as by details or illustrations; clarify by expanding._Electricity._ to increase the amplitude of; cause amplification in._Archaic._ to exaggerate.
> 
> *Synonyms*:
> increase, intensify, heighten.widen, broaden, develop.
> 
> *Origin of amplify*
> 1375-1425; late Middle English _amplifyen_ < Middle French _amplifier_ < Latin _amplificāre_ to increase, augment. See ample, -ify.
> 
> -Dictionary.com


Ah - now *this* is interesting, seems the *geneticists* and the physicists need to quarrel over who's using the word right since geneticists use the word to mean something entirely different: 




> *Amplify*
> *Genetics: Make multiple copies of (a gene or DNA sequence).*
> 
> *Example sentences:*
> We performed PCR on wild-type mouse genomic DNA to *amplify* sequences flanking transposon insertion sites for use as probes.Genes were *amplified* from genomic yeast DNA using specific oligonucleotides and the polymerase chain reaction.Primers were designed to *amplify* this gene sequence specifically.
> 
> *Origin:*
> Late Middle English (in the general sense 'increase, augment'): from Old French _amplifier_, from *Latin* _amplificare_, from _amplus_ 'large, abundant'.
> 
> -Oxford Dictionaries


Should we thus chastise physicists for using the word "amplify" because they don't use it in a technically-correct way from the point of view of the geneticists??? 

Any of those 'specialty' fields are going to use common/old words in new ways, to apply to some particular technical angle in their own field of work. That doesn't mean that the rest of us have to follow suit.  :Smile:  

Although, after reading this thread, the next time I'm in a room full of physicists (like, never)  :Smile:  I will refrain from using the word "amplify" at all, lest I use it in a way that they're not accustomed to. I could just put it on my list of other words that are too controversial to use anymore...  :Frown:  nah...  :Smile:

----------


## Jess L.

> It should be said that not all vibrations are equal.  
> 
> An object can oscillate side to side, like the pendulum of a clock or the tines of tuning fork.  Call that a transverse wave or vibration.
> 
> Or an object can oscillate along its length, like repeatedly pulling on the end of a long spring (like a Slinky toy), so the motion of one end is transmitted along the length of of the spring.  Call that longitudinal wave, or a compressional wave, because the spring is being compressed and expanded by the motion of your hand.  
> 
> Sound travels through air by compressional waves, by repeated compression and rarefaction of the air molecules, with the molecules vibrating back and forth along the direction of sound travel.  Sound can travel through any medium that carries vibration, but our ears and brain usually process compressional waves in air, so that is how sound is usually described.
> 
> Plucking a mandolin string causes the string to vibrate from side-to-side, in a direction perpendicular to the length of the string.  That is a tranverse motion.  It does cause compressional waves in the air, but they don't sound loud to us because  a string has a small surface area; it doesn't move much air.
> ...


For me, that explains everything, thank you!  :Mandosmiley:   :Smile:  I can almost picture or get a 'visual' of the soundwaves being transformed from the strings' side-to-side (transverse) motion, to the soundboard's compressional waves that our ears notice better. (Did I get that right?) I like your explanation because it reduces all the mystery to something I can visualize and thus understand a little bit better. Thanks again!  :Smile:

----------


## murrmac

> Anyway, all that aside... I patently refuse to discontinue my use of the word "amplified"  in its hundreds-years-old *tried-and-true* meaning of *"now it's louder than it was before"*. As others have pointed out here, and I've already commented on, the word "amplify" existed centuries prior to humans harnessing electricity, whereupon specialists and technicians and physicists etc gave the word a new narrowly-defined technical meaning. The original and *commonly-used* by the masses version of "amplify" means *"make it louder"*, regardless of how that is accomplished, whether via electricity or just a megaphone. The *method* of amplification is a mere trivial technical detail in that context, generally speaking the average person doesn't want to know how/why it's louder (whether purely mechanical, or electrical), they just know it's louder and that it's a good thing.


Bullseye ...

----------

Jess L.

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## Dave Cohen

I don't know if anyone has stated this before, but after all the entropy in this thread, this is about all I can offer

Plucked string instruments are mechano-acoustic devices - systems of coupled oscillators assembled for the purpose of getting vibrations in a fluid (usually air) to a human listener's ears.  If you use a definition from genetics, or a dictionary definition from common usage, to claim that the instruments are amplifiers, you are taking the instruments out of their context.

There is a compelling reason why a string instrument body is not an amplifier; i.e., it is not amplifying anything, and especially not the strings.  In particular, it is not making the "sound" from the strings louder.  The strings _do_ make some sound, and that sound from the strings is _part_ of what you hear.  The total output from a string instrument is the _sum_ of the individual outputs from each of the component oscillators - the strings, air vibrated by the outsides of the plates, and air vibrated by the vibrating air in the region(s) of the soundhole(s).  Even if some motion of one of the oscillators is amplified by, say, 10%, it has to be _multiplied_ by a factor of 1.1, but no such multiplications are taking place.  Again, the sound output from a plucked string instrument is a _sum_ of component oscillator outputs, and _not a multiple_ of anything.  In fact, the 2nd law efficiency of a plucked string instrument is in the neighborhood of 4%.  Which means that most of  the energy, about 96%, that comes from initially displacing a string (potential energy) and letting it go (kinetic energy) is lost to heat and entropy.

One might be able to do a semantic dance and claim that an instrument body is an _apparent amplifier_, but many things that are apparent do not hold up to closer scrutiny.  There are apparent exceptions to the 2nd law of thermodynamics too, but none that have held up to closer examination.

----------

Bertram Henze, 

Eric Foulke, 

peter.coombe

----------


## JeffD

For the record - and specific to my way of learning - Dave Cohen and John Hamlett are two of the best explainers around. Many many times they have cleared the fog for me.

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## Bertram Henze

What have we achieved? I mean, we could have answered the original question with a terse "remove the body and you'll hear for yourself what its function was", but I bet the OP knew that. 
But we are here for talking, and we have yet again learned a little bit about communication and its pitfalls, probably more than we learned about instruments. The differences in vocabulary are not obstacles for this, they are the fuel.

----------

billhay4, 

Mark Gunter, 

Tom Haywood

----------


## dschonbrun

A single string vibrating in air creates a sound wave that is omnidirectional.  As a result, the sound dissipates quite quickly over distance (i.e. it's soft unless you're next to it).  A hollow body (chamber) with a thin vibrating face (sound board) with a hard back and sides is able to focus the energy from the vibrating string and create a sound wave that is amplified because it's moving more air, and directional since the back and sides of the chamber are relatively stiff... therefore the air movement is limited to coming off the front face (sound board).  The result is a more focused sound wave (i.e. louder).

----------

CJFizzix

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## fatt-dad

. . . late to the party!  

My answer?  The function of the body is to make a mandolin sound like a mandolin, or a guitar sound like a guitar, or a fiddle sound like a fiddle. They all sound different for physical reasons that I don't quite understand. . .

f-d

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## billhay4

Dave,
With all due respect, no one asked you to contribute to this conversation at all. Your choice. If it's burdensome to you, don't chime it. And I know it has gotten burdensome for you. Thus all the comments about the inefficiency of the internet for such discussions.
Frankly, though, life is entropy. It is not the orderly process you chemists prefer.
Bill

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## Hadji36

Since air _is_ a fluid, and sound waves move longitudinally through fluids, I would think that the difference between a good and great mandolin would be how those sound waves are manipulated within the sound chamber, as well as other factors.  That would put into play those sound waves reflecting off of and directed by the back board, as well as other factors such as the efficiency of the bridge transferring the vibrations of the strings to the soundboard.  We all know that when we add mass to the bridge, we lose volume (lessens the efficient transference of the vibrating strings to the soundboard) and when the back of the mandolin is tight against our bellies, it somewhat dampens the sound.  I would think that other factors, such as backboard wood species would come into play as well.  We've heard that softer back and side woods give softer tone/sound.  I would think that this would be a factor of absorption or less than efficient sound wave reflection.

Of course I could be way off...but, I did stay at a Holiday Inn Express last night.  

Here is an interesting quick read on sound waves which may play into the discussion:

http://www.physicsclassroom.com/clas...gitudinal-Wave

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## billhay4

Thanks for the link Hadji36.
Bill

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## sblock

The discussions of the meaning of the word "amplify" are beginning to sound like the parable of the blind men and the elephant!  Yes, words can be used in many ways.  If you want to use "amplify" to just mean "make it sound louder," then fine.  But please realize that when you do so, you seem to miss an important point, stressed by many of the scientists on the forum who've chimed in, which is this:

An acoustic stringed instrument cannot amplify (that is, increase) the ENERGY associated with a vibrating string. Once a string has been set into motion (say, by flatpicking it), it carries a certain amount of vibrational energy.  That energy cannot increase thereafter because there is no further input of energy from any other source. Energy is conserved. The string eventually loses all its vibrational energy, and rings down. The vast majority of that energy goes right into heat (pure damping).  A small portion of the energy goes into driving other vibrations, and it is _this_ energy that mostly contributes to the sound that we eventually hear.  In most acoustic instruments, that energy is used to vibrate the tonewoods (i.e., the walls of the soundbox) and to vibrate a partially enclosed volume of air (the air cavity of the soundbox). These structures, in turn, radiate their sound into the air surrounding the instrument, which eventually reaches our ears. 

The "purpose of the soundbox" is to _couple efficiently the energy of vibration of strings, through the intermediate of the wood and air that comprise the instrument's soundbox, into airborne vibrations in the region outside the instrument_. *No more, and no less*.  And generally speaking, the more efficiently the soundbox functions, the louder we hear the sound. This improvement in coupling efficiency (which makes things sound louder) is not, strictly speaking, a form of "amplification" in any sense that a physicist might use the word. That's because the energy is always getting lost, and never increased!  But the higher the soundbox efficiency, the less the loss at the level of your ears. So, if you tend to think of "less loss" as being a kind of "gain", then go ahead and call it "amplification."  But realize that this is equivalent to saying "I just bought a fuel-efficient car that gets more miles to the gallon, and am now saving fuel.  My new car _amplifies_ the fuel!"

----------

peter.coombe

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## Dave Cohen

> Dave,
> With all due respect, no one asked you to contribute to this conversation at all. Your choice. If it's burdensome to you, don't chime it. And I know it has gotten burdensome for you. Thus all the comments about the inefficiency of the internet for such discussions.
> Frankly, though, life is entropy. It is not the orderly process you chemists prefer.
> Bill


That is some strange logic.  No one _invites_ anyone to post, nor for that matter, to initiate messy threads.  With the comment about "orderly process", you are making an assumption about something with which you are not very familiar.  No scientist will tell you that science is completely orderly.  We try to bring some order to it after going through the process.  We make hypotheses, and perform some experiments.  More of those experiments _don't work_ than do. Same goes for the hypotheses.  Then we start over, and repeat, and repeat, and,,,,until we have some results that can support some conclusions.  Takes a lot of time and effort.  Not very orderly, imo.

It _has_ gotten "burdensome" for me, for some of the reasons outlined by Bertram.  New members keep asking the same old questions.  We answer those questions over and over, and get a great deal of uninformed pushback every time.  Worst yet, more than a little of that pushback is _ad hominem_ and personal.  I had to have a heckuva lot of patience during my years in the classroom.  What was most trying to the patience of any teacher was the assumption on the part of students that because we didn't present the information in a way that was "just right" for them to get it without any effort on their part, we were somehow deficient and were not putting sufficient effort into our work.  In fact, I brought work home with me most evenings, often working very late.  I am older and crankier now, with less patience.  If I were a better Dave than I am, I might have maintained that patience, but _sumus quod sumus_, i.e., we are what we are.

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## sblock

> A single string vibrating in air creates a sound wave that is omnidirectional.  As a result, the sound dissipates quite quickly over distance (i.e. it's soft unless you're next to it).  A hollow body (chamber) with a thin vibrating face (sound board) with a hard back and sides is able to focus the energy from the vibrating string and create a sound wave that is amplified because it's moving more air, and directional since the back and sides of the chamber are relatively stiff... therefore the air movement is limited to coming off the front face (sound board).  The result is a more focused sound wave (i.e. louder).


Actually, no, the problem is not (just) one of directionality, and of focusing the radiated sound field. The problem is that the energy in a vibrating string couples _only very weakly_ to the air around it.  A moving string is very thin, and it moves very little air around it as it vibrates.  It therefore produces very little sonic output, irrespective of the direction!  You can experience this directly by plucking the string of a solid-body electric guitar (one that's not plugged in).  Almost no volume.  You can focus this if you like, but that won't help much.

As I have written before, the soundbox of an acoustic instrument _not only_ focuses the sound (akin to acting like a megaphone in that regard), but it also _couples the vibrational string energy into acoustic waves_, by causing comparatively flat tonewood surfaces and partially enclosed air cavities to be set into vibration.  The detailed physics of this coupling is complex, and involves resonances, elastic properties, and a whole bunch of stuff.  But the underlying idea is simple:  lose less vibrational energy to damping, and put more of it into radiated sound.

----------

CJFizzix, 

Mark Gunter, 

peter.coombe

----------


## billhay4

Again, Dave,
You don't have to participate in such discussions. 
Bill

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## billhay4

I'd like to clarify my original post on this topic a bit now that much helpful information has been related. I, of course, had a general understanding of sound and the function of the soundboard and sound box when I posed the original questions.
It is my impression (and I may well be wrong here) that much scientific research has been done on the theoretical questions of acoustics and music. Like all scientific research, this has followed a strict protocol as outlined by Dave Cohen above.
Has anything like this been done vis a vis specific instruments, concerning very practical considerations? For example, have there been any controlled studies of the effect of the shape of the soundbox on the sound of the instrument? How about the use of particular woods? Or the shape of soundholes? These would have to isolate a particular variable and measure the effects of certain changes in that variable from one instrument to another. A valid standard of measurement would have to be used. In short, they would have to follow a scientific protocol.
Is the issue here the subjectivity of sound? Or is it the time and expense of doing such research? Or something else? Or is it that there are just so many variables in the sound an instrument produces that the effect of one or another is too small to measure or make a difference?
I am interested in such information regarding the mandolin specifically because that is what I play and build. I suppose this removes the question from the theoretical realm to the practical, but I find the question pertinent anyway.
What I'd really like to see is a foundation dedicated to such musical research. Is there one?
Bill

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## Tom Haywood

I'm reminded of a discussion that took place in a physics class at a university in Nashville in the early 1970s. The professor (a sho' nuff  captured WWII German physicist) was working with Yamaha to create the first truly electronic keyboard that could sound like multiple instruments. They worked for several years with tone generators and computers to produce the fundamentals, harmonics, all overtones, all attacks and dampening, and everything they could measure and replicate for each instrument. Each time the physicists had done all they could do, they had players and ordinary folks listen to the different sound files to determine which was best. In every case, the listeners said the files sounded only vaguely like real instruments. The class confirmed this and observed that the horn files sounded much more real than the string instrument files. In the end, Yamaha simply recorded sound samples from several versions of each instrument, mixed the instrument samples together, and put that in the keyboard computer chip. The professor wanted us to understand that there is an incredible amount of sound information coming especially from string instruments and, as beautiful as physics theories and mathematics are within themselves, physics after all this time and effort has barely scraped the surface of data and understanding music instruments – which calls into question, as it should, whether generally accepted physics is on the right path with string instruments. For this reason, I can't accept the statement of a physicist that the question of what the mandolin body does and how it does it has been answered by physicists or anyone else.  Therefore, I see the need to maintain the limited definitions so as not to dismantle what has been learned, and at the same time maintain the broader definitions so as not to exclude ideas that will help lead to the deeper ideas and understandings.

