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 $ . If the speed of sound is $345\,m/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,
$v=18\, km / h=5\, m / s$
Speed of sound, $v=345\, m / s$
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.
$v_{a}'=\left(\frac{v+v_{0}}{v}\right) v_{a}$
$=\left(\frac{345+5}{345}\right)\left(\frac{345}{340}\right) \times 272$
$=\left(\frac{350}{340}\right) \times 272=\frac{35}{34} \times 272\, Hz$
$ =36 \times 8=280\, Hz$
Thus, number of beats beared by the person is
$v=v_{a}'-v_{0}=280-272=8$