A locomotive approaching a crossing at a speed of $20 \,ms ^{-1}$ sounds a whistle of frequency $640 \,Hz$ when $1 \,km$ from the crossing. There is no wind and the speed of sound in air is $330 \,ms ^{-1}$. What frequency is heard by an observer $\sqrt{3} \,km$ on the straight road from the crossing at right angle ......... $Hz$
Medium
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(c)
$\tan \theta=\frac{\sqrt{3}}{1}$
$0=60^{\circ}$
If at any instant the line joining moving source and stationary observer makes an angle $\theta$ with the direction of motion of source,
$f^{\prime}=f\left(\frac{c}{c-v \cos \theta}\right)$
Where $c$ is speed of sound and $v$ is speed of source
$f^{\prime}=640\left(\frac{330}{330-20 \cos 60^{\circ}}\right)=640\left(\frac{330}{320}\right)$
$f=660\,Hz$
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