mitch lees wrote: ↑
Mon Oct 16, 2017 7:36 am
At the risk of becoming a nuisance, is the relevant equation available on line anywhere?
If you google "Helmholtz resonator" you will likely find a number of formulae for the resonant frequency of a Helmholtz resonator, including this one
. The problem is that they assume the body of the vessel is rigid, which a guitar most certainly is not, and so give an incorrect answer that is far more misleading than being of any real use. However, the equations given usually show you which direction things move if you select a variable and change it; it's just that the magnitudes are all wrong. To get the magnitudes right, you need to be a lot
more sophisticated in your modeling, taking into account the mass, stiffness and mobility of the other main vibrating components of the "vessel", namely the top, back and sides of the instrument, all of which couple with the main air mode and alter its frequency.
You then need to be able to ascertain what is the "right" answer, for your set of circumstances, i.e. what resonant frequency are you aiming for and why is that a "good" frequency, and how will that frequency relate and react to the other major low order resonances of the guitar, which all couple. All of a sudden you're into modal tuning. The modes of vibration of a finished guitar are what you hear when an instrument is played and so define the sound of that particular guitar. What differs from guitar to guitar are the amplitude, bandwidth and center frequencies of those modal resonances, and indeed, whether or not a particular modal resonance exists on a particular instrument. If you want to change the sound of a guitar, it's the modal resonances that you have to deal with and you have to be able to link those modal resonances to particular features of the woodwork. Free plate tuning only gets you some of the way, because there is no easy pathway between free plate modes and completed instrument modes because of the substantial changes in conditions between one and the other: constrained edges, coupling effects, the effect of additional components likes bridges, finish, etc..
So yes, a guitar "is a lot more complicated than it ought to be" as Alan is wont to say. But many of the hard yards have been done.