question_answer

A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beat per second. If the velocity of sound in air is340 m/s, the frequency of horn of the toy car is close to:   JEE Main Online Paper (Held On 10 April 2016)

A) 340 Hz                     

B) 170 Hz

C) 510 Hz                     

D) 680 Hz

Correct Answer: B

Solution :

             5 beat sec \[{{F}_{air}}=\left( \frac{340}{340-5} \right)f\] \[{{f}_{\operatorname{i}nd}}=\left( \frac{340}{340+5} \right)f\] \[{{f}_{ind}}-{{f}_{air}}=5\] \[\left\{ \left( \frac{340}{340+5} \right)\left( \frac{340}{340+5} \right) \right\}f=5\] \[340\left\{ \frac{10}{(300-5)(340+5)} \right\}=5\] \[f=\frac{340\times 5}{10}\] \[f=170\,\,Hz\]