That this is possible is confirmed by some historical acoustic research and by a recent research paper entitled "
The Relationship Between Resonant Frequency, Sound Hole Diameter, and Body Depth in Acoustic Guitars" by Alyssa Fernandez. Basically, and as tinguitar mentions, the instrument's lowest resonant frequency is a coupled mode of vibration consisting of low frequency modes of vibration of the top, back, ribs, and what is called the Helmholtz resonance. The latter is a resonance related to the volume of air inside the box and the diameter of the soundhole. Changing the frequency of any of these should affect the frequency of the coupled resonance, which may produce an audible effect on the tone of the instrument.
Changing the depth of the body should have little effect on the plates but it has a direct effect on the volume of air in the body, which affects the Helmholtz resonance frequency. This in turn
should affect the frequency of the lowest resonance of the instrument.
We have available to us a mathematical model (an equation) that predicts what the Helmholtz frequency will be, based on body volume and soundhole diameter. The problem is that this equation is only valid under certain constraints, and these constraints are just
barely met by typical instrument construction. Some of these constraints include:
- The hole must be placed in the center (not near an edge) of a plate of large area (relative to the hole area);
- The plate the hole is in must be thin;
- The body must be considerably deeper than the diameter of the hole.
What Fernandez' research did was to compare measured and theoretical low frequency resonance frequency of a "guitar body" that could be varied in body depth and soundhole diameter. The results were essentially that if the body was considerably deeper than is conventional, or the soundhole was considerably smaller than is conventional, then measured frequency was close to the frequency predicted by the model equation. Now, here's the important part for this discussion: If the body was shallower than is conventional or if the soundhole was larger than is conventional, then measured frequency was not close to frequency predicted by the model equation. Under these circumstances, the frequency tended to move in the predicted direction (for example, making the body more shallow did in fact raise the resonant frequency) but it did not change it very much.
So, long story longer (!), noticeably shallower-than-conventional bodies may very well
not result in large audible changes in the lowest resonant frequency of the instrument.
There are implications here for soundhole diameter changes as well of course, but they are not related directly to this discussion. Plus, I've yammered on long enough.