The air pressure variations in a sound wave cause the eardrum to vibrate. (a) Fo

Question

The air pressure variations in a sound wave cause the eardrum to vibrate.
(a) For a given vibration amplitude, are the maximum velocity and acceleration of the eardrum greatest for high-frequency sounds or low-frequency sounds?
low frequency sounds
high frequency sounds

(b) Find the maximum velocity and acceleration of the eardrum for vibrations of amplitude 6.0 10-9 m at a frequency of 24.0 Hz.
vmax = ________ m/s
amax = ________ m/s2

(c) Repeat (b) for the same amplitude but a frequency of 24.0 kHz.
vmax = _______ m/s
amax = _______ m/s2

Explanation / Answer

a) low frequency sounds b) From SHM we have x = A*cos(?t) where ? = 2pf = 2p*24 = 150.768 rad/s Now v= -?A*sin(?t) and a = -?^2*A*cos(?t) So v max = ?A = 150.786*6.0x10^-9m = 904.608x10^-9m/s = 0.904*10^-6 amax = ?^2*A = (150.786)^2*6.0x10^-9 = 135691.2x10^-9 m/s^2 = 1335.691*10^-6 c) Now if f = 24000Hz we have ? = 2pf = 2p*24000 = 150768 rad/s Now vmax = 150768*6.0x10^-9 = 904.608x10^-6m/s and amax = 150768^2*6.0x10^-9 = 136.385 m/s^2

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