We assume that the glottal end is closed, but the mouth is open. This is the configuration we are referring to:

The acoustic tube is uniform, and its length is L. The glottis, located at x=-L, is closed (infinite impedance) and the mouth, located at x=0, is open (impedance zero). Now, pressure variation p(x) along this uniform acoustic tube is expressed as:

where f represents frequency in Hz, and c is the speed of sound: at 37° C.

According to the boundary conditions (the impedances at both ends), the solution is:

where is the peak in sound pressure. On the other hand, we have a relation between pressure and volume velocity

is a constant representing the tube’s area. Now, volume velocity can be expressed as

where equals the average atmospheric density ( at 37°C).

As U(−L) = 0, resonances Fn of the acoustic tube are

where n=1, 2, 3… And that’s it. We can see that the area function does not affect the location of resonances. Finally, remember that, in average, the male oral tract has a length of 16.9 cm, and the female tract has an average length of 14.1 cm.