Nice equation!

It follows that if you can tap test a piece of wood, analyse the tap tone and determine the material properties (a technique pioneered by Australian physicist and luthier Graham Caldersmith over 30 years ago), you should also be able to reverse the process and determine from the material properties what dimensions it needs to be to give a specific vibrational performance.  No one said it was easy, but it can be done.  The above equation is the solution to a set of fourth order partial differential equations where h is the target plate thickness.  The equation, in its original form, was derived in a scientific paper The fundamental frequency of vibration of rectangular wood and plywood plates, R.F.S. Hearmon, 1946 Proc. Phys. Soc. 58 78-92.  I made a few modifications so it would better suit my purposes.

I programmed it up in my computer so now I just tap the wood, analyse the sound produced using my computer and it gives me the target plate thickness for that particular piece of wood for my target vibrational performance on the gutiar. It removes a lot of the guesswork. 

The best plates are the ones made from wood that delivers the target vibrational performance for the lowest mass.  They are the easiest for the strings to drive as they have the lowest inertia.

RETURN