----------

billhay4, 

CJFizzix, 

Mark Gunter

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## Larry Simonson

The mandolin (and other instruments) is a tough puzzle and scientists will continue enjoying the job to reveal its inner truth but one fact remains and that is that science has not brought us new mandolins that are widely accepted as being superior to those made some 90 years ago.

Let me pose a question:  Is the bridge position on Loar inspired mandolins the optimum place for coupling between the string and the body?

----------

Jess L.

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## dschonbrun

> Actually, no, the problem is not (just) one of directionality, and of focusing the radiated sound field. The problem is that the energy in a vibrating string couples _only very weakly_ to the air around it.  A moving string is very thin, and it moves very little air around it as it vibrates.  It therefore produces very little sonic output, irrespective of the direction!  You can experience this directly by plucking the string of a solid-body electric guitar (one that's not plugged in).  Almost no volume.  You can focus this if you like, but that won't help much.
> 
> As I have written before, the soundbox of an acoustic instrument _not only_ focuses the sound (akin to acting like a megaphone in that regard), but it also _couples the vibrational string energy into acoustic waves_, by causing comparatively flat tonewood surfaces and partially enclosed air cavities to be set into vibration.  The detailed physics of this coupling is complex, and involves resonances, elastic properties, and a whole bunch of stuff.  But the underlying idea is simple:  lose less vibrational energy to damping, and put more of it into radiated sound.


dbloch, I appreciate the elegance and thoughtfulness of your response.  You clearly have a deep grasp of the physics and acoustics.  Thank you for adding to the conversation.

Best,
D

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## billhay4

> Is the bridge position on Loar inspired mandolins the optimum place for coupling between the string and the body?


Well, the bridge position is determined by the scale length, isn't it? You can modify the body so that it lands in a different spot on the body, but the length of the scale is fixed (or, if not fixed, then must be modified to move the bridge relative to the nut).
Bridges have been placed at various places on the body of instruments, but I don't know if any systematic study of this has been made.
Tommando: I'm guessing that was Vanderbilt University an old stomping ground of mine when I was at Sewanee.
Bill

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## fscotte

The Griffith A Loar may have the ideal bridge position.

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## peter.coombe

> I can't accept the statement of a physicist that the question of what the mandolin body does and how it does it has been answered by physicists or anyone else.


Well what the mandolin body does has already been answered here.  We keep coming back to my original point about efficiency.  Basically the body increases the efficiency of conversion of kinetic energy in the string to sound energy by improving the air coupling.  This process is complex and non linear so the conversion function is different for each individual instrument which is why they sound different.   How it does the energy conversion is not fully understood at the moment, but some day in the probably distant future the physics of it all will be fully understood - i.e. some one will eventually come up with a computerised mathematical model that closely fits reality.  This sort of thing has been done with guitars, with some limited success, so we part of the way there.  A music instrument is a physical system so it can and eventually will be described fully according to the laws of physics.

I do wish people will stop using the work amplify.  In physics "amplify" means there is a _net increase in energy_ involved which there is not.  In other contexts "amplify" can mean other things, but we are in the realm of physics here so amplify is not the appropriate word to use.  Dictionary definitions are not helpful because they are out of context.  The discussion seemed to go way off an a tangent there.

----------

billhay4, 

Mark Gunter, 

sblock

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## sblock

> IFor this reason, I can't accept the statement of a physicist that the question of what the mandolin body does and how it does it has been answered by physicists or anyone else.  Therefore, I see the need to maintain the limited definitions so as not to dismantle what has been learned, and at the same time maintain the broader definitions so as not to exclude ideas that will help lead to the deeper ideas and understandings.


You're welcome to ignore what all the physicists are telling you, but that doesn't mean you're wise to doubt what they're saying: you'd be foolish to do that, in fact. 

It does _not_ require a detailed knowledge of exactly how sound energy flows from the string to the remainder of the instrument to understand how a soundbox works, at least on a more general level!  To offer an analogy, if you tell me that a basketball player has a vertical leap of 39", I can tell you the speed with which he left the ground (close to 10 miles per hour, vertically). And to figure that speed out, I do _not_ need to know details of how he generated that lift, such as how his muscles worked, or his jump timing!  I just need to know the physical principles involved.

What a mandolin body "does" is, very obviously, too complex and open-ended to answer in its full sense, any more than answering a question about what your human body "does"!  At the broadest level, the body of an acoustic instrument simply turns the energy of a vibrating string into some sounds that we hear better.  That is, it takes the vibrational energy from the string and transduces it (albeit with a lot of energy loss) into the vibrational energy of the air surrounding the instrument. Which we hear.  Furthermore, it does so _much more efficiently_ (that is, with far less energetic loss) that if it were just the string vibrating alone, in the absence of the body.  This is not a hard concept to fathom!  Soundboxes were developed very early on in the history of stringed instruments, for the purpose of making these instruments sound louder.  

Soundboxes can also shape the sound, and make instruments sound "better"  (but "better" means very different things to different people, and "better" sound for a violin is not the same as "better" sound for a guitar).  So, the _quality_ of the sound that's radiated into the air is something else again. The timbre and duration of the sound, the fundamental and overtone series, the attack, the resonances, and ALL THAT other stuff that we care so much about here on the MC --  the qualities that make a mandolin sound like a mandolin, but a cello sound like a cello -- these things are ALL affected by the soundbox, too. If luthiers (or physicists) knew exactly how to predict all the sonic qualities based on the physical characteristics of soundboxes, they could make all instruments sound equally great, I suppose.  No one knows how to do that. Not physicists and not luthiers.  

But the question posed by the thread's OP is "what is the function of the body?"  Importantly, his question was NOT "how does the body function." That's different.  It seems to me that you and some others are trying to get a handle on how the body of a mandolin actually works (functions), and not what the _function of the body_ is.  These are _very_ different things.  The function of the body is to transduce sound energy produced by the strings.  It's really not hard to answer.  But how it does this, exactly, is something else altogether, and very complicated/mysterious.

----------

billhay4

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## Mark Gunter

Peter, you make great points here, and others have made the point about specialized vs. common usage of the word "amplify." The input of the physicists here is of great value, so it behooves me to acquiesce to the narrower meaning of "amplify" in the interest of being understood and of keeping the scientists engaged - but, all who participate here are not physicists, and it seems unreasonable to expect those of us who are not physicists to speak in the language of physicists. I sincerely doubt that those (myself included) who use the word "amplify" in a wider sense intend to convey that energy is added to that which is present in the excited string. I believe they intend to convey that the sound is louder, thus "amplified", due to the coupling properties of the soundbox. I do not believe there is a patent problem in we laymen speaking this way _except for the fact that it makes communication with the experts more difficult_. For me, that is reason enough to eschew the term in the way I used it before. It has always been apparent to me that the gain in volume is due to the efficiency of the vibrating soundbox vs. the vibrating string. Your expositions, as well as those of sblock, Dr. Cohen, Bertram Henze and other experts here are always enlightening when on point.

----------

Jess L.

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## David Lewis

I have found this a fascinating and enlightening discussion. Thank you all.

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## fscotte

On the contrary Mark, I don't think I've ever heard someone refer to a banjo as amplified, or that a mandolin was amplified, or had more amplification, when sitting around in a jam session or listening to your favorite group.  The common laymen term we use is loud, or louder, to describe that an instrument was, well....loud.  But suddenly in this thread about what a soundbox does, we see the technical term amplify being used, instead of the word loud.  So I don't think it's correct nor justification to imply that laymen are just using the word in place of loud.  No... Using amplify means you're implying an increase of energy whether you know it or not.  Thus the confusion and falsity of the conclusion.

Multiplied, amplified... They sound the same and they mean the same.

----------


## Mark Gunter

I'm not sure which part, exactly, of my previous post you are controverting. I never said that people sit at jam sessions speaking in this or that manner. My point was that it is not an incorrect non-technical usage to equate "amplify" with "make louder" by whatever means. There is evidence that the word has been used in that manner through history, I have used it here in that manner, and others have used it here in that manner. I believe it's immaterial whether I've discussed this at any jam sessions or what language I've used at jam sessions.

A major point of my previous post was to _acknowledge_ the technical meaning, and I pointed out that using the word as I did in this discussion leads to misunderstanding by the experts. Your last post is a perfect example of such . . .




> So I don't think it's correct nor justification to imply that laymen are just using the word in place of loud. No... Using amplify means you're implying an increase of energy whether you know it or not. Thus the confusion and falsity of the conclusion.


. . . in which your confusion about the intentions of those of us who've used the word here is apparent. In my case, the word was not used in place of the word "loud", if there were a better word for me to have used it might have been _enlouden_ but I'm not even sure that is a legitimate word. The meaning implied is _to make louder_ or _to increase volume_. Not simply as a synonym for "loud". To you and others, this implies an increase of energy, whether I know it or not; for me and for others who have spoken this way here an increase of energy is not implied; rather, an increase of volume or loudness. Which part of that are you controverting when you write, "To the contrary"?

----------

Jess L.

----------


## Wes Brandt

> To me sound boxes just amplify better. For instance, a mandolin with a sound box against a solid bodies mandolin!


Amplify!?!?  Oh no! You are in big trouble now  :Wink:

----------


## sunburst

The box does not make the strings louder. The box takes energy from the vibrating strings and converts that energy into sound. In doing so, it takes energy away from the vibrating strings, so the strings stop vibrating sooner than they would otherwise. We could even say that the box makes the strings _quieter_ because it is stealing energy from them that they would be using to move air (making sound) for a longer time. The sound from the strings is a sound, mentioned here somewhere, similar to a Les Paul that is not plugged in. We don't hear a louder version of that sound when we hear a mandolin. That's what we would hear if we amplified the sound of the strings, what we hear is different. If is the sound of the box moving air (making sound) using a portion of the energy that it gets from the vibrating strings.
I hope this is quick-and-dirty attempt at lay language explanation of the distinction between what an acoustic instrument body does and amplification serves to get more people "on the same page" on this bit of language. Even in non-scientific terms, the box does not amplify the sound of the strings, meaning it does not make them louder. Instead, he box makes sound from the energy it gets from the strings.

Although I've managed to avoid this discussion (that I wasn't invited to enter anyway) for the better part of 4 pages, perhaps this post will serve to clarify why some of us don't like using the term "amplify" incorrectly to describe the workings of an acoustic instrument body.

----------

billhay4, 

Marc Berman, 

Vincent Capostagno

----------


## Vincent Capostagno

A very clear, consise and nontechnical explanation of the function of the sound box.  This should close this part of the discussion.  Two further points.  The OP surmised the harp had no sound box.  Perhaps he was thinking of the Lyre...Graham McDonald gives examples of several ancient stringed instruments that had no soundbox, so they are not absolutely necessary.  Just desirable.  If I recall correctly, the harp from ancient Ur has a soundbox and it dates from 2500 BC (U Penn museum in Philadelphia).
Also, we don't need air to hear.  We have an alternate mechanism:  Plug your ears and put a tuning fork on your mastoids (or forehead). Bone conduction.

----------


## Wes Brandt

Maybe they played the Lyres pressed against the tops of their skulls to keep things simple.

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## Jim Adwell

> Maybe they played the Lyres pressed against the tops of their skulls to keep things simple.


Someone needs to photoshop that.

----------

Jess L.

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## billhay4

The discussion of amplify has, indeed, distracted from my original post. I would simply request that, when you use the term, you explain which meaning of it you are intending.
I attempted to redirect this thread to more specific questions about the mandolin body and studies of the effects of certain variables on the sound produced by the instrument. The lack of responses to this leads me to believe that there is very little study of this (other than anecdotal) but I still think it worthy of consideration. There was a small effort made to introduce the question of bridge position but it seems to have been swallow  up in amplification.
I would like to see this, and the other questions I posed, discussed in more detail.
Bill

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## fscotte

> In my case, the word was not used in place of the word "loud", if there were a better word for me to have used it might have been enlouden but I'm not even sure that is a legitimate word.


A common laymen, by which you are desiring to be in this discussion, would use the word "louder".  Instead, you chose the word "amplify", which has a completely different meaning.  So it is unusual why you would be a laymen in this discussion, yet use the word "amplify" to describe what a soundbox does.  If you were sitting in a jam session, and a much louder mandolin was given to you, I'm pretty sure you would use the term in the following manner.. "This mandolin is much louder".  I'm pretty sure you wouldn't say, "this mandolin is really amplified.. because it gives a different meaning.

So, all that said to say this, in the context of this topic you absolutely cannot use the word "amplify" unless you are referring to an increase in sound energy.  That's why we have discussions like this and why folks like the good Dr Cohen get so annoyed because people throw around technical terms so loosely, then try and re-cant by saying it's "just their way of saying thus and thus..."

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## billhay4

You just can't stop, can you?
Bill

----------

Earl, 

Jess L.

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## Wes Brandt

I'm definitely late to the party here and it took some reading to catch up. I'll put in my two cents worth.

I think there is just an inherent problem with being a specialist or specialization in general, sort of an occupational hazard.
How many times have you listened to someone explaining something and been somewhat or totally lost simply because they are speaking in ways that they have become very used to, in their own world, and don't realize they are using words or terminology that is alien to the average person and most of the time if they just switch over to the "common" words, terminology or concepts, it quickly becomes clear what they are talking about. I don't know about most of you but I have experienced this many times. So it works both ways.

I don't think anyone who has posted on this thread is stupid enough to think that energy from nowhere is magically added into the system .and I would guess everyone knew what was meant . 

First to come up on a google of amplify, definition---- note the the synonyms  "louden"ha ha!

am·pli·fy

verb

"increase the volume of (sound), especially using an amplifier.
"the accompanying chords have been amplified in our arrangement"
synonyms:	make louder, louden, turn up, magnify, intensify, increase, boost, step up, raise."

----------

Jess L., 

Mark Gunter

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## sunburst

Even so, the box does not "louden" the sound of the strings. The box _makes_ sound using energy from the strings.
Layman's term or technical term, neither "louden" nor "amplify" correctly describes the function of the body in terms of what it does with energy from the strings, and when those words are used, it makes it more difficult for folks like Dave (who has waded into this discussion despite being blatantly told he wasn't invited, to try to _correctly_ give an overview of the function of the body) to explain things more correctly.
We can argue from now on about what we mean by "amplify", but even if we mean 


> make louder, louden, turn up, magnify, intensify, increase, boost, step up, raise…."


we have not correctly described what the body does with energy from the strings. It is not the strings we hear, made louder, it is the air set in motion by the body (mostly).

