Electric guitar sustain calculation

[Volodymyr]

Hi. Now I am working on my term paper on "Influence of constructive elements of electric guitar on its sound" and faced with the task to build a mathematical model of instrument sustain. So far I have not found any good source that would help me with this. Now I have this formula:

But I don't know how to prove its correctness. Could you help me with this? And can you advice me some sources about this?

 

[Tazerfish]

I mean, what it's saying it just that the energy decays exponentially. The energy loss is proportional to the energy.

That's a testable hypothesis.

Pluck a string, record the sound. See how the amplitude decays. If the hypothesis is correct, then it should be exponential in time. When displayed on a decibel scale, which is logarithmic, it will be a straight line.
Well, at least that would be true assuming that the energy loss is proportional to the radiated sound power, which seems like a decent assumption to me.

Hey, why don't you check the web?
Maybe someone's done the experiment it already?
That formula hasn't fallen from the sky after all!

I'm a bit mystified about why the guitar mass—I'm assuming that's what the M stands for—is inversely proportional to energy loss.
Are you telling me, if I encase it in massive block of cement, it barely makes any sound but vibrates for ages?
Is that a thing? Do heavy guitars "ring" longer?

Although it seems strange, it again is a testable hypothesis. Get a heavy and a light guitar and see if they ring longer/shorter.
However, weight differences might be marginal and these constants K in the equations may be different between guitars, making the whole experiment ...
Not very insightful.

Theory-wise this formula is hardly a stroke of genius. To me, it just seems like semi-random first guess/simple model.
"Lots of things are exponential or power laws; let's see if this is exponential"

If it fits the data we'll, that's great!

 

[sophiecentaur]

But I don't know how to prove its correctness.

Without a set of guitars of the same type only different masses then how could you do it experimentally? What sort of simplified model are you using to arrive at your test formula? To calculate loss of sound energy in the guitar body then wouldn't you need to consider flexing of the various parts?
Oh yes - what does that constant k represent?

 

[pinball1970]

Hi. Now I am working on my term paper on "Influence of constructive elements of electric guitar on its sound" and faced with the task to build a mathematical model of instrument sustain. So far I have not found any good source that would help me with this. Now I have this formula:
View attachment 349646
But I don't know how to prove its correctness. Could you help me with this? And can you advice me some sources about this?

I would look into the Travis Bean, unusual because it had a metal neck.
"You could hold a note forever" Denny Laine.

One end of the spectrum in terms of materials

 

[BWV]

Why does the mass of the electric guitar matter? (Or at least why would a doubling of the mass half the decay rate?).

 

[Arjan82]

With these kind of questions I always think about this video, good insights I would say:


I would say sustain is mainly influenced by stiffness of the guitar body and damping of the vibratory modes of the body, which are very high and low respectively for may guitars I would say.

[EDIT]
apparently he also tested sustain:

[/EDIT]

 

[BWV]

apparently he also tested sustain:

[/EDIT]

And the only things he found came down to either technique or non-faulty instrument setup (action, bridge saddle etc). Always had heard that straight-thru necks (like a les paul) had better sustain than bolt-on necks (like a strat), but could not find any evidence when I looked.