Question

Two whistles A and B each have a frequency of 500Hz. A is stationary and B is moving towards the right (away from A) at a speed of 50 m/s. An observer is between the two whistles moving towards the right with a speed of 25 m/s. The velocity of sound in air is 350 m/s. Assume there is no wind. Then which of the following statements are true :

• A. The apparent frequency of whistle B as heard by A is 444 Hz approximately
• B. The apparent frequency of whistle B as heard by the observer is 469Hz approximately
• C. The difference in the apparent frequencies of A and B as heard by the observer is 4.5 Hz.
• D. The apparent frequencies of the whistles of each as heard by A and Bare the same.

Answer 1

Answer: (B), (C)

The correct options are
B The apparent frequency of whistle B as heard by the observer is 469Hz approximately
C The difference in the apparent frequencies of A and B as heard by the observer is 4.5 Hz.

Applying Doppler's effect equation,

$n_A^{\prime }=\frac{350-25}{350}500=464.28Hz$

$n_B^{\prime }=\frac{350+25}{350+50}500=468.75Hz$

options "B" and "C" are correct.