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## billhay4

Please, why can't we get along. The question of louden and amplify has been beaten to death. I am politely asking all of you to stop on that topic and consider some of the other questions raised in this thread. John's explanation is fine; now all of you grow up.
Bill

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## Dave Cohen

> It is my impression (and I may well be wrong here) that much scientific research has been done on the theoretical questions of acoustics and music. Like all scientific research, this has followed a strict protocol as outlined by Dave Cohen above.
> Has anything like this been done vis a vis specific instruments, concerning very practical considerations? For example, have there been any controlled studies of the effect of the shape of the soundbox on the sound of the instrument? How about the use of particular woods? Or the shape of soundholes? These would have to isolate a particular variable and measure the effects of certain changes in that variable from one instrument to another. A valid standard of measurement would have to be used. In short, they would have to follow a scientific protocol.
> Is the issue here the subjectivity of sound? Or is it the time and expense of doing such research? Or something else? Or is it that there are just so many variables in the sound an instrument produces that the effect of one or another is too small to measure or make a difference?
> What I'd really like to see is a foundation dedicated to such musical research. Is there one?
> Bill


1.  Shape of the soundbox is way down the list for most experimental researchers.  In the first place, you have to ask yourself.  What do you want to know about the effect of soundbox shape?", followed by "What will you measure to determine the effect?", followed by,,,,,,,.  If you just ask someone to "determine the effect on the sound", you are looking for that big picture.  It needs to be resolved into its' component parts before anything can be done.  Violinmaker Joe Curtin has made some unusually-shaped violas (possibly violins as well.  If you do a search on him, you will likely find something of interest to you.
Otoh, if you are referring to theory, Leissa has written a two volume treatise entitled "Vibrations of Plates" and "Vibrations of Shells".  Once you deviate from the simplest shapes, i.e., circles and rectangles, the mathematical going gets pretty involved.  For the simplest cases of circular plates and rectangular plates, mathematical solutions for those things have been around for more than a hundred years.  The famous text by Morse has those, as does Fletcher & Rossing, as does,....
2.  Re the use of particular woods:  Much has been written about this.  In particular, Daniel Haines wrote several extensive papers on properties of woods pertinent to musical acoustics, some published in JASA, a couple in CASJ.  Also, Voichita Bucur (from Nancy, FR) has written an entire volume on the properties of musical instrument woods - a bit pricey, available from the ASA.  There have been some more recent shorter papers as well, e.g., in _Savart Journal_, which you can find through the GAL site, luth.org.
3.  The _shape_ of soundholes is way down my list.  More important in terms of magnitude of effect are the area, perimeter, and placement.  A single oval hole vs two ff-holes, f'rinstance, has a measurable effect on sound radiation from the higher air modes.  I summarized some of my data on that in my chapter in Rossing's 2010 book, "The Science of String Instruments".  Nevertheless, there was one recent paper on the effect of the shape of soundhole, discussed in this forum, as well as others.  The author's flow equations were OK, but his experiments were limited, and he greatly overstated the importance of the shape, especially considering his results.  You can do a search for that discussion.
4.  Subjectivity and perception of sound are indeed problems, but there are ways around that.  We can acquire, f'rinstance, time-averaged sound spectra or accelerance spectra.  You can even find some material on that in the violin chapter in Fletcher & Rossing, also the 2010 Rossing book.  Also, there are references to the primary literature in both of those works.

5. Re a foundation:  You will have to find a generous someone (or someones) with a lot of discretionary money.  I don't know of any researchers in musical acoustics who are receiving any grant money, save one.  Thom Moore, down at Rollins U., did get a grant from a piano company to do some interferometry and other experiments on piano soundboards, but that is it.  Of course, Joe Curtin did win a MacArthur Foundation (i.e., "genius") grant several years ago now, but that is not quite the same thing.  Musical acoustics is just way down on everyones' list of need for research money.

I just outlined in this post a large amount of literature pertinent to (most of) your specific questions.  It may not be suitable to your learning style, but at least you know it is there.

----------

billhay4, 

Marc Berman, 

Mark Gunter, 

peter.coombe, 

StuartE

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## billhay4

Thanks, Dave,
Refreshing to see someone address the issue. 
Send me a bill.
:-)
Bill

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## Eric Foulke

Bill,

Outside of all that acoustics stuff, the body simply provides nifty places to attach your strap. :Grin:

----------

billhay4, 

Jess L.

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## Bill McCall

And to add to the reading list, help those sleepless nights, and gain some insight into the pleasantries of music, one could start with a classic, 'On the sensations of tone as a physiological basis for the theory of music' by Helmholz.  One might like chapter 5, 'On the differences in Quality of Musical Tones'.  An oldie but a goodie, 1862.

----------

billhay4

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## fscotte

> You just can't stop, can you?
> Bill



With all due respect Bill, unless someone is violating the terms of forum, there is no reason to ask anyone to stop, whatever that entails.  Unlike a real conversation, if someone injects something here you don't agree with, you can simply ignore it and reply to the post you feel is more relevant.  There is absolutely nothing wrong with trying to get everyone to use proper descriptions and meanings, especially when the topic comes up as technical as "what is the function of the body".

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## sblock

> I've been mulling this over in the quiet moments before I fall asleep.
> It occurred to me that a harp doesn't have a sound board or sound box, yet it still makes beautiful music. So, what exactly are the functions of a sound board and sound box? Do they focus the sound, add certain qualities to it, amplify it, or something else?
> That being asked, I'm led to a bigger question: what exactly is sound? I assume it's vibrations that are at a frequency the human ear detects and converts to certain signals to the brain. But is it just vibrations of the air? or of something else (the ether? disturbances in the space/time continuum? what?) I know sound travels through other mediums besides air, so what exactly has to vibrate to create sound? I'm being a bit silly here but I would like a concise definition of sound from someone who understands this better than I do.
> For now, however, I am going on the assumption that my definition of sound is more or less correct which leads me back to my original question: how does the mandolin shape, size, construction, composition produce the particular sounds we associate with the instrument? Can they be produced another way?
> Papers due at 12:00. No cheating.
> Bill


Perhaps we should go back to viewing the original posting of this thread, and recap some answers?

1) The OP was dead wrong about at least one important thing, because a harp _does_ have a soundbox!  The Celtic harp and the pedal (concert) harp both have these things.

2) "So, what exactly are the functions of a sound board and sound box? Do they focus the sound, add certain qualities to it, amplify it, or something else?"  Yes indeed, a sound board or a sound box can act to focus the sound (i.e., change the shape of the sound radiation field), but that's _not all_ that they do.  Yes, they can also add certain qualities to the sound -- they can affect the timbre, strengthen/weaken or introduce harmonics, affect the attack and decay of notes, and much more.  But NO, they do NOT "amplify" the sound, if you define amplification as an _increase in the energy_, which is what a physicist or engineer means by that term. Soundboxes and soundboards do, however, function to transduce the mechanical vibrations of a string into sound waves that can propagate through the air to the listener's ear, and they manage to do this much _ more efficiently_ than a string alone can.  Put another way, they _do_ make a vibrating string sound louder to the listener than it otherwise would. 

3) "What is sound?"  Easy!  Sound is simply mechanical vibrations, whose oscillatory frequencies happen to lie within the audio range, which is (for humans) from roughly 20Hz up to about 20,000 Hz. Sound can propagate though a solid (wood, metal), through a liquid (water, alcohol), or through a gas (air, helium).  So NO, sound is NOT "just vibrations in the air."  It isn't in "the ether" (no such thing).  Furthermore, _every physical thing_ is part of the space/time continuum, so that is not useful!

 4) "How does the mandolin shape, size, construction, composition produce the particular sounds we associate with the instrument?" Oh, come on!  This a vast topic, and clearly beyond the scope of any thread on the MC. To be blunt, though, I think it's a pretty darned silly question for someone to pose in a forum post, but then, the OP did confess that this was something he mulled over before falling asleep. When you get right down to it, neither expert luthiers nor acoustic scientists know how, exactly, to get a particular sound out of ANY acoustic instrument (let alone a mandolin) from first principles. That doesn't mean that they are not influenced by working guidelines, long experience, knowledge of acoustics, traditions, and all that.  But asking how the "shape, size, construction, composition" affect sound is tantamount to asking about everything there is to know about luthiery!! A silly (and arguably, somewhat impertinent) question, I'd contend.

5) "Can they [_mandolins_] be produced another way?"  Why YES, _of course_ they can!  Look at the many varied shapes and sizes of mandolins that already exist (bowlbacks, flattops, A models, F models, bandolims, and much more) and the many varied materials used to form these (everything from softwoods to hardwoods to metals to carbon fiber -- and even concrete!).  But these all sound a little different.  Come to think of it, just about any two mandolins -- even with otherwise identical construction -- sound a little different, if your ear is good enough to hear it.  No two are likely to be the same, I'd say.  Same for violins, guitars, etc.

There.  I hope we're done with this (but I doubt it).   :Laughing:

----------

Mark Gunter

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## billhay4

> With all due respect Bill, unless someone is violating the terms of forum, there is no reason to ask anyone to stop, whatever that entails. Unlike a real conversation, if someone injects something here you don't agree with, you can simply ignore it and reply to the post you feel is more relevant. There is absolutely nothing wrong with trying to get everyone to use proper descriptions and meanings, especially when the topic comes up as technical as "what is the function of the body".


I have just as much right to ask you to stop obsessing about something as you do to obsess about it especially when it is derailing a topic I started and have a strong interest in.
Bill

----------

Jess L., 

Mark Gunter

----------


## Jess L.

The original poster wrote: 




> ... There was a small effort made to introduce the question of *bridge position* but it seems to have been swallow up in amplification.
> *I would like to see this*, and the other questions I posed, *discussed in more detail*.


About bridges and soundboards:

I can attest that bridge position **does** make a *huge difference* on at least some stringed instruments that I used to be familiar with: including fretless banjos, both hide-head *and wood-top* ones. I used to experiment with bridge placement on them in the 1960s and '70s. You get entirely different tonal quality depending on whether the bridge is nearer to the edge of the 'soundboard'/head (nearer to the tailpiece) or if the bridge is nearer to the middle of the 'soundboard'/head. I found that the modern standard bridge placement for *fretted* banjos, was not optimal for my style of playing, although *some* of the older (late-1800s) fretted banjos were designed such that the bridge was in the position I preferred for my style of playing, where the bridge is a little further back towards the tailpiece instead of plonked down right near the center of the head. Yes I realize that a hide-head or plastic-head banjo 'soundboard' is much more flexible and probably (?) vibrates in a whole different way compared to mandolins, but my point is that the sound varies a lot (on the exact SAME INSTRUMENT) depending on where the bridge is at. I'm not just talking about pitch, obviously, either. 

The differences in soundboard type, obviously, are - among others -  that mandolin soundboards are much less flexible than standard hide/plastic banjo 'soundboards', and mandolins have bracing (or if that's not the right term, then whatever the right term is for those wooden bar-like things that are glued onto the undersides of mandolin soundboards). I do not think it reasonable to assume that a banjo hide head is a simple drumhead, because the pressure of the bridge surely makes it into a real 'soundboard' that does all the usual functions of a soundboard (louderizes  :Wink:  the sound etc). 

*Further*, at one point I actually owned several other types of *WOOD-TOP* fretless instruments (with various types of necks, some had bolt-on former-mandolin necks, some had regular-length former-guitar or banjo necks, etc) that I cobbled together out of a big box of spare old parts from other leftover stuff, and I noticed that bridge placement made a big difference on those too. As I recall, all the wood tops had variations of some sort of simple 'bracing' or tone bars or whatever it's called, on the underside (I think in the case of those not-top-dollar instruments I was experimenting with, the 'bracing' was probably more designed to actually "brace", that is, to prevent the top from collapsing due to the pressure of the bridge.) 

However, on the wood top instruments, I didn't go so far as to remove/reposition the *bracing* every time I moved the bridge, and that is probably an important factor... 

I realize that my observations are merely anecdotal and likely subject to being summarily dismissed as unimportant peasant* ramblings by some of the more scientifically-minded folk. However, maybe it's a *start* to get the discussion back on track... 

So, has anyone else done any experimentation with bridge placement when building or putting together musical instruments?


----------
*** Not necessarily a bad thing, & I am one.  :Smile:

----------

billhay4, 

Larry Simonson

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## Tom Haywood

Bill, I sent you a PM.

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billhay4

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## Larry Simonson

I have raised the question about bridge location earlier in this thread to see if anyone had published a study of such.   i do this as I am building my 3rd instrument and have not cut out the neck yet.  As I see it, gluing the fingerboard on defines where the 12th fret is and therefore where the bridge needs to be located, assuming traditional string length and ignoring any minor compensation.  Now I have a drummer friend who tells me about the "sweet spots" on his drums so I was wondering if such spots may exist on mandolin bellies.  Maybe if the bridge position was moved to such a sweet spot by strategically locating the fingerboard there might be some improvement in the efficiency of transmitting plucked string energy to sound.  I have no idea how this will turn out but I find it interesting and am in the position to give it a try, so that is what I am planning.

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Jess L.

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## Bertram Henze

why don't we just say the body makes the instrument open up  :Grin:

----------

Jess L., 

Tom Wright

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## sblock

> why don't we just say the body makes the instrument open up


Agent provocateur!

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billhay4

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## fscotte

The question of bridge position reminded me of this mandolin.



Seems Mr Gilchrist thought it sounded better in the traditional position with 14th fret at the crosspiece.

----------

Larry Simonson

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## pops1

> I have raised the question about bridge location earlier in this thread to see if anyone had published a study of such.   i do this as I am building my 3rd instrument and have not cut out the neck yet.  As I see it, gluing the fingerboard on defines where the 12th fret is and therefore where the bridge needs to be located, assuming traditional string length and ignoring any minor compensation.  Now I have a drummer friend who tells me about the "sweet spots" on his drums so I was wondering if such spots may exist on mandolin bellies.  Maybe if the bridge position was moved to such a sweet spot by strategically locating the fingerboard there might be some improvement in the efficiency of transmitting plucked string energy to sound.  I have no idea how this will turn out but I find it interesting and am in the position to give it a try, so that is what I am planning.


Larry, I did something like this with a National I was refurbishing for someone that wanted it to play in tune. I put in the 12th fret and clampled the fingerboard on the neck and strung up to move it to where it intonated. You could do the same thing by moving the fingerboard and stringing it up in the white and moving the bridge somewhat to see if it makes a difference.

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## billhay4

Pops1,
I don't think this is what Larry was getting at, or maybe I'm misreading your post, but ya'll can correct me if I'm wrong.
I think he was wondering where on the body from head to tail the bridge gives an optimal sound. This cannot be adjusted if your scale length is fixed as it has to be located where the scale needs to end.
However, you can design an instrument to have various bridge placements. You can vary the scale length, or the body shape and the location of the f-holes (most bridges are centered on the little notches in the f-holes) to achieve this. Dave Cohen comments on this briefly in post #98 but I have not read his cites fully yet.
I asked about this because placing soundholes at the rim of an instrument appeals to me aesthetically and from a building standpoint. I am just finishing one like this now and will report anecdotally on the results when I get it strung up.
Bill

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## fatt-dad

The body converts the vibration of a two dimentional material (i.e., the string) to a three dimentional object (i.e., the body volume).  That affects the sound.

f-d

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Jess L.

