Sound Waves A block with a speaker bolted to it is connected to a spring, as sho

Question

Sound Waves

A block with a speaker bolted to it is connected to a spring, as shown below. The speaker emits sound waves at frequency 400 Hz and sound level 96 decibels. (a) Suppose the speaker is stationary. Find the wavelength and displacement amplitude of sound waves emitted by the speaker. (The density of air is 1.29 kg/m^3, the speed of sound in air is 343 m/s, and the reference intensity at the threshold of hearing is 1 times 10^-12 W/m^2.) (b) Now suppose the speaker oscillates in simple harmonic motion with amplitude 60 cm and frequency 20 Hz, and a person moving in the negative x direction at constant speed hears a maximum sound frequency of 525 Hz. At what speed is the person moving, and what is the minimum frequency of sound he can detect while moving at this speed?

Explanation / Answer

given, frequency of speaker, f = 400 Hz

sound level, P = 96 decibels

a. stationary speaker

speed of sound in air, v = 343 m/s

wavelength of sound = lambda

lambda*f = v

lambda = v/f = 343/400 = 0.8575 m

now, P = 20log(p/20*10^-6)

96 = 20log(p/20*10^-6)

so displacement amplitude, p = 0.6324 Pa

b. speaker osscilations

amplitude, A = 0.6 m

frequency, fo = 20 Hz

so w = 2*pi*f = 125.663 rad/s

maximum velocity of speaker , Vo = wA = 75.39 m/s

the person is moving towards the sound source, v' = ?

maximum sound frequency heard, f' = 525 Hz

from doppler's effect

f' = (v + v')f/(v - vo)

525 = (343 + v')400/(343-75.39)

v' = 8.238 m/s

at this sdpeed minimum frequency = f"

f" = (343 + 8.238)400/(343+75.39) = 335.799 Hz

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