Question

A source of sound $S$ emitting waves of frequency $100\, Hz$ and an observer $O$ are located at some distance from each other. The source is moving with a speed of $19.4\,ms^{-1}$ 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 $330 \,ms^1).$ is

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

Answer 1

Answer: (D)

Here,
Frequency of source, $v_{0}=100 \,Hz$
Velocity of source, $v_{s}=19.4 \,ms ^{-1}$
Velocity of sound in air, $v=330\, ms ^{-1}$
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
$v=v_{0}\left(\frac{v}{v-v_{s} \cos 60^{\circ}}\right)$
$=(100 Hz )\left(\frac{330 ms ^{-1}}{330 ms ^{-1}-\left(19.4\, ms ^{-1}\right)\left(\frac{1}{2}\right)}\right)$
$=(100 Hz )\left(\frac{330 ms ^{-1}}{320.3 ms ^{-1}}\right)=103\,Hz$