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?
a. high frequency sounds
b. low frequency sounds


(b) Find the maximum velocity and acceleration of the eardrum for vibrations of amplitude 1.2 10-8 m at a frequency of 20.0 Hz.
vmax = ____m/s
amax = _____m/s^2

(c) Repeat (b) for the same amplitude but a frequency of 20.0 kHz.
vmax = ____m/s
amax = _____m/s2

For part A: it is "A"
For part B: I got 1.5 x 10^-6 for "v max"
For Part C: I got .0015 for "vmax"

I could not get the other parts. if you can please help me./

Explanation / Answer

From SHM we have x = A*cos(wt) where w = 2pf = 2p*20 = 125.66 rad/s Now v= -wA*sin(wt) and a = -w^2*A*cos(wt) So v max = wA = 125.66*1.2x10^-8m = 1.50x10^-6m/s amax =w^2*A = (125.66)^2*1.2x10^-8 = 1.89x10^-4 m/s^2 b) Now if f = 20000Hz we have w = 2pf = 2p*20000 = 125663.70 rad/s Now vmax = 125663.70*1.2x10^-8 = 1.50x10^-3m/s=0.0015 m/s and amax = 125663.70^2*1.2x10^-8 = 189.49m/s^2

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