Question

A sound source $(S)$ emits frequency of $180Hz$ when moving towards a rigid wall with speed $5m/s$ and an observer $(O)$ is moving away from wall with speed $5m/s$. 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 $=355m/s$ )

Answer 1

Answer: 5

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,
$f_2=\left(\frac{V_S-V_0}{V_S}\right)f^{\prime }\&f^{\prime }=\left(\frac{V_S}{V_S-V_{\text{source }}}\right)f_0$
$\therefore f_2=f_0$
$\therefore$ No. of beats $=f_2-f_1=\left(180-\frac{350}{360}\times 180\right)$
$=\frac{180\times 10}{360}=5$ beats $/s$