question_answer

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

Correct Answer: C

Solution :

 Original frequency of whistle \[{{v}_{0}}=272\,Hz\] Speed of the person,\[v=18\text{ }km/h=5\text{ }m/s\] Speed of sound,    \[v=345\text{ }m/s\] 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. \[v_{a}^{}=\left( \frac{v+{{v}_{0}}}{v} \right){{v}_{a}}\] \[=\left( \frac{345+5}{345} \right)\left( \frac{345}{340} \right)\times 272\] \[=\left( \frac{350}{340} \right)\times 272=\frac{35}{34}\times 272\] \[=35\times 8=280\text{ }Hz\] Thus, number of beats beared by the person is \[v=v_{a}^{}-{{v}_{0}}=280-272=8\]