Question

There are four possible relative motions between the source of a sound and the listener
1) source moves towards stationary listener
2) source moves away from stationary listener
3) listener moves towards stationary source
4) listener moves away from stationary source
In which of the cases, the change in frequency is the same. The magnitude of velocity of source or listener being the same.

• A. 1 and 2
• B. 2 and 3
• C. 3 and 4
• D. 1 and 4

Answer 1

Answer: (C)

3 and 4

We know that, when there is relative movement between the source and receiver, Doppler's effect is seen. So, the frequency received by the observer is given by :

$f=\left(\frac{C+V_r}{C+V_s}\right)\times f_o$

where, f is the frequency received by the observer and $f_o$ is the actual frequency from the source.

C is the velocity of sound in air, $V_r$ is the velocity of the receiver/observer, $V_s$ is the velocity of the source.

$V_r$ is positive if the observer is moving towards the source and negative otherwise.

$V_s$ is positive if the source is moving away from the observer and negative otherwise.

So, the change in frequency $\delta f$ is the same in magnitude when the listener/observer is moving towards or away from a stationary source.