Question

A person carrying a whistle emitting continuously a note of $272Hz$ is running towards a reflecting surface with a speed of $18km/h$ . If the speed of sound is $345m/s,$ the number of beats heard by him are

• A. 4
• B. 6
• C. 8
• D. 10

Answer 1

Answer: (C)

Original frequency of whistle Speed of the person,
$v=18km/h=5m/s$
Speed of sound, $v=345m/s$
Observed apparent frequency of reflecting surface
$v_a=\left(\frac{v}{v-v_s}\right)v_0$
$=\left(\frac{345}{345-5}\right)272=\frac{345}{340}\times 272$
Observed apparent frequency by the person, considering the reflecting surface as source.
$v_a^{\prime }=\left(\frac{v+v_0}{v}\right)v_a$
$=\left(\frac{345+5}{345}\right)\left(\frac{345}{340}\right)\times 272$
$=\left(\frac{350}{340}\right)\times 272=\frac{35}{34}\times 272Hz$
$=36\times 8=280Hz$
Thus, number of beats beared by the person is
$v=v_a^{\prime }-v_0=280-272=8$