answer the question below

Question

Listener1 is moving at 60m/s towards the source and listener2 is moving away at the same speed. The frequency of the sound is 880Hz. This is in air at 20°C where the speed of propagation of sound is 343m/s. Calculate the apparent frequency for listener1 and listener2.

Answer 1

The general relationship between

speed v,

wavelength λ, and

frequency f is

v = λf

Let

v0 = 343 m/s be the speed of sound in air,

f0 = 880 Hz be the frequency of the sound,

λ = v0/f0 be the wavelength of the sound.

The two listeners experience the sound as having the same wavelength λ,

but arriving at them with different speed.

v1 = v0 + 60 m/s is the speed with which the sound arrives at listener 1.

v2 = v0 - 60 m/s is the speed with which the sound arrives at listener 2.

In general, suppose that some listener experiences the sound arriving at him

with speed v0+w.

Then he experiences frequency

(v0+w)/λ = (v0+w)/(v0/f0) = f0(v0+w)/v0 = f0(1+w/v0)

Listener1 experience frequency

f1 = f0(1 + 60/v0) = 880(1 + 60/343) = 1034 Hz

Listener2 experience frequency

f2 = f0(1 - 60/v0) = 880(1 - 60/343) = 726 Hz