Determining the Damping Factors in Guitar Bodies: A Scientific Inquiry

[Landru]

My question is fairly simple, but I'm having a hard time finding the answer.

A guitar body dampens the vibration of a guitar string to some degree by contorting slightly as the string oscillates, and then producing sound waves and heat in turn.

My question is; is it the mass the of the guitar, or the rigidity of the guitar, or somehow both, that contribute to the damping ratio it imparts on the strings?

Also, in either case, will the damping ratio be frequency dependent, and if so, what causes that to be the case?

 

[tech99]

I would define damping ratio as 1/Q, or the energy stored in the vibrating string divided by the energy lost each cycle. If there were no sound radiation or heat produced then the string would go on for ever. The body of the guitar moves because it is coupled to the string by the mechanical construction, and in doing so it acts as a piston moving the air. Some of the energy given to the air is just stored, like a spring. and some is lost for ever as radiation. The latter portion is the energy taken from the string.
So energy is taken from the string because the guitar body has a large area and couples some of the energy to the air. This means that more energy is lost by the string for each cycle, and therefore the vibration dies away faster.
You ask about what makes the body a good radiator. No doubt, to respond to the vibration it should have small mass, and be freely mounted, and have large area. Just like a loud speaker cone. It will, of course, have resonances which alter the characteristics at certain frequencies. There may also be air inside the body, which also has resonances and is part of the radiation mechanism.

 

[cosmik debris]

Damping on a guitar does depend on those factors but also on the coupling impedance of the sting to the neck where the sting is fretted. This is variable on most instruments and produces dead spots (lack of sustain) on some necks. This article is worth a look:

https://www.unibw.de/lrt4/mechanik/mitarbeiter/ehem-mitarbeiter/hfleischer/deadspots-en

Cheers

 

[Landru]

Thanks for the responses and the link.

After reading more from that linked page, I think the answer to my question is that it's only the degree of stiffness of the guitar that determines what it's damping ratio will be in the context of the oscillating string, and that the overall mass of the guitar is only relevant in terms of how much more or less stiff it might serve to make the guitar.

As for why the dampening is frequency dependent, I take it this is because the guitar body represents "structural / hysteric damping" instead of the "viscous damping", and hysteric damping takes into account the resonant frequency or frequencies of the damping structure.

 

[tech99]

Thanks for the responses and the link.

After reading more from that linked page, I think the answer to my question is that it's only the degree of stiffness of the guitar that determines what it's damping ratio will be in the context of the oscillating string, and that the overall mass of the guitar is only relevant in terms of how much more or less stiff it might serve to make the guitar.

As for why the dampening is frequency dependent, I take it this is because the guitar body represents "structural / hysteric damping" instead of the "viscous damping", and hysteric damping takes into account the resonant frequency or frequencies of the damping structure.

Further to the losses in the structure etc, the radiation resistance and hence the radiated power will increase rapidly with frequency, as the dimensions of the body become greater than half the wavelength.

 

[Landru]

Further to the losses in the structure etc, the radiation resistance and hence the radiated power will increase rapidly with frequency, as the dimensions of the body become greater than half the wavelength.

Are the higher frequencies dissipated faster than lower ones due to the overall size of the guitar, or is because wood dampens higher frequencies more than low ones, both or neither?

 

[cosmik debris]

I suppose there is the player to consider as well. The guitar is held against the body (for most styles) and the hand is holding the neck.