Question

The human ear canal has a typical length of about 2.2 cm and can be modeled as a tube open at one end and closed at the eardrum.

a) Calculate the fundamental frequency that humans should be expected to hear best. Assume that the speed of sound is 345 m/s in air.

Looking deeply down your friends throat, or perhaps looking at a photograph, you observe the vocal tract. At the bottom of the vocal tract, when you aren't swallowing, are membranous folds that close and open to modify the pressure at the vocal folds.

b) If the vocal tract with closed vocal folds is modeled as a pipe closed only on one end, predict the length of the vocal tract corresponding to the fundamental frequency for the hearing just calculated in part (a).

c) Calculate the fundamental frequency of the human voice if L=17cm

Answer 1

a)

Given,

Length, L = 2.2 cm = 0.022 m

The speed of sound, v = 345 m/s

The fundamental frequency, f₀ = v / $\lambda$

= v / 4L

= 345 / (4 * 0.022)

= 3920.45 Hz

c)

L = 17 cm = 0.17 m

The fundamental frequency, f₀ = v / $\lambda$

= v / 4L

= 345 / (4 * 0.17)

= 507.35 Hz