Air

 The vibration of the top plate causes the air inside to move back and forth resulting in Helmholtz resonance. At the sound hole a “plug” of air move. If the air moves in it compresses the air inside, then the pressure forces the air back out and the momentum of the air overcompensates and the air inside the guitar rarifies. Now the air inside sucks air back in and the process repeats. This can be measured quantitatively in Helmholtz resonance.  (how does a guitar work?)

To find the frequency we use the equation:

Where S is the cross sectional area, L is the length of the air in the neck, V is the volume of the air, and c is the speed of sound. The volume of air changes depending on how the neck is resonating.

In a guitar the “plug” of air would be about 1.7 times the radius of the hole and .85 times the thickness of the pipe (which is only about 2.5 mm thick). So with a circular hole with radius r, then S=πr², and L=1.7r we get:

Equations from: http://www.phys.unsw.edu.au/jw/Helmholtz.html