Question

A source of sound $S$ emitting waves of frequency $100Hz$ and an observer $O$ are located at some distance from each other. The source is moving with a speed of $19.4m{s}^{-1}$ at an angle of $60^{\circ }$ with the source observer line as shown in the figure.

The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330m{s}^1).$ is

• A. 106 Hz
• B. 97 Hz
• C. 100 Hz
• D. 103 Hz

Answer 1

Answer: (D)

Here,
Frequency of source, $v_0=100Hz$
Velocity of source, $v_s=19.4m{s}^{-1}$
Velocity of sound in air, $v=330m{s}^{-1}$
As the velocity of source along the source observer line is $v_s\cos 60^{\circ }$ and the observer is at rest, so the apparent frequency observed by the observer is
$v=v_0\left(\frac{v}{v-v_s\cos 60^{\circ }}\right)$
$=(100Hz)\left(\frac{330m{s}^{-1}}{330m{s}^{-1}-\left(19.4m{s}^{-1}\right)\left(\frac{1}{2}\right)}\right)$
$=(100Hz)\left(\frac{330m{s}^{-1}}{320.3m{s}^{-1}}\right)=103Hz$