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## Larry Simonson

Common plans for Loar inspired mandolins have the 15th fret at the binding cross piece which defines where both the nut and the bridge are located.  My idea (I'd be mighty surprised if it is original) it that I want to optimize the position of the bridge first and then let that define where the nut needs to be.  The challenge, of course, it to find that sweet spot, if one exists.  My plan is to get the instrument built and see how it performs with various bridge positions and if this works, I will then know where to permanently position the finger board. It seems to me, that since every instrument is pretty much unique and that the bridge so important it is worth a bit of experimenting.

  I have an A model built by Jack O'brien with the 13th fret at the cross piece and it is a canon, fscotte mentioned one with it at the 14th fret above and older Gibson As had this at the 12th fret, so here is some history, though unknown to me.

----------

billhay4

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## Tom Haywood

Interesting idea that the top plate may have a sweet spot. All mandolins I've played have a sweet spot for sound that occurs between the nut and the bridge, usually when the strings are struck somewhere above the neck block. I suspect this has to do with harmonics, but I don't know of any specific studies.

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## billhay4

The idea of "sweet spot" is the real question here to me. I'd have to have a much better understanding of the relationship of the motion of the bridge to the vibrations of the body  and the resulting sound before I could understand this concept. Or, on the other hand, I suppose it could be found by trial and error. But how?
There is another approach, also. One could construct the body shape around the bridge location to maximize it's effectiveness. There are other reasons one might want to modify body shape: ergonomics, aesthetics. So all this would constitute a totally new approach to the mandolin.
Interesting topic and just what I was getting at in my inartful original post.
Bill

----------

Jess L.

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## ProfChris

As a simple example of the 'sweet spot' consider a soprano ukulele, which has a similar scale length to a mandolin. It's simple because the top is flat or very slightly domed, no substantial arching or graduation to complicate matters. All the good-sounding sopranos I've ever seen have the bridge pretty much in the middle of the lower bout, which (so I read from those who have studied these things) is the main vibrating part of the top.

Locating the bridge closer to the tail produces more treble (undesirable on an instrument which lacks bass anyway) and thus a sound usually described as 'thin'. No-one ever puts it closer to the sound hole, though I suppose one could - no idea how that would sound.

On the other hand, on a banjo ukulele with the same scale the bridge is normally located a little distance aft of the middle of the head. If the bridge is in the middle the sound is usually described as 'tubby', i.e. the higher frequencies are not emphasised as much as players seem to like from that instrument.

My guess, and it is only a guess, is that this relates to the efficiency of the coupling between the strings and the top. I'd expect locating the bridge in the effective centre of the plate to be most efficient at moving the plate (vibration), because the plate becomes stiffer as you approach its edges and therefore harder to move. I think I have read that lower frequencies are harder to produce than higher (requiring greater efficiency of coupling?) I suspect the physicists posting here would be able to say whether this is correct or not.

My other guess would be that a guitar, which has a much larger plate, allows more latitude in bridge placement without sacrificing efficiency too greatly.

If both these guesses are right, I'd predict that a mandolin would sound loudest, and produce a greater amplitude of bass frequencies, if the bridge were in the middle of the vibrating area of the top (but I have no idea where that would be). Of course this might not produce the desired sound. Looking at some images I see that most bowlbacks have the bridge forward of the middle of what I'd predict to be the main vibrating part of the top, as do F holes. A styles are either just forward or in the middle. But then, all these tops are of more complex shape and thickness than a ukulele top, and this might move the most efficient bridge location. Or, mandolins might sound better with the bridge in a slightly less efficient location.

----------

billhay4, 

Jess L., 

Mark Gunter

----------


## Bertram Henze

> I suspect the physicists posting here would be able to say whether this is correct or not.


I dare you...

But that is quite simple, I'll say. A vibrating plate with a fixed border will oscillate with a maximum amplitude somewhere in the middle (at least for the so-called (0,0) mode, which is the most simple and predominant in a mandolin top, like in a trampoline). That point of maximum amplitude suggests itself for bridge position because that's where the top is easiest to move.
There is a downside to that, however: triggering only one mode of oscillation also means concentrating the output around one resonance frequency where the instrument may be very loud but rapidly going quieter outside that frequency (a bit like in a small room or a bathtub where even flat noises like a splash of water take on a tone -> "tubby sound"). So you might want to move the bridge a bit out of that point to make the instrument more balanced frequency-wise. 

It's a compromise, so to speak, to find throatiness between tubbiness and thinnicity  :Grin: 

I hope no common usage words or idoms were harmed in this post  :Cool:

----------

Jess L., 

jhowell, 

Larry Simonson, 

Mark Gunter, 

ProfChris

----------


## Dave Cohen

> I dare you...
> 
> But that is quite simple, I'll say. A vibrating plate with a fixed border will oscillate with a maximum amplitude somewhere in the middle (at least for the so-called (0,0) mode, which is the most simple and predominant in a mandolin top, like in a trampoline). That point of maximum amplitude suggests itself for bridge position because that's where the top is easiest to move.
> There is a downside to that, however: triggering only one mode of oscillation also means concentrating the output around one resonance frequency where the instrument may be very loud but rapidly going quieter outside that frequency (a bit like in a small room or a bathtub where even flat noises like a splash of water take on a tone -> "tubby sound"). So you might want to move the bridge a bit out of that point to make the instrument more balanced frequency-wise. 
> 
> It's a compromise, so to speak, to find throatiness between tubbiness and thinnicity 
> 
> I hope no common usage words or idoms were harmed in this post


That is _partly_ correct.  In principle, when you excite _anywhere_ on the plate, all of the normal modes of the plate will be excited, unless you happen to be exciting the plate right at a nodal line for a particular mode or modes.  In that case, that mode or those modes will either be weakly excited or not excited at all, while all of the rest of the modes will be excited as usual.  It is true that the antinode, which would be approximately at the geometric center of the plate for the (0,0) or T(1,1) mode, should be the location of greatest compliance, so one should be able to get the greatest amplitudes for a given amount of exciting force in the middle of the plate.  However, that location is often close to the the nodal line of the (0,1) or T(1,2) or longitudinal rocking mode, which would mean weaker excitation for that mode.  Similar considerations for other modes.

In practice, I haven't observed very selective excitation of particular modes.  In Rossing's lab, I usually placed my stinger magnet right on the bridge, with the coil positioned over the magnet.  In most cases, that excited all of the modes without any problems.  The bridge locations were usually pretty close to the node for the (0,1) mode, but the mode was excited anyway.  That is likely because the nodal line is infinitesimal in width.  Only occasion, the excitation of the (0,1) mode was a bit weak, in which case I moved the magnet and coil off the bridge top and put it on the top itself.  That strengthened the excitation of the (0,1) mode.  More recently, in Thom Moore's lab, I have been exciting remotely with a speaker, and all of the modes were excited readily.  One of the biggest problems with observing modes other than the (0,0) is that in different mandolins, some modes will overlap in frequency significantly with other modes, so one has to sort out the mixing of those modes in the interferograms.  Can be a bit confusing at times.

Both the (0,0) and (1,0) (= sideways rocking) modes are pretty strongly excited in most mandolins (with the possible exception of Neapolitans).  For that matter,  the rest of the modes are excited pretty easily too.  The relatively lightweight mandolin plates are pretty easily excited, compared to something like, say, a steel drum.  There doesn't seem to be much experimental justification for the excessive excitation of just the (0,0) mode.  What's more, the (0,0) is really the main event, so I haven't seen any particular notes suffer from excessive (0,0) mode excitation.  I did see a splitting of the (1,0) mode peaking at 440 Hz in one mandolin.  Found that the 440 Hz A strings together had enough mass to do that.  Problem was solved by damping all of the strings with a small piece of foam between the strings and the fretboard.

The "tubbiness" vs "throatiness" in  mandolins comes mostly from the nature of the interaction between the (0,0) modes and the first or Helmholtz air resonance.  In oval hole mandolins, the lower (0,0) mode is usually found at around 200 Hz, and the Helmholtz is usually around 210 Hz, so pretty strong coupling there.  In ff-hole type mandolins, I've seen the lower (0,0) at anywhere from ~250 Hz to over 300 Hz.  The Helmholtz is usually around ~280 Hz.  Seems that the variations in "throatiness" also come from the proximity in frequency of the lower (0,0) to the Helmholtz.  I can't say this with absolute certainty, but I don't think the "tubbiness" vs "throatiness" in mandolins is all that sensitive to bridge position on the plate compared to the properties of the plates themselves.

I am posting this even though the OP has reminded me that I was not invited to post here.  I think the information is important enough that people should see it. Once again, there is more detail on this in my chapter in the 2010 Rossing book.

----------

Bertram Henze, 

CarlM, 

dave vann, 

jhowell, 

Jim Adwell, 

Larry Simonson, 

peter.coombe, 

ProfChris, 

sunburst, 

Tom Wright, 

tom.gibson

----------


## CarlM

Dr. Cohen, Have you or anyone you worked with done finite element models to study the modes and resonance?

----------


## fatt-dad

"Funny Elephants!"

f-d

----------


## Dave Cohen

> Dr. Cohen, Have you or anyone you worked with done finite element models to study the modes and resonance?


Some have long since been done for violins, also guitars.  In addition to FEM, there is also a newer version, called boundary element matrix ("BEM").  I haven't bothered with FEM or BEM.  Those things are good exploratory tools.  If you haven't yet done any experiments,, they can give you an idea of what to expect.  They can also tell you what happens if you vary specific properties or geometries.  Other than that, they tell you that if you put in the right values for parameters, you get the right results.  I started doing the interferometry with Rossing in 1999.  Not much point in doing the FEM at this point, maybe later, or maybe not.  I have derived a naive 4-oscillator model, but haven't yet crunched numbers.

----------


## billhay4

> I am posting this even though the OP has reminded me that I was not invited to post here.


The OP did no such thing. He reminded you that you were not obliged to post here if it was painful for you. He did so because you were not contributing to the conversation, but complaining about it. It is very refreshing when you choose to illuminate matters that are raised.
Bill

----------

Jess L.

----------


## sunburst

> Dave,
> With all due respect, no one asked you to contribute to this conversation at all.


That's how I read this post too.

----------

Dale Ludewig

----------


## Tavy

It's been mentioned here before - but the issue of "sweet spot" has been investigated in Howard Wright's thesis "The Acoustics and Psychoacoustics of the Guitar" - the idea is a simple one - there is a particular impedance associated to the coupling between each string and each mode.  The closer the string-bridge contact point is to the anti-node the lower the impedance and stronger that mode is excited by the string, while the closer the string-bridge contact point is to a node, the higher the impedance, and the lower the excitation.

It's worth pointing out that this was investigated for guitar pin-bridges, not floating bridges with multiple feet.  Also, that as long as you're somewhere vaguely near an anti-node, the difference in impedance will be minimal.  Or to put it another way, you have to be quite close to a node before the impedance really starts to rise and the coupling disappears.

There is one interesting exception to the above though - the main side-to-side rocking mode (which seems to be rather important for the tone of the instrument) has a node passing right through the middle of the bridge.  Wright highlights this as a potential issue for the D and/or G strings of a guitar depending how symmetrical the bracing is.

It would be interesting to know how much of an issue this is for mandolins, and whether mono-vs-bi-pedal bridges make any difference (subjectively they can sound very different in some mandolins, and much less so in others).

----------

Jess L., 

Larry Simonson, 

Mark Gunter, 

tom.gibson

----------


## fscotte

When Dr Cohen sneezes, I learn something.  No one owns a topic, so if Dave wants to sneeze, I'm all for it.  As a newbie, I learned so much from him, find myself going back many years in a forum search to read his insights.  Someone should compile his replies into an online book.

----------


## murrmac

There is a substantial difference between "not being invited to post" and "being invited not to post" .

Personally, I find all this excitement and excitation is too much for me ... I'm going to have to go and lie down ...

----------

Jess L.

----------


## JEStanek

Let's reduce the amplitude of the ruffled feathers here, folks.  We are often given insights (often with links to sources) into the physics of the mandolin.  I won't pretend that I understand it all but, I haven't done much googling to expand my knowledge on the concepts presented.

There's nothing to win here other than following the pathway of previous studies to gain understanding of how a system of parts generates sound.  Lets try and remember that we can use many tools at our disposal.

Jamie

----------

Dale Ludewig, 

Jess L., 

Mark Gunter, 

Scott Tichenor

----------


## CarlM

Dr. Cohen, the finite element models would seem like a good tool for investigating the effect of changing geometry, like arching, graduation, tone bar placement on the structural modes without building dozen of mandolins.  It would eliminate the wood property variable but getting a good material model could be difficult.  BEM is a good tool for studying fluids, like the air in the cavity but not as strong for structural analysis.  It would be quite a lot of work correlating to the interferometry and I am not sure if things like string mass and tension could be incorporated without overwhelming computer hardware.  I have seen some basic stuff done on guitars but nothing really in depth.  Anyway it was just a thought and thanks for your reply.

----------

Jess L.

----------


## fatt-dad

you could certainly adjust a lot of variables in an FEM. I'd think it hard to know all the modeled variables when building though.  It would be interesting to make a reliable model though!

f-d

----------


## Dave Cohen

> Dr. Cohen, the finite element models would seem like a good tool for investigating the effect of changing geometry, like arching, graduation, tone bar placement on the structural modes without building dozen of mandolins.  It would eliminate the wood property variable but getting a good material model could be difficult.  BEM is a good tool for studying fluids, like the air in the cavity but not as strong for structural analysis.  It would be quite a lot of work correlating to the interferometry and I am not sure if things like string mass and tension could be incorporated without overwhelming computer hardware.  I have seen some basic stuff done on guitars but nothing really in depth.  Anyway it was just a thought and thanks for your reply.


Carl, I didn't mean to imply that FEM is useless.  But I am not at the point where I can begin to think about things like minor variations in arching, etc.  I am still trying to fill in the pieces of the puzzle that is "what do these things do, as is?"  Currently, I am working on perturbations of the body modes by (body+neck) bending modes.  The main advantages of FEM are the ability to evaluate the goodness of parameter values (e.g., elastic moduli, effective masses of parts & air, & etc.) by comparison w/ experiment.  At this point, I am more interested in simpler models, and those can be complicated enough.  The dissertation which Tavy referred to a few posts back largely used the three-mass or three oscillator model, developed in the 1970s & '80s by some of the swedes at KTH, along w/ Graham Caldersmith.  One of the better early modelers was a Frenchman, Antoine Chaigne.  You can find some of his papers in CASJ.  

