Question

A man is watching two trains, one leaving and the other coming with equal speed of $4m{s}^{-1}$. If they sound their whistles, each of frequency $240Hz$, the number of beats heard by the man is :
(velocity of sound in air = $320m{s}^{-1}$)

• A. $6$
• B. $3$
• C. $0$
• D. $12$

