Question

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

• A. 4
• B. 6
• C. 8
• D. zero

Answer 1

Answer: (C)

$v_{s}=18 \,km\, h ^{-1}=18 \times \frac{5}{18} m / s =5 m / s$
If $v'$ is the frequency received by the reflecting surface, then
$v'=\left(\frac{v}{v-v_{s}}\right) v_{0}=\left(\frac{345}{345-5}\right) \cdot 272 Hz$
$\Rightarrow v^{\prime}=\left(\frac{345}{340}\right) \times 272 Hz$
The person hears the echo from the reflecting surface at a frequency $v^{\prime}$,
$v^{\prime \prime}=\left(\frac{v-v_{L}}{v}\right) v^{\prime}=\left(\frac{345-(-5)}{345}\right) \times v^{\prime}$
$=\left(\frac{350}{345}\right) \times\left(\frac{345}{340}\right) \times 272 Hz =\left(\frac{350}{340} \times 272\right) Hz$
$=280 Hz$
The person hears the original frequency $272\, Hz$ and the echo at $280 \,Hz$. Hence he heard 8 beats per second.