For me, a naive four-oscillator model is more important right now - an extension of the earlier three-oscillator model with the (neck+ribs) as the fourth mass.  Even with just four masses, the derivation I did requires eleven parameters to be optimized to each other.  But the four oscillator model will be a good start to understanding what the neck bending motions are doing to the body modes.  After that, I will look at perturbations of elliptical plate eigenfunctions by the air mass and the (neck+ribs) mass, kind of a "two plates + two masses" model.  Then, if I am still alive and sentient, we will look at comparisons w/ FEM modeling.  I'll need some good luck and good health.

----------

CarlM, 

Tom Haywood

----------


## jhowell

For that real geek in all of us  :Whistling:  NASA, of all places, seems to chat this up very well with a publication (NASA SP-160, Vibration of Plates) from the early 1970's.

Full disclosure:  while I had some calculus 40 years ago, the math in the NASA paper goes well beyond my capabilities, but I still have a deep appreciation for how rigorous the application is.

----------


## Dave Cohen

> For that real geek in all of us  NASA, of all places, seems to chat this up very well with a publication (NASA SP-160, Vibration of Plates) from the early 1970's.
> 
> Full disclosure:  while I had some calculus 40 years ago, the math in the NASA paper goes well beyond my capabilities, but I still have a deep appreciation for how rigorous the application is.


The texts by Arthur Leissa which I referred to in an earlier post were sponsored by NASA.  I haven't seen the NASA publication you referred to, but it may well be Leissa's work, or at least extracted from Leissa's work.

----------


## jhowell

I believe that it is his work and turns out it was published in 1969.

----------


## CarlM

> For that real geek in all of us  NASA, of all places, seems to chat this up very well with a publication (NASA SP-160, Vibration of Plates) from the early 1970's


.

NASA has a natural interest in vibration and natural frequencies because very bad things can happen if you excite one of them during liftoff among other times.  Most of my experience with modes has come from off road construction equipment dynamics where bad things come from coupling or exciting certain modes.  Also from dealing with colleagues and friends doing modeling of structural excitation for earthquake loads on buildings.  

One of the most fascinating things about physics to me is when the underlying math and principles are at work in a broad set of seemingly unrelated phenomena.  The same math has applications in electronics also in buckling and collapse as well as music.

----------

jhowell

----------


## Bertram Henze

> ...where bad things come from coupling or exciting certain modes.  Also from dealing with colleagues and friends...


 :Wink:

----------


## David Lewis

> .  NASA has a natural interest in vibration and natural frequencies because very bad things can happen if you excite one of them during liftoff among other times.  Most of my experience with modes has come from off road construction equipment dynamics where bad things come from coupling or exciting certain modes.  Also from dealing with colleagues and friends doing modeling of structural excitation for earthquake loads on buildings.  One of the most fascinating things about physics to me is when the underlying math and principles are at work in a broad set of seemingly unrelated phenomena.  The same math has applications in electronics also in buckling and collapse as well as music.


Remember ovation was originally aircraft engineers.

----------


## David Lewis

> .  NASA has a natural interest in vibration and natural frequencies because very bad things can happen if you excite one of them during liftoff among other times.  Most of my experience with modes has come from off road construction equipment dynamics where bad things come from coupling or exciting certain modes.  Also from dealing with colleagues and friends doing modeling of structural excitation for earthquake loads on buildings.  One of the most fascinating things about physics to me is when the underlying math and principles are at work in a broad set of seemingly unrelated phenomena.  The same math has applications in electronics also in buckling and collapse as well as music.


Remember ovation was originally aircraft engineers.

----------


## CarlM

Bertram, my dearly beloved wife also hears portions of sentences and edits them selectively for me....always entertaining  :Smile:

----------


## billhay4

> It is true that the antinode, which would be approximately at the geometric center of the plate for the (0,0) or T(1,1) mode, should be the location of greatest compliance, so one should be able to get the greatest amplitudes for a given amount of exciting force in the middle of the plate.


How does one determine the geometric center of a plate?
This is an attempt to address the question posed by Larry in post #77 in a way that will make sense to non-technical people. I am inferring from Dave Cohen's post that this is the optimal place for a bridge, but if I'm wrong, please correct me.
Bill

----------


## Dave Cohen

Before you chase in circles looking for the geometric centers of mandolin plates. pay careful attention to my post #119, and to Tavy's post #125.  My post cited my experiment results, and Tavy's post cited Howard Wright's dissertation (under Bernard Richardson) with both theoretical and experimental rationale, for the idea that positioning the bridge exactly at the antinode of the (0,0) mode is not necessarily an "optimal" location for a bridge.  And further, there may not be an "optimal" location for a bridge.

----------


## billhay4

So where is the optimal postion of the bridge? If there is none, why not?
Bill

----------


## jhowell

I believe that 'optimal' would be in the ear of the beholder.   :Whistling:

----------


## kkmm

> A sound chamber isn't strictly necessary... (muhahaha)
> https://vimeo.com/110633932


Hey, the man is standing in this huge sound chamber. I can see it. Can you?




> To me sound boxes just amplify better.


Yes, it does amplify sound but also produce the tone based on its material and its shape.

----------


## ProfChris

> I believe that 'optimal' would be in the ear of the beholder.


This is what I think too.

From the discussion I took away that the geometric centre of the plate might be the optimal place for the bridge to produce the greatest amplitude of vibration from the top. BUT, placing it there might mean that certain notes are damped or suppressed partially (non-technical senses of those words).

Thus a placement near (but not at) the geometric centre might result in a 'better' balance of frequencies being produced by the top, in the sense that the spread of amplitudes of each frequency would be more even.

Every bridge position produces a different set of frequency amplitudes, and thus the ear would hear differences. Which of the placements is 'best' depends on what that ear prefers.

----------


## fscotte

The Gibson Griffith Loar A has a bridge that is not centered and sounds fantastic, and there are many others built this way that sound fantastic.  So if using the word "optimal" means you're looking for the optimal sound, then you'll be chasing that optimal sound a long time cause it doesn't exist.  Too many samples of bridge positioning suggest that the "optimal" position has a fairly wide margin.

----------


## Dave Cohen

Locating the bridge in a particular position does not necessarily mean that some notes or frequencies would be damped or suppressed.  What both my post #119 and Tavy's post #125 stated is that some _modes_ might be more weakly excited.  Or not.  That does not necessarily imply any connection with certain notes on the instrument.  In my post #119, I stated that in practice, most of the modes are excited quite easily.  What should be taken from both posts is that there does _not_ seem to be any single, precise, optimal location for a bridge, and in fact experiment suggests that there is considerable latitude in bridge location.

As to the question "If not, why not?", it would make just as much sense to ask "If so, how?"

----------


## Tavy

> So where is the optimal postion of the bridge? If there is none, why not?
> Bill


You have to ask _optimal for what?_  Tone? Volume? Sudden banjo deaths?

Plus optimal for one mode, might not be optimal for others - so might get an amazingly dark and thick bottom end by optimizing excitation of the main trampoline (0,0) mode, but loose excitation of modes that give the top end character and volume.  Plus it's a rather complex system  :Wink: 

In practice, somewhere near the top of the arch, which should be near the centre of the top, would seem to be a reasonable compromise... which is not to say that other designs can't be interesting too.  I suspect that as long as you don't go too far out on a limb design wise you should be able to make it work.  

Perhaps more important than bridge position is freedom of each of the main modes to vibrate freely, and not get choked off by bracing or whatever...

----------


## Bertram Henze

> experiment suggests that there is considerable latitude in bridge location.


I think the "shape" of optimization is very important; if, as in this case, quality varies little with bridge position, you could say "Yes there is an optimal position but it's almost as good as the next, so why bother".

That sufficiently answers the "why not" question for me. It also reminds me a bit of that night* I was driving home late from a cinema show and being stopped by a police patrol:
"Have you been drinking, Sir?"
"No"
"Why not?"

(*) true story, puzzling me still

----------


## Dave Cohen

> You have to ask _optimal for what?_  Tone? Volume? Sudden banjo deaths?
> 
> Plus optimal for one mode, might not be optimal for others - so might get an amazingly dark and thick bottom end by optimizing excitation of the main trampoline (0,0) mode, but loose excitation of modes that give the top end character and volume.  Plus it's a rather complex system 
> 
> Perhaps more important than bridge position is freedom of each of the main modes to vibrate freely, and not get choked off by bracing or whatever...


I haven't found any experimental justification for selective excitation of the (0,0) over the higher modes, other than the fortuitous excitation exactly on a nodal line of a mode which I mentioned earlier.

The idea that modes "...can be choked of by bracing or whatever,..." is a persistent one, but again, no justification for it.  Michael Kasha thought that the X in X-braced steel-string guitars would be a nodal point, and inhibitory, because of its local stiffness.  That was wrong from a theoretical standpoint.  Also, I and others have done interferometry on steel string guitars, and have seen no evidence at all for a node induced by the X.  Braces, other than distributing static load, do a couple of things for the motion of the plates.  One is influencing the lateral vs the longitudinal stiffness.  That has an impact on, e.g., the frequencies of modes involving sideways, or across-grain, bending.  The only instances in which a brace can induce a node is in the case of the very high-frequency modes (which have several nodes already) and a massive brace (such as a waist bar in a classical guitar).  In those instances, the massive brace looks like a location of excessively high impedance to the mode, and one of its' nodal lines may follow the brace location.  I have seen that, but never an instance of a brace "choking off" a mode.  Modes don't just get stopped by objects.  They are either transmitted if they don't "see" a sudden large change in impedance, or reflected if they do "see" a sudden large change in impedance.

----------


## billhay4

What I'm wondering here is what all this science tells us about the mandolin. All these studies and we still cannot say where it is best to position a bridge. All these studies and we still cannot say how high an arch to carve. All these studies and we still can't say how deep the body should be.
So, what do we know about mandolins?
I'll be told to read the source material, some of which I have done, but for everyday builders the questions are different than those addressed in the research (or seem to be to me).
I am not trying to question the science here, but trying to find a source of commonality between the science and everyday building concerns.
Bill

----------


## fscotte

At the same time you're using words like "best" and then wondering if science can determine the "best" in building.  I think you're way off base here.  Best to one person is not best to another.  It's like asking what is the best woman a man can find.  Different for each of us.

And even if you were to replace "best" with "efficient" you'd still be off base.  A super efficient mandolin may not be the "best" sounding.

----------


## Eric Foulke

I agree with fscotte, ultimately, the question has too many variables, both human and material: each person is different as is each tree. Eventually you might be able to solve the material side of the equation, but the human side is beyond calculation. (IMHO)
We cannot build the perfect mandolin simply because we cannot (and probably will never) agree on what that really is.

I can live with that, I enjoy the diversity of different voices. I pay attention to the latest research, but I proceed empirically down my own path of discovery. (that's the fun part)

----------


## Tavy

> I haven't found any experimental justification for selective excitation of the (0,0) over the higher modes, other than the fortuitous excitation exactly on a nodal line of a mode which I mentioned earlier.
> 
> The idea that modes "...can be choked of by bracing or whatever,..." is a persistent one, but again, no justification for it.  Michael Kasha thought that the X in X-braced steel-string guitars would be a nodal point, and inhibitory, because of its local stiffness.  That was wrong from a theoretical standpoint.  Also, I and others have done interferometry on steel string guitars, and have seen no evidence at all for a node induced by the X.  Braces, other than distributing static load, do a couple of things for the motion of the plates.  One is influencing the lateral vs the longitudinal stiffness.  That has an impact on, e.g., the frequencies of modes involving sideways, or across-grain, bending.  The only instances in which a brace can induce a node is in the case of the very high-frequency modes (which have several nodes already) and a massive brace (such as a waist bar in a classical guitar).  In those instances, the massive brace looks like a location of excessively high impedance to the mode, and one of its' nodal lines may follow the brace location.  I have seen that, but never an instance of a brace "choking off" a mode.  Modes don't just get stopped by objects.  They are either transmitted if they don't "see" a sudden large change in impedance, or reflected if they do "see" a sudden large change in impedance.


I suspect we may be coming at this from different standpoints - I have seen quite noticeable shifts in the relative strengths of different resonances (as measured by "bonk testing") while gradually trimming braces down to size.  Much more of a difference there, than in the frequency of the resonances - which are surprisingly hard to shift by very much (in flat top instruments at least).

As ever hard to be precise about this stuff, as we don't all measure every possible parameter on every instrument - who would have time for that?

----------


## billhay4

Again, not trying to doubt the science here, but what light does it shed on a question like: "Where should I place the bridge on this instrument?"
Bill

----------


## Marty Jacobson

> Again, not trying to doubt the science here, but what light does it shed on a question like: "Where should I place the bridge on this instrument?"
> Bill


Under da strings.

----------

Bertram Henze, 

billhay4, 

hank, 

JEStanek

----------


## Eric Oliver

Bill,
I am not sure that even if science could answer your questions and wonderings that I would want to follow "their parameters."
If science could build a L. Loar-sounding mandolin every time (if that is the goal), boy, I think the urge to create, to try different variables, would be dulled.
Eric

----------

billhay4

----------


## Dave Cohen

> I suspect we may be coming at this from different standpoints - I have seen quite noticeable shifts in the relative strengths of different resonances (as measured by "bonk testing") while gradually trimming braces down to size.  Much more of a difference there, than in the frequency of the resonances - which are surprisingly hard to shift by very much (in flat top instruments at least).
> 
> As ever hard to be precise about this stuff, as we don't all measure every possible parameter on every instrument - who would have time for that?


So how did you measure amplitudes?  How did you control your "bonks"?  I've done brace location experiments with interferometry, and didn't experience what you are describing.  Also, trimming braces to size is a bit different than changing brace location.  More, I have observed that changing the dimensions of braces that are primarily longitudinal in orientation effects relatively little change in plate frequencies.  But braces that are primarily cross-grain in orientation are another story.  The plate itself is anywhere from 7x to ~20x less stiff across grain than it is along the grain.  Shave those braces, and you see relatively larger changes in frequency as you go.

With regard to BillHay4 and what the science can tell us for building:  If you are looking for validation of a preconceived idea, science may fortuitously reinforce that, or it may not.  More likely the latter.  If you want to know what to do with the science, try re-adjusting your expectations based on what the science tells you.  If you think apples, and the science unexpectedly says oranges, try seeing what you can do with oranges. To be more specific, what the science tells me is that there is no single "optimum" location on a top plate for a bridge, even assuming that I know what "optimum" means for my needs.  Instead I have some latitude w/ regard to bridge location.  I can locate a bridge based on what I want from, e.g., scale length, number of frets to the body, body shape,....., and still other factors that I haven't thought of at the moment.

