question_answer

A man is watching two trains, one leaving and the other coming in with equal speeds of 4m/ sec. If they sound their whistles, each of frequency 240 Hz, the number of beats heard by the man (velocity of sound in air = 320 m/sec) will be equal to     

A)  6

B)  3     

C) 0

D) 12

Correct Answer: A

Solution :

[a] Frequency of sound heard by the man from approaching train. \[{{n}_{a}}=n\left( \frac{v}{v-{{v}_{s}}} \right)=240\left( \frac{320}{320-4} \right)=243\,Hz\] Frequency of sound heard by the man from receding train \[{{n}_{r}}=n\left( \frac{v}{v+{{v}_{s}}} \right)\] \[=240\left( \frac{320}{320+4} \right)=237\,Hz\] Hence, number of beats heard by man per sec \[={{n}_{a}}-{{n}_{r}}=243-237=6\]