Question

A sound source $(S)$ emits frequency of $180 \,Hz$ when moving towards a rigid wall with speed $5 \,m / s$ and an observer $(O)$ is moving away from wall with speed $5 \,m / s$. Both source and observer move on a straight line which is perpendicular to the wall as shown in figure. Find the number of beats per second heard by the observer. (Speed of sound $=355 \,m / s$ )

Answer 1

For direct sound from the source,
$f_{1}=\left(\frac{V_{S}-V_{0}}{V_{S}+V_{\text {source }}}\right) f_{0} $
$V_{S}=$ velolcity of sound
$V_{0}=$ Velocity of observer
$V_{\text {source }}=$ Velocity of source
$=\frac{350}{360} \times 180$
For sound heard after reflection,
$f_{2}=\left(\frac{V_{S}-V_{0}}{V_{S}}\right) f' \,\&\, f'=\left(\frac{V_{S}}{V_{S}-V_{\text {source }}}\right) f_{0}$
$\therefore f_{2}=f_{0}$
$\therefore $ No. of beats $=f_{2}-f_{1}=\left(180-\frac{350}{360} \times 180\right)$
$=\frac{180 \times 10}{360}=5$ beats $/ s$