----------

Marc Berman, 

Mark Gunter

----------


## billhay4

Okay, I can accept that. Science does not answer the question of where to place the bridge on a top plate. If I were designing a mandolin, I would then place the bridge where I thought it best, using my own senses and perceptions, not only of sound but of aesthetics, structure, and other factors. Is that a fair conclusion?
What questions about mandolins is the current science addressing? Are these of value to luthiers and players? In other words, do they illuminate questions those people are asking? That's what seems to be the next question.
Bill

----------


## sunburst

Sometimes science tells us, in a rather indirect way, to _not_ waste time on certain ideas. If Dave's (and other's) data shows that the position of longitudinal braces (tone bars) is of little importance to the sound of the instrument, that tells me that I don't need to spend time experimenting with moving them side to side to see where they sound best. That leaves me with time to experiment with something else, or to try to figure how to get better at carving scrolls or something like that that might actually bring in more money.  :Wink: 
In other words, seldom has the evidence from a scientific study told me what to do, where to put something, or otherwise directed me to doing some specific thing. It is much more often that science has told me what _not_ to do, or at least what things are more than likely a waste of time. I don't feel a need to think about where to put my braces, where the bridge should go (it's fine where it is, as far as I can see), or other things where I have seen no evidence to support an improvement from doing something different. 
To me, it all comes down to the normal modes of motion and coupling. When I ponder some aspect of building, I ask myself; "how will it affect the normal modes, or at least how do I _think_ it will affect the normal modes?".
So, How does bridge placement affect the normal modes? We just got an answer from Dave Cohen. 
How does body depth affect normal modes? Information on that has been published, we can read up on that.
How does hide glue affect the normal modes? Very little if at all.
How does "varnish" affect the normal modes?...
...and on it goes...

----------

billhay4, 

CarlM, 

jhowell, 

Marc Berman, 

Mark Gunter

----------


## billhay4

I understand the value of learning what one does not have to waste time on. Is that the sole role of the science of mandolins?
Seems like some big questions are still out there to me.
Bill

----------


## sunburst

> Seems like some big questions are still out there to me.


Me too. Science is incremental, and so is my understanding of it.

----------

JEStanek

----------


## fscotte

Simply tapping the top plate after its assembled into the rim will tell you where it taps best.  Don't think its really all that difficult to determine the best spot.. even way back yonder when people were building instruments for the first time.  Mandolin sounds worse as I tap towards the edge, mandolin sounds better in center, me will build mandolin with bridge in center..

----------


## Larry Simonson

I asked this question knowing there are a zillion things that could be experimented on the mandolin,  but like the positioning and strength off the tone bars, these experiments would be very difficult and they are not going to get done anytime soon.  However it seems to me that it is feasible to look at IF (notice I didn't say 'why') the bridge position appreciably affects tone and/or volume (subjectively, of course) on a given mandolin. I encourage all builders to have a go at this and see if there exists a "sweet spot".   Now it could be true that Loar looked at this 80 -90 years ago but I am not aware of it nor found it written about it.   My guess is that the current positioning is about as good as can be found,  but it would be a shame if we missed discovering that a better place was nearby.  

This has been an interesting and informing thread and I thank all that contributed.

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## fatt-dad

there's science and there's engineering. The former for the benefit of knowledge and the latter is the practical application of such knowledge.

Just making the distinction, as an engineer. . .

f-d

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hank, 

Marty Jacobson

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## Dave Cohen

> What questions about mandolins is the current science addressing? Are these of value to luthiers and players? In other words, do they illuminate questions those people are asking? That's what seems to be the next question.
> Bill


Doing science on mandolins is about finding out what mandolins do.  If, and only if, your questions are about what mandolins do, science may eventually be able to answer your questions.  If you want to know what a mandolin does, then scientific investigations into the mandolin's function are of value to you.  Science can only illuminate your mandolin questions if you allow those questions to be decomposed into their component parts.

If you are going to ask questions like "What is the optimal location (on the top plate) for the bridge, and when a scientist tells you that there may not be an optimal location for the bridge, turn that into something like "See, those scientists can't answer my question, so science is of no use to mandolin builders...", then you will miss what science has to offer you.  To take advantage of what science has to offer you, your first order of business should be to understand the science to the best of your ability, and you can not do that in a single sitting.  I suggested a lot of references for you to look up.  Some of them are very general, while others are actually pretty specific to some of your questions.  It will take you quite some time to digest that material.  If you take that time, you will be rewarded with a perspective that will start to put some pieces together for you, while simultaneously raising other questions that you will not have thought of before then.  On the other hand, if you are going to just say something like "that doesn't suit my learning style", then we have nothing to discuss.  In our graduate level scientific training, we learn how to teach ourselves.  Every day in the lab, we are faced with "How do I find out something about this new topic about which I currently know nothing?"  If we want to know something badly enough, we do whatever it takes to learn about it.  If you don't want it enough to spend however much time ti takes (to learn), then you won't get the goodies it has to offer.  Your choice.

----------

hank, 

jhowell, 

Marc Berman

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## Bertram Henze

> Seems like some big questions are still out there to me.


I'll say. But are you prepared to hear the answer?

----------

hank

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## jadonming145

Why but it hink it is necessary why you just said in my openion we wtrickly have to use ?? Marty For what reason can you tell me ??

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## Tom Haywood

> Why but it hink it is necessary why you just said in my openion we wtrickly have to use ?? Marty For what reason can you tell me ??


 I don't understand these questions, but I would like to. Can you restate them?

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## Wes Brandt

I have to ask this question... 

For those of you who are  into the kind of deep scientific analysis spoken about about in this thread... when you pick up a well made, higher end, Loarish F5 or A5 ...or even oval hole versions, that also performs well... and I'm talking about, say the top 20% or less of instruments, not the ones that don't impress but the ones that do impress... do you typically say to yourselves, "this is a really good mandolin but there's still something that isn't quite right that could be improved"? 

Or to put it simply, are you trying to figure out how to build the ultimate mandolin? (in the Gibson-esq tradition that is)

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## sunburst

For me, none of that.
I simply seek to understand how the thing works, and try to let that knowledge direct my building toward constant improvement.

----------

JEStanek

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## Dave Cohen

Given that people's impressions of what constitutes "good" in a mandolin are so very subjective and vary so widely, I can't even be sure a what a given customer wants in a mandolin.  Also, given the wide variation in properties of the materials that we start with, I am all but certain that I can't guarantee a customer that I can make a mandolin that will sound like such-and-such an instrument, or like so-and-so's instrument.  When potential customers ask me if I can make a mandolin that sounds just like X, or like Y, I just have to say, "No, but I will make the very best mandolin I can with the materials I have available.

Having gotten the disclaimers out of the way there are some specific things I do strive for.  First, I don't think at all in terms of making an instrument sound at all like a historical example.  Rather, I try to maximize (i) volume, (ii) responsiveness, (iii) bandwidth, and (iv) avoid any harshness.  The volume part should be obvious to all.  An instrument with good volume can also be played softly, but an instrument without good volume can not be played loudly.  The responsiveness comes from building light.  In its' most naive form, it has to do with inertia.  A more massive instrument will require more force from the player to be set in motion.  By "bandwidth", I mean good response throughout the playing range of the instrument.  I don't think in terms of maximizing the bass response by compromising the treble response, or vice versa.  For that, building light is also important, but is not all there is to it.  You get the low-end and midrange, and the 'warmth", by maximizing the coupling between the main mode (aka (0,0)) doublet and the main air resonance.  So I think in terms of plates that are light, but (a) also have the "right" relationship between the compliances of the top and back plates, and (b) have the lower main mode frequency in the assembled instrument below the main air mode frequency, but close enough for strongest coupling.  I'm not sure what I do to avoid harshness - maybe dumb luck.  The only mandolin I have made with any harshness is Fronkenshteen, which has a hollow CF composite neck, and CF cloth in the insides of the ribs.  In conventionally made mandolins, even with CF reinforcement bars buried in the neck, I haven't experienced any harshness so far.

----------

Bob Clark, 

CarlM, 

hank, 

JEStanek, 

jhowell, 

Marc Berman

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## Tom Haywood

I think what Dave just said is a very good and accurate description of what most builders realize they can and can't do. But there is a marketing thing going on where builders claim to reproduce the sound of vintage instruments. So as not to pick on any fine mandolin builders I will give the example of Martin Guitar company claiming to re-create the sound of certain specific vintage guitars. I think that leads to an interest in studying the physics and engineering aspects as a means to finding repeatable techniques to produce that sound. The claim is that it can be done. The marketing aspect makes it legitimate in my mind to question whatever physics are brought to bear in the advertising claims. Martin refers in a general way to physics, chemistry and engineering studies they have performed or looked at to come up with their method for pre-aging the wood. Do they really expect me to believe that these "scientific" approaches that can be applied in a few weeks in any way comes close to what the vast vagaries of mother nature took 75 years to accomplish? To me it simply proclaims the limited perspective we can get caught up in when we claim science as the high ground and ignore what the rest of our mind and senses are showing us. Clearly the logical mind wants to understand, and science and math are a huge help with that, but there is a lot more going on than we have even observed and no real reason to assume that all the answers will be logical. That to me is the problem with the focus on modes. They represent a strong logical understanding of the plate vibrations, but we begin to see that there may be something else going when we say that our conclusion seems to not always apply, or when we discuss the difficulty of obtaining a predictable result when we place a large piece of wood over mode boundaries that are infinitesimally small. Logic begins to break down at infinite. We have some logical constructs to deal with that, but our logical mind has trouble with the idea that there may be no actual boundary between two distinctly measurable modes and that we therefore may be misunderstanding what we are observing. As long as what we understand is working for what we are doing we'll keep that description, just as we continue to keep Newton's description of gravity even though we know there's a lot more to it than that.

----------

Hudmister

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## peter.coombe

Most of us use trial and error to get the sound we want.  "Want" being a subjective thing.  Try something different, if it works then keep doing the same thing.  If it doesn't work then don't do it again.  It is important to change one thing at a time, but that is almost impossible to do because wood is so variable.  Over the years the experience of trial and error adds up to lots of small improvements which ends up as one big improvement.  If we could understand better how a mandolin works, then what you do would be more predicable, and the end result would be far more consistent.  Consistency is one of the most difficult things to do.  You want to reproduce the sound of your favourite (i.e. "best") mandolin each and every time.  If you knew exactly what makes it the "best" because you know how it works then it is much easier to know how to reproduce that result and/or how to change it.  My methods are empirical, but I know that if I do a,b,c,d,e,f... then it will end up as a good sounding instrument.  Almost certainly will sound different, but will sound good - i.e. will sound how I like it, and most other players are likely to like it as well.  What I like is similar to Dave's criteria with maybe more emphasis on achieving a clean, sweet sound.  As for making a mandolin that sounds just what a customer wants is difficult because you don't really know what he wants until he/she drops in for a visit and plays a selection of instruments and picks one.  Sometimes the customer will change their mind after playing a few mandolins - i.e. He wanted A, but now he likes B more, so the plans change.  Otherwise I just use that accumulated experience and pick wood that I think probably will produce the sound the customer wants and just make it the best I know how.   Usually works, but in practice it has my characteristic sound and it probably doesn't sound all that much different from the last mandolin I made.  But then again they do surprise sometimes.  Now if I knew how a mandolin works and could accurately model it I could reproduce that surprise sound exactly.  We are a long way from that yet.

----------

Emmett Marshall

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## billhay4

> We are a long way from that yet.


I'd say.
However, I wonder if someone could summarize what you do to achieve loudness, responsiveness, sweetness, and breadth. Just a list. So far, I have heard build light, pick the right woods, and be consistent. But, I'd like some specifics if that's possible. What do you do to build light? What specifically do you look for in wood? etc.
Bill

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## Dave Cohen

> I think what Dave just said is a very good and accurate description of what most builders realize they can and can't do. But there is a marketing thing going on where builders claim to reproduce the sound of vintage instruments. So as not to pick on any fine mandolin builders I will give the example of Martin Guitar company claiming to re-create the sound of certain specific vintage guitars. I think that leads to an interest in studying the physics and engineering aspects as a means to finding repeatable techniques to produce that sound. The claim is that it can be done. The marketing aspect makes it legitimate in my mind to question whatever physics are brought to bear in the advertising claims. Martin refers in a general way to physics, chemistry and engineering studies they have performed or looked at to come up with their method for pre-aging the wood. Do they really expect me to believe that these "scientific" approaches that can be applied in a few weeks in any way comes close to what the vast vagaries of mother nature took 75 years to accomplish? To me it simply proclaims the limited perspective we can get caught up in when we claim science as the high ground and ignore what the rest of our mind and senses are showing us. Clearly the logical mind wants to understand, and science and math are a huge help with that, but there is a lot more going on than we have even observed and no real reason to assume that all the answers will be logical. That to me is the problem with the focus on modes. They represent a strong logical understanding of the plate vibrations, but we begin to see that there may be something else going when we say that our conclusion seems to not always apply, or when we discuss the difficulty of obtaining a predictable result when we place a large piece of wood over mode boundaries that are infinitesimally small. Logic begins to break down at infinite. We have some logical constructs to deal with that, but our logical mind has trouble with the idea that there may be no actual boundary between two distinctly measurable modes and that we therefore may be misunderstanding what we are observing. As long as what we understand is working for what we are doing we'll keep that description, just as we continue to keep Newton's description of gravity even though we know there's a lot more to it than that.


Maybe you don't understand something about normal modes of motion.  Normal modes of motion, by definition, are the motions characteristic of an object.  That means that the normal modes of motion are what the object does, and more important, it does not do other things, i.e., no motions other than the normal modes of motion.  There are mathematical constraints dictating that the plates can _not_ move in ways other than the normal modes of motion.  Still think there is a lot more going on than the normal modes?  It is true that there is plenty more to be understood about string instruments, but it is not true that what will be understood will not include further understanding of normal modes of motion.  Nor is it true that an incomplete physical understanding of string instruments must mean the the current level of understanding is not useful.

Also, don't confuse the 'science' you see coming from manufacturer's advertisements with the physics of plucked string instruments published in peer-reviewed journals.  Those are two completely different things.  Commercial interests can at times make for some pretty strange 'science'.

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## billhay4

> There are mathematical constraints dictating that the plates can not move in other ways that the normal modes of motion.


This makes no sense to me, Dave, and I'm not trying to be difficult here. My understand is that math is conceptual, so how can it constrain motion. I can see how there would be "physical" constraints such as mass, rigidity, etc., but I can't understand the phrase "mathematical constraints" except in the context of mathematics itself.
Thanks for clarifying this.
Bill

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## Dave Cohen

F'rinstance, Instrument plates are essentially plates that are clamped at their edges.  That means no motion at the edges of the plate, or in other words, the edges of the plates are always nodes.  Zero amplitude at the edges of the plates is a _constraint_ on the possible solutions to the equation(s) of motion.  All solutions to the equation(s) of motion have to obey that constraint.  Also known as a _boundary condition_.  On the experimental side, the modes of motion we observe w/ interferometry are always observed to obey those boundary conditions.  You don't see any interference fringes representing amplitude at the edges of the plate, unless they are an artifact from the edge of the instrument translating in some whole-instrument motion independent of the vibrational mode.  The mathematics is not only conceptual; it is also a _description_ of the motion, and dictates what motion is allowed.  Just as surely as the edges of the plates are physically clamped by the rim/ribs/sides, their motions (throughout the plates) is described by the mathematical relationships dictated by the boundary condition.  Unless you have taken differential equations, you probably won't get this, but there it is.

