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. Firstly, the two trains are approaching the stationary observer from opposite sides with the same speed which is 1% of the velocity of sound in air. The number of beats that he will hear between the frequencies of A and B as heard by him will be (per second) :

• A. 10
• B. 2
• C. 0
• D. greater than 10

Answer 1

Answer: (C)

0

The apparent frequencies heard by the stationary observer due to the approaching trains are each given

$f^{\prime }=f\frac{v_s}{v_s-v}=f(\frac{v_s}{v_s-\frac{v_s}{100}})=\frac{100}{99}f=\frac{100}{99}kHz$

This same frequency is reached to the observer by both the trains. Hence the beat frequency has heard by the observer is zero.