Question

A person carrying a whistle emitting continuously a note of $272Hz$ is running towards a reflecting surface with a speed of $18km{h}^{-1}$. The speed of sound in air is $345m{s}^{-1}$. The number of beats heard by him is

• A. 4
• B. 6
• C. 8
• D. zero

Answer 1

Answer: (C)

$v_s=18km{h}^{-1}=18\times \frac{5}{18}m/s=5m/s$
If $v^{\prime }$ is the frequency received by the reflecting surface, then
$v^{\prime }=\left(\frac{v}{v-v_s}\right)v_0=\left(\frac{345}{345-5}\right)\cdot 272Hz$
$\Rightarrow v^{\prime }=\left(\frac{345}{340}\right)\times 272Hz$
The person hears the echo from the reflecting surface at a frequency $v^{\prime }$,
$v^{\prime \prime }=\left(\frac{v-v_L}{v}\right)v^{\prime }=\left(\frac{345-(-5)}{345}\right)\times v^{\prime }$
$=\left(\frac{350}{345}\right)\times \left(\frac{345}{340}\right)\times 272Hz=\left(\frac{350}{340}\times 272\right)Hz$
$=280Hz$
The person hears the original frequency $272Hz$ and the echo at $280Hz$. Hence he heard 8 beats per second.