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billhay4

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## Mark Gunter

I understand what nodes are in a standing wave, but would like to know more about "the _modes of motion_ we observe w/ interferometry" - I've only begun reading some of the material Dr. Cohen has suggested in recent months, and only able to comprehend bits of the information due to a lack of prerequisite knowledge of some of the ideas and terminology. I'll continue to study independently, but wonder if anyone could illuminate what is meant by "the modes of motion"? Has this been covered in another thread that someone could point to?

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## Bertram Henze

> This makes no sense to me, Dave, and I'm not trying to be difficult here. My understand is that math is conceptual, so how can it constrain motion. I can see how there would be "physical" constraints such as mass, rigidity, etc., but I can't understand the phrase "mathematical constraints" except in the context of mathematics itself.
> Thanks for clarifying this.
> Bill


The full idiom would be "physical constraints described as border conditions to mathematical equations". Since physicists describe everything with equations, we like to use the odd linguistic shortcut now and then, taking the rest as implied.

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billhay4

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## Dave Cohen

> I understand what nodes are in a standing wave, but would like to know more about "the _modes of motion_ we observe w/ interferometry" - I've only begun reading some of the material Dr. Cohen has suggested in recent months, and only able to comprehend bits of the information due to a lack of prerequisite knowledge of some of the ideas and terminology. I'll continue to study independently, but wonder if anyone could illuminate what is meant by "the modes of motion"? Has this been covered in another thread that someone could point to?


The simplest way to say it for you is that the normal modes of mandolin plates in an assembled mandolin are the shapes or patterns of the allowed vibrational motions.  A plate in a mandolin does not vibrate in just any way, nor at any frequency.  Instead, the plate vibrates in specific patterns (modes), and each pattern has a corresponding specific peak frequency.  If you use the search function for "normal modes of motion", there are a few recent threads in which I posted the interferograms for the first five top plate and back plate modes of a 1924 F5.

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## CarlM

In the simplest case, a one dimensional object like a guitar or mandolin string, the normal modes of motion would represent the harmonics.  When you sound a harmonic (or chime) by touching at the twelfth, seventh or fifth fret you are touching one of the nodes for certain normal modes.  You are preventing other modes from vibrating.  In a string the normal modes are integer divisions of the string length, one half, one third, one fourth, etc.  There are higher harmonics where you divide the string by 7 or 8 or whatever number but they are usually too weak to hear clearly.  In mode zero, the main mode, which is the note you tune to, the entire length of the string vibrates.   Mode 1, the first harmonic at the 12th fret, the waves are in each half of the string, etc.

The interferometry shows two or three dimensional pictures of the same phenomena.  It becomes a lot more complicated with a three dimensional shape that is not symmetrical.  The mode numbering describes different shapes and divisions across and along the plate and different orientations.  There are a lot of other implications of these ideas with respect to structural buckling and collapse as well as signal processing applications in electronics.

The classic example of a normal mode failure, where a normal mode or natural frequency was excited is the Tacoma Narrows Bridge collapse, shown in this you tube video.  

https://www.youtube.com/watch?v=nFzu6CNtqec

The bridge shed vortices in the air currents as the wind blew up the river channel.  These vortices were spun off at a rate which was very close to one of the natural frequencies or normal modes of the bridge.  It would move, shaking......a lot, a whole lot till it shook itself apart and fell down.

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## sunburst

The comparison of plate modes to string modes is a good one, but an important distinction between the two is that the normal modes of motion in a plate (top or back) are not harmonic in the way the modes of motion in a string are. The frequencies of string modes are predictable (the harmonics) in a way that the frequencies of plate modes are not.

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## CarlM

The finite element approach that I asked Dr. Cohen about earlier can predict the frequencies and shapes of the plate modes at least on a theoretical (eigenfunction) basis.  It also can predict frequency response to a driving function.  Material variations and difficulties of modelling wood make these predictions less than perfect but it does well enough to design structures to not fall down in an earthquake.  That is why I asked him about it.  In theory it is a possible thing though the practice of getting good, correlated results could be challenging.

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## Bertram Henze

> wonder if anyone could illuminate what is meant by "the modes of motion"?


There's a common demonstration for plate oscillation modes using sand on a metal plate, with a speaker underneath, as typically shown in physics lectures in the first year. Depending on the tone frequency, the grains dance and stay put along changing node lines. Different modes = different node lines. The modes also depend on the shape of the plate, how it is fixed and where it is excited.




There is also a very simple variation of this:

----------

Bob Clark, 

Spencer

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## Dave Cohen

> The finite element approach that I asked Dr. Cohen about earlier can predict the frequencies and shapes of the plate modes at least on a theoretical (eigenfunction) basis.  It also can predict frequency response to a driving function.  Material variations and difficulties of modelling wood make these predictions less than perfect but it does well enough to design structures to not fall down in an earthquake.  That is why I asked him about it.  In theory it is a possible thing though the practice of getting good, correlated results could be challenging.


Since FEM has been brought up, I think some clarification is necessary.  FEM stands for "finite element matrix".  What you do with FEM is draw your object (instrument) as accurately as possible.  The FEM software then subdivides the object spatially into little rectangular hunks, or "elements", essentially discretizing the object.  The program then moves each element using Newtonian mechanics, but also "couples" each element to its' nearest neighbors, essentially with a spring constant for each nearest neighbor interaction.  In that way, the program uses the coupled motion of all of the elements to generate a simulation of the motion of the entire object.  The problem with all that is that you need good values for the constants, which essentially relate to the Young's or elastic moduli of the materials.  With a real instrument, it is more complicated than that.  For one thing, all of the materials - woods - in a real instrument are anisotropic, meaning that they have significantly different moduli in different directions.  They are also somewhat inhomogeneous.  Worse yet, the instrument has several different materials (e.g., spruce, maple, ebony,...,), and they all have different densities and moduli.  To get really good simulations, you need good values for all of your input parameters, and you don't get those without experiment.  So I think it is important to state that FEM and other simulations are no substitute for experiment.

Experiment is always at the top in science, but we always evaluate it in the context of theory and other experiments.  The theory part is where FEM comes in.  For objects having simple geometries, such as circular plates or rectangular plates, there are simple mathematical descriptions which can be stuffed into equations of motion (e.g., Newton's) which are then 'tractable', meaning 'doable'.  For objects with more complicated shapes, such as instruments, solving the equations of motion becomes all but impossible, and that is where software such as FEM becomes useful.  But I want to stress again that FEM is no substitute for experiment.  Rather, it is useful for comparison with experiment.  I could say more, but this is probably enough, possibly too much.

----------

Marc Berman

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## billhay4

> However, I wonder if someone could summarize what you do to achieve loudness, responsiveness, sweetness, and breadth. Just a list. So far, I have heard build light, pick the right woods, and be consistent. But, I'd like some specifics if that's possible. What do you do to build light? What specifically do you look for in wood? etc.


I'd like to repeat this question although the discussion of modes is very illuminating and I hope it continues.
Bill

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## sunburst

To build light, I try to use light materials where possible and practical without getting too exotic. I also try not to leave much excess wood. Tapered pegheads, slim graceful neck heels, slightly thinner fingerboards, that sort of thing. There is no one particular weight-saving thing that I do, just a collection of little weight savings here and there that add up.
Reducing weight (mass) in general can be a good thing, but in the same way that the pounds saved using allow wheels on a car increase performance more than an equivalent weight saving in the body of the car, reducing mass in the moving parts of a mandolin improve performance more than equivalent weight savings elsewhere. Sure my paulownia linings and corner blocks save some mass, and that is probably a good thing, but it doesn't do as much for the performance of the mandolin as using low density top wood (and back wood). 

(Although low density tops (and backs) tend to give us more responsive instruments, I like the sound I get from using red and sitka spruce, so I use them for quite a few builds, as opposed to lower density top woods like certain engelmann and such. Those mandolins with denser top wood tend to require a little more effort from the player, in other words they are not as responsive as less dense top woods, but the sound is good (IMO), and they hold up to hard playing with ease. In general, density and stiffness track pretty closely, so denser tops can be carved thinner, and some weight it saved because of that.)

----------

billhay4

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## Petrus

This is an interesting page I found on Chladni patterns and modes / nodes of resonance both on the large (sound) and small (atomic) scale.  It illustrates many different possible modes of vibration and shows some original sketches by Chladni from 1809 showing that this phenomenon has been known for a long time. Notice the subtle differences between using a square plate versus a circular plate. It also gets into Louis de Broglie's theory of the wavelike resonance of electrons.

http://skullsinthestars.com/2013/05/...adni-patterns/

I'm interested in how this also works on the quantum scale, where the "medium" transmitting the vibration is not air but an abstraction, the square root of a given probability or something like that.  Not much to do with mandolins but interesting in showing how the same phenomenon works on all levels. (On the really large scale, it probably works with gravity waves too.)

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## billhay4

Fascination article, Petrus,
The like on pinch harmonics is quite interesting too.
As to transmitting a vibration in an abstraction, you're way over my head. Wait a minute, maybe you're not. Ideas are abstractions. Transmitting ideas....
Well, never mind.
Bill

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## ProfChris

> I'd like to repeat this question although the discussion of modes is very illuminating and I hope it continues.
> Bill


I fear that you will get a range of answers! Let me give you an example from the world of flat top instruments. There are, broadly, two camps: build everything light so the sides and back are excited by the top's vibration, or build very sturdy backs and sides so all the energy stays in the top. Either route can produce an excellent instrument. 

For tops there is more consensus, which I think translates to carved tops as well. We want the lowest mass which is still usable. This links to longitudinal stiffness - at some point, the top will fold up under string tension. At a greater stiffness by leaving it more massive, it will make little sound at all when played. Somewhere between those two is the ideal. 

But even this varies between makers because the top is a system which includes it's braces/tone bars. These add back stiffness. Some builders like thin tops and fatter braces, others the opposite. Both can work. 

So, just like bridge placement, there is a range of solutions which produce good answers, and the best depends on your conception of good. 

Add in cross-grain stiffness and ...

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## billhay4

I am aware there is a broad range of possibilities. I'd like to see any and all answers. I am interested in what particular builders do to achieve their sound, range, etc.
I am also interested in new ideas to achieve certain goals. For instance, new materials to lighten an instrument. I think Dave Cohen alluded to using carbon fiber in his braces. I have used it in a body (but never finished the instrument so I have no feedback on it). It sure can diminish weight and add stiffness.
But Dave also alluded to poor results from using a carbon fiber neck on an instrument. I think this was more than simply carbon fiber reinforcement in a neck.
I have a bridge I'm working on now that I'm thinking of hollowing out as it's a fixed, full contact bridge in ebony. I'll do some weighing first.
I can see where head and tail blocks could be hollowed too to save weight.
I've also long been interested in seeing someone do titanium tuners for weight saving. They'd only cost $1500 or so. Tuners are a real source of excess weight. 
I expect we'll see more of this kind of stuff as technology improves (changes). 
The real question of whether a lighter mandolin is really better has yet to be addressed, too.
Bill

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## Dave Cohen

> I am also interested in new ideas to achieve certain goals. For instance, new materials to lighten an instrument. I think Dave Cohen alluded to using carbon fiber in his braces. I have used it in a body (but never finished the instrument so I have no feedback on it). It sure can diminish weight and add stiffness.
> But Dave also alluded to poor results from using a carbon fiber neck on an instrument. I think this was more than simply carbon fiber reinforcement
> Bill


I do _not_ use carbon fiber in my top plate braces.  I tried that early on, saw no special benefit w/ regard to mass, & abandoned it.

The neck in the "Fronkenshteen" mandolin is a hollow molded carbon fiber shell, with some more CF composite reinforcement inside.  Very light, and very stiff.  I did not say the results were poor, only that there was a bit of high-frequency harshness in the instrument.  The instrument is very loud, very responsive, and not too bad tonally; it just has a bit of what might be called 'edginess", possibly from some untamed high frequency components.  I would not describe it as having "poor" tonal qualities; some observers have said they liked it quite a lot.  I have used it, and played in the CMSA en masse orchestra with it.  I prefer mandolins that are somewhat warmer than Fronkenshteen.

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## David Lewis

Could someone please explain how a string is a one dimensional or two dimensional object: it has width, height and depth?

Thanks in advance.

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## billhay4

You certainly are mighty touchy, Dave.
I did not accuse you of using carbon fiber in your top braces. I said you alluded to using it, meaning, as you said, that you had tried it. If you didn't find it helpful, just say so and give us the reason why.
I did not use the term "poor" results to mean sub-standard results but results you didn't like, but you yourself said you really didn't prefer it.
Give all of us a break here and get off your high horse and try to contribute to the conversation instead of attacking everything I, and others, say.
Bill

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## brunello97

What's the function of the body?  That's pretty clear.

Mick

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billhay4

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## CarlM

> Could someone please explain how a string is a one dimensional or two dimensional object: it has width, height and depth?


A string can be mathematically idealized as a one dimensional object because the length is immensely greater than its width and depth.  In the real world it is obviously three dimensional.

For the purposes of this discussion of the modes, you can stop the string to get a harmonic or chime along its length.  You cannot split the width or height to get harmonics.  You cannot put your finger halfway in the middle of the width of it.  So for those purposes  the one dimension only really matters along with the stiffness/tension and mass per length.

----------

David Lewis

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## peter.coombe

> What do you do to build light? What specifically do you look for in wood? etc.


Lightweight and stiff is what we look for.  Wood cut exactly on the quarter will have maximum stiffness across the grain so that also helps.  However, as John has already pointed out, using low density woods will not always produce the sound you want.  Recently I made two identical oval hole mandolins, one with a lightweight Tasmanian blackwood back, the other with a gorgeous dark reddish hard and heavy back.  The tops weighed about the same.  I was expecting to prefer the lighter mandolin, but bugger me, we all ended up preferring the sound of the heavier one.  So it is a bit more complicated than just lighter is better.  Often it is, but not always.  As John pointed out, Red Spruce on average is denser than Engelmann, but can be driven harder so you can end up with just as much volume (or more) by adding more energy through the pick.

On my flattop mandolins, it does appear that lighter is better does apply to tops.  The lighter I make the tops the better the mandolins do seem to sound.  However, lighter usually means less stiff and thus the top is more likely to collapse.  So on these mandolins I use Engelmann Spruce bracing and carbon fibre.  The carbon fibre is glued on the top of the braces.  It is to increase stiffness without adding significant mass, and one advantage of carbon fibre is it has no memory.  The top of the brace is well away from the axis of bending (braces are tapered at the ends) so that makes a very strong structure because carbon fibre is very resistant to being pulled.  Flat top mandolin tops have a nasty tendency to collapse and this is a good way of adding strength while keeping the mass low.  The carbon fibre and the epoxy glue is only about 2% of the total weight of the top but adds far more than 2% stiffness.  This doesn't really work as well on arch top mandolins because most of the stiffness is in the top, not the bracing, and the top of the braces are closer to the axis of bending so the carbon fibre would be less effective.   The mass of the bracing on an archtop is only about 2% the weight of the top so you are not going to save any significant weight.  On the other hand, the braces make up around 20-23% of the weight of a flat top mandolin top even when using lightweight Engelmann Spruce bracewood.

