Physics Chapter 3# 157

Question

A source of sound moves toward you at speed v_{\rm{s}} and away from Jane, who is standing on the other side of it. You hear the sound at twice the frequency as Jane.

What is the speed of the source? Assume that the speed of sound is 340 m/s

Answer 1

The relation between frequency f heard by a resting observer and the  frequency f₀ emitted by a source moving with speed v is given by:

f = f₀ /(1 ± v/c)

(c is the speed of sound)

+ for source moving away from observer

- for source moving toward observer

So the frequency you hear is

f₁= f₀ /(1 - v/c)

frequency observed by Jane is

f₂ = f₀ /(1 + v/c)

You hear twice the frequency as Jane:

f₁/f₂ = 2

<=>

(1 + v/c) / (1 - v/c) = 2

<=>

(1 + v/c) = 2(1 - v/c)

<=>

v/c = 1/3

<=>

v = c/3 = 340m/s / 3 = 133.3m/s