Question

The observer is moving with velocity $v_0$ towards the stationary source of sound and then after crossing moves away from the source with velocity $v_0$. Assume that the medium through which the sound waves travel is at rest. If $V$ is the velocity of sound and $n$ is the frequency emitted by the source then the difference between apparent frequencies heard by the observer is

• A. $\frac{2n \, v_0}{v}$
• B. $\frac{n \, v_0}{v}$
• C. $\frac{v}{2n \, v_0}$
• D. $\frac{v}{n \, v_0}$

Answer 1

Answer: (A)

$\frac{2n \, v_0}{v}$

Answer 2

Using doppler effect formula
Case I : Observes approaching the source.
$V ^{1}=\left(\frac{ V + V _{ o }}{ V }\right) n \,\,\,\ldots$ (I)
Case II : Observes moving away from the source
$V ^{1}=\left(\frac{ V - V _{ o }}{ V }\right) n \,\,\,\ldots$ (II)
Different between 2 frequencies
$( I )-( II )=\frac{2 V _{ o } n }{ V }$