question_answer

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

A) \[4\]              

B) \[6\]

C) \[8\]              

D) \[10\]

Correct Answer: C

Solution :

Original frequency of whistle Speed of the person, \[v=18\text{ }km/\text{ }h=5\text{ }m/s\] 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. \[v{{'}_{a}}=\left( \frac{v+{{v}_{0}}}{v} \right){{v}_{a}}\] \[=\left( \frac{345+5}{345} \right)\left( \frac{345}{340} \right)\times 272\] \[=\left( \frac{350}{340} \right)\times 272=\frac{35}{34}\times 272Hz\] \[=36\times 8=280Hz\] Thus, number of beats beared by the person is \[v=v{{'}_{a}}-{{v}_{0}}=280-272=8\]