Approximately a third of people with normal hearing have ears that continuously

Question

Approximately a third of people with normal hearing have ears that continuously emit a low-intensity sound outward through the ear canal. A person with such spontaneous otoacoustic emission is rarely aware of the sound, except perhaps in a noise-free environment, but occasionally the emission is loud enough to be heard by someone else nearby. In one observation, the sound wave had a frequency of 1678 Hz and a pressure amplitude of 1.13 × 10-3 Pa. What were (a) the displacement amplitude and (b) the intensity of the wave emitted by the ear? The air density is 1.21 kg/m3 and the speed of sound is 343 m/s.

Explanation / Answer

given

f = 1678 Hz

Pa = 1.13*10^-3 Pa

a. Pa = rho*c*w*A

rho = 1.21 kg.m^3

c = 343 m/s

w = 2*pi*f = 10543.185 rad/s

hence

A = Pa/rho*c*w = 2.582*10^-10 m

b. Sound intensity I = 2*pi*pi*f^2*A^2*rho*c

hence

I = 1.5383*10^-9 W/m^2

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