Question

A and B are two identical point sources of acoustic waves, each producing sound of 1 kHz. They are located in two trains, one in each of the engines of the trains which runs on two close parallel tracks. An observer is standing in between the tracks and listening to the sound received from each of the sources. If one of the trains remains stationary while the other train recedes from the observer with a speed which is 1% of the velocity of sound in air, the number of beats heard by the observer per second will be (in Hz) :

• A. 0
• B. greater than 10
• C. 3.5
• D. 9.9

Answer 1

Answer: (D)

9.9

Apparent frequency due to receding train = $f\frac{v_s}{v_s+v}=f\frac{100}{101}=\frac{100}{101}kHz$

Frequency heard from the stationary train does not change.

Thus the number of beats heard by the observer per second = $1kHz-\frac{100}{101}kHz=\frac{1}{101}kHz=9.9Hz$