Question

A sound source $S$ is moving along a straight track with speed $v,$ and is emitting sound of frequency ${\nu }_0$ (see figure). An observer is standing at a finite distance, at the point $O$, from the track. The time variation of frequency heard by the observer is best represented by:
($t_o$ represents the instant when the distance between the source and observer is minimum)

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Frequency heard by the observer
${\nu }_{\text{observed}}=\left(\frac{{\nu }_{\text{sound}}}{{\nu }_{\text{sound}}-\nu \cos \theta }\right){\nu }_0$

Initially, $\theta$ will be less so $\cos \theta$ more.
$\therefore {\nu }_{\text{observed}}$ will be more initially.
At the time $t_0,$ when the distance between source and observer will be minimum, the observed frequency will be the actual frequency of the sound and then it will decrease after that.