After all this, what is "better".  "Better" is in the ear of the beholder so what one person perceives as better is not necessarily better to the next person.

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billhay4

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## fatt-dad

A string is mathematically 2-d - length. Its movement adds time and radial displacement - two addition dimensions. The displacement varies down the length - another dimention. 

f-d

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## sblock

> A string is mathematically 2-d - length. Its movement adds time and radial displacement - two addition dimensions. The displacement varies down the length - another dimention. f-d


Of course, _all_ objects in the real world are three-dimensional (with time often treated as a fourth dimension).  But from the standpoint of using simple physics to determine its vibrational frequencies, it is vastly easier to idealize a string as a *one-dimensional* (and not a two- or three-dimensional) object.  That is to say, its tension, length and mass/unit length are the only properties that really matter, to a good approximation. A real string has a finite, round cross-section, however and therefore has thickness (gauge) in the other two dimensions, but these distances don't matter -- much -- in determining the pitch. Good physicists often know which quantities they can safely neglect and which ones to keep when formulating mathematical models of interest.  

The true three-dimensionality of a string comes into play in several ways, and these produce much smaller -- but quite audible -- perturbations in the pitch from the ideal, one-dimensional case, which considers only the length.  We all know how a high action can lead to a string going just a bit sharp when fretted. The basic pitch is set by the string length from the fret to the bridge (at a given tension and mass/unit length), of course, but that small extra rise in pitch is strictly associated with the extra tension in pulling the string to the side -- in a second dimension. But some height in the action is absolutely necessary in all stringed instruments, because real strings vibrate in both of the transverse dimensions (not just in the plane they're plucked).  So three-dimensionality matters here, too.  And the three-dimensionality also matters a great deal when considering subjects like _compensation_ at the bridge, which tries to adjust for non-idealities associated with fretting strings of different thickness, windings, action, and elastic properties.  

In summary, a one-dimensional approximation is great for getting the basic frequency right, and to within just a few percent. But it's not quite perfect.  All three dimensions of the string matter whenever you need to do a whole lot better than that (i.e., to within a few cents).  And please note that because a string fresh out of the box has a perfectly round cross-section, two of the additional dimensions (the transverse ones) are identical, which simplifies the math, but only a little.  In fact, a well-worn string may have small kinks or worn spots in its windings, and such a string will also display minor differences in its behavior in the 2nd and 3rd dimensions, too.

It is not very easy to model a full three-dimensional string, and analytical (closed-form) solutions don't really exist.  One is forced to use numerical models on a computer, in most cases. These are a whole lot of work to implement, and only sometimes lead to useful insights, because they're much harder to generalize. You get 99% of the way there with the simple 1-D model.  After that, it is sometimes easier to just work empirically, and not theoretically.  Both approaches have their place!

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CarlM, 

David Lewis

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## JEStanek

Bill, Dave has everyright to post.  Further, I don't see that he's on a high horse, rather, I think he's frustrated that people aren't understanding the things he's said (repeatedly).  Frankly, the physics is pretty advanced and doesn't lend itself to light conversation and there are people putting forth a lot of positions that aren't based on any data that has been previously presented.

I think someone could easily earn a doctoral dissertation out of a study on how the body functions in various stringed instrument systems.  The method development alone to investigate them would likely earn a Masters or a PhD.  I don't think you're going to find easy answers to the more specific questions of what is the body's function beyond providing a resonance chamber for stringed instruments without getting into a lot of physics involving theory and a lot of math.  We're lucky to have Dave here to repeatedly talk about these complex aspects of dynamic systems.

Jamie

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jhowell, 

KOakley, 

sblock, 

Tom Wright, 

Vincent Capostagno

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## Bertram Henze

> A string is mathematically 2-d - length.


Ah, but this is just a part of the eight dimensions * we live in:
- left
- right
- top
- bottom
- back
- front
- past
- future
 :Wink: 
OTOH, this is nothing compared to the ten dimensions of real string theory **  :Whistling: 

(*) That is apart from our own special eight dimensions:
- G
- G
- D
- D
- A
- A
- E
- E
(**) Caveat: common sense breach alert

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David Lewis, 

jhowell, 

Tom Haywood

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## Tom Haywood

I like the old ad showing Kim Breedlove drawing the shape of the body while looking at a nude female model. Maybe the function has to do as much with biology as physics.

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## fatt-dad

Between sblock and Bertram, I'm totally dismissed?  O.K. I don't belong here, I guess. . . I do stand by my original comments, however and do not feel stupid for making them.

f-d

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billhay4

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## billhay4

I don't think sblock dismissed you f-d. He did address all three dimensions of a string and it vibration. But I understand your frustration.
Bill

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## Mark Gunter

> But I understand your frustration.
> Bill


And, ya gotta let go o' d' frustration. Anything you post here can be dismissed either philosophically, scientifically, semantically or otherwise - and will be. Best program is to just read the thread and try to learn something. There are axes to grind and egos to stroke, but plenty of interesting info along the way.

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## fatt-dad

Sorry, I got my feelings hurt. . .

My point being, the engineering behavior of of a string can be described by the line between the two points that form its ends along with the material properties described by density and moduli (elastic, shear and section).  The dynamic response relates to the length.  I'm a bit curious how to model the radial coordinates of motion (i.e., in cross-section). The longitudinal sine and cosign (amplitude and magnitude) make sense.  I really don't know, I'm just reading through my filter as an engineer.  

f-d

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David Lewis

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## Bertram Henze

No offence meant, f-d.

A cylindrical object like a string is physically best described in polar coordinates length, radius and azimuth. Those sine waves it does are there, and more than one, the biggest base wavelength being twice the string length, then 1/2 of the base, 1/4 and so forth, making the overtones, their proportion depending on where the string is plucked.

P.S. thinking about this, I guess I get what f-d meant by 2 dimensions: the plane the string is supposed to oscillate in, is that it? Vibration in a plane is an assumption made for simplicity, and it works for understanding most of the process, but strike a string on your instrument and look at it from every angle: the string vibrates in all directions. With the pickstroke, we input not only momentum for side-to-side motion, but also angular momentum making the string rotate like a skipping-rope.

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## fatt-dad

. . . meaning a line is the intersection of two planes and that line is two dimensional.  I'd think the mathematical description would be in Cartesian coordinates - at least that would be my inclination. . .  The striking of the string will be in every plane that is consistent with the coordinates of the line.  That motion seems to occur in radial coordinates.

With the description of section modulus we can remove the cylindrical properties of the actual string.  Just like we'd do in beam analyses.  The elastic modulus would inform lengthening as the string deforms and reforms from vibration.  Not sure how shear modulus would play into this, but it could.

I'm just intellectualizing and thinking of how a FEM model may be developed.  Simple modeling is often easier.

To all the builders out there, I know little about any of this and really should beg out.  I'm just enjoying the thought process, science and engineering that comes to mind as I read this thread.

Again, I do apologize for getting unnecessarily provoked.  Deep down, I know we are all friends and brothers/sisters in music and for that I'm thankful!

f-d

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## Dave Cohen

Carl, Bertram was referring to what is sometimes called "cylindrical polar coordinates", a 2D polar plane described by a radius vector and a polar angle, plus a Z-axis, as in cartesian coordinates.  The Z-axis is what he called an azimuth.  That is the most friendly coordinate system for a string, which is essentially a very long, thin cylinder.  In the extreme of a string with no volume,i.e., a line, the motion is still described in the polar plane.  You might have been thinking of spherical polar coordinates, which would indeed be clumsier for describing string motion.

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## sblock

> . . . meaning a line is the intersection of two planes and that line is two dimensional.  ...
> 
> Again, I do apologize for getting unnecessarily provoked.  Deep down, I know we are all friends and brothers/sisters in music and for that I'm thankful!f-d


Yes, cylindrical polar coordinates (theta, phi, z) are the most convenient for developing analytical expressions of 3D cylinders, if you want to treat the string in all three dimensions as a long, thin cylinder.  Most (but not all) computer models of fairly complex shapes, such as FEM models, are numerical and don't need to worry about analytical simplicity for the math, and they tend to use Cartesian coordinates (x, y, z), where all three coordinates are equivalent.  But the coordinate system is a trivial matter, and one of convenience: simple formulas can be used to convert from one system to another.

That said, the intersection of any two planes forms a LINE, and such a line is a one-dimensional object, not a two-dimensional one.  This goes back to Euclid.  An abstract line has length, but no breadth.

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## Bertram Henze

> a 2D polar plane described by a radius vector and a polar angle, plus a Z-axis, as in cartesian coordinates.  The Z-axis is what he called an azimuth.


Actually, what I called azimuth is the polar angle. The Z-axis is what I called length (for the lack of a better word, but Z-axis is of course correct).
This leads me back to my diploma thesis when I spent time with vortices (think: tornadoes), which are the home of cylindrical coordinates.

A line with no thickness is 1-dimensional, because you need only one coordinate number to describe a position on it (positive or negative, counting from some point of origin). Defining a line as the intersection of two planes is interesting, because intersection always takes away one dimension: intersecting two 3-dim spaces makes a 2-dim plane, intersecting two 2-dim planes makes a 1-dim line, intersecting two 1-dim lines makes a 0-dim point.

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## Wes Brandt

Just to get with the spirit of the conversation, isn't a 1 dimensional line only possible in theory because if you represent it with something, that something has to have thickness and width, no matter how minimal?

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## billhay4

Well, I'll observe that your getting your feelings hurt led to a fascinating discussion (albeit over my head) of the math and modelling involved here. This thread has had over 8700 views and 200 posts partially because some people have gotten their feelings hurt and I find it a very valuable thread.
Bill

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## Bertram Henze

> Just to get with the spirit of the conversation, isn't a 1 dimensional line only possible in theory because if you represent it with something, that something has to have thickness and width, no matter how minimal?


in reality yes, but physics is all about models, i.e. simplified abstraction of reality. The art lies in knowing what to leave out, but if your assumptions were too simple nature is setting you right during your next experiment...

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## CarlM

Dave
That wasn't me.   I understand cylindrical vs spherical.  I've been staying out of this food fight :Smile:

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## billhay4

> physics is all about models, i.e. simplified abstraction of reality


Bill

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## fatt-dad

CarlM.  Dave is using my given name, which we share.  

f-d

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## CarlM

Welcome to the conspiracy :Smile:

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billhay4

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## Dave Cohen

> in reality yes, but physics is all about models, i.e. simplified abstraction of reality. The art lies in knowing what to leave out, but if your assumptions were too simple nature is setting you right during your next experiment...


Physics isn't _all_ about models.  Physics, like all branches of science, has _experiment_ at the top of the hierarchy.  We build models to help interpret the experimental results.  The simplified models relate the more complex experimental systems to simpler systems for which we can more easily visualize the behaviors.  For example, we _model_ a string instrument body as a system of coupled masses on springs (the two-mass and the three-mass models).  It is possible to build that model because guitar plates are elastic, i.e., springy, and they have mass.  Same deal for the masses of air in the soundhole(s).  They are essentially attached to a "spring" of air inside the instrument body cavity.  Nor are those simple models necessarily complete abstractions.  You can actually make physical two-mass and three-mass -and even multi-mass- models for demonstration purposes and directly observe the resonance behavior.  Iirc, Tom Rossing did just that at an ASA meeting many years ago.  

Models are _good_ to the extent that they work, i.e., describe real behavior.  So do the two-mass and three-mass models work? In fact, they work quite well for the lowest frequency body resonances and for the Helmholtz air resonance - well enough that for another 30 yrs or so, few if any payed much attention to deriving a more complex model.

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## sblock

> Just to get with the spirit of the conversation, isn't a 1 dimensional line only possible in theory because if you represent it with something, that something has to have thickness and width, no matter how minimal?


Well, yes and no.  As I'm sure you realize, ALL physical objects in our real world are always three-dimensional (ignoring time, and the possibility of higher numbers of compactified dimensions that string theorists sometimes contemplate).  No more and no less. Actually, there are _no such things as one- or two-dimensional objects_ -- not physical ones, anyway.  Such things are purely theoretical constructs, but they are incredibly useful, and they go back to the time of the ancient Greeks (like Euclid) and even before that. Points (0D), lines (1D) and planes (2D) do not actually exist.  All matter takes up space (it's all 3D).  But we still study points, lines, and planes in elementary and junior high school.  These are not very hard concepts to grasp, in fact, and children usually get it.  It's much harder to try to "understand" (i.e., develop a physical intuition for) 4 spatial dimensions -- like the tesseract (4D analog of the cube).

In physics, it is incredibly useful, and mathematically much easier, to develop certain theories in less than 3 dimensions.  The results from these can apply, and sometimes in _excellent approximation_, to real-world objects.  1D waves in lines can model pretty accurately (but not perfectly) the vibrations of strings, which are hundreds-to- thousands of times longer than they are wide.  2D waves on surfaces can model pretty accurately (but not perfectly) things like ripples on a pond.  Or the vibrations of the top plate of an instrument, which is tens-to-hundreds of times thinner than it is across.  

But the answer to your real question is definitely "NO."  If, in a mathematical theory, you choose to represent a string as being 1D, or a surface as being 2D, then NO, you are not required to "represent it with something that has to have thickness and width."  The width or thickness become precisely zero in these mathematical approximations.  Despite that, these approximations can be quite accurate.  Reduced dimensionality plays an important and time-honored role in physics.  Physicists understand esoteric things like superconductivity, phase transitions, and relativity from models with reduced dimensionality, as it happens.  Einstein's famous theory of special relativity was first worked out in a single dimension, as a matter of fact.

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## David Lewis

> CarlM.  Dave is using my given name, which we share.  f-d


Did someone call me?  :Wink:

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## fscotte

This is all good and stuff, but a 1923 Lloar still sounds as good as anything.  What else is there after that?

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Clinton Johnson, 

Mark Gunter

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## plinkey

In order to know the eagle, one shall become an eagle himself.
Bill, I am certainly not suggesting that you transform yourself into a mandolin. :Wink: 
However, one obvious way to get a deeper understanding of the mandolin is to keep building them and/or play music on them. 
That is clearly a difficult and lengthy process, and many spend their lifetime on it, and there is still not a definitive answer given at the end of it all. Yet, most often, it should be a very gratifying process too.

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Mark Gunter

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## Larry Simonson

This is a follow-up of my posting back in February (#107) where I wrote: 

" Now I have a drummer friend who tells me about the "sweet spots" on his drums so I was wondering if such spots may exist on mandolin bellies. Maybe if the bridge position was moved to such a sweet spot by strategically locating the fingerboard there might be some improvement in the efficiency of transmitting plucked string energy to sound. I have no idea how this will turn out but I find it interesting and am in the position to give it a try, so that is what I am planning."  

I have glued the top of my current build onto the rim and last night my drummer friend came by and thunked the top along center line from one end to the other and declared that the best sound came from a point at the intersection of a line between the inner notches of the f-holes and the centerline, exactly where the bridge is normally located.  So maybe Loar had this figured out long ago.

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billhay4, 

David Lewis, 

Mark Gunter

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