question_answer

A boy and a girl start running with speed of 4 m/s and 3 m/s respectively around a circular track in a park from same point and in same direction. The radius of track is \[\left( \frac{4}{\pi } \right)m\]. If boy blows whistle at t = 4 s and t = 6 s with frequency of 160 Hz, then difference of apparent frequency heard by girl at these moments will be (assume speed of sound in air = 330 m/s)

A)  3.64 Hz                

B)  2.42 Hz

C)  160 Hz                 

D)  1.68 Hz

Correct Answer: B

Solution :

At \[t=4\,\sec \] Boy is at location 1 and girl at location 3. Thus, relative velocity of approach/recede becomes zero. \[{{f}_{1}}={{f}_{0}}=160\,\,Hz\] At \[t=6\,\,\sec \]. Boy lies at 1 and girl at 4. \[{{f}_{2}}={{f}_{0}}\left( \frac{330+3\cos {{45}^{o}}}{330-4\cos {{45}^{o}}} \right)\] \[\Delta f={{f}_{2}}-{{f}_{1}}=2.42\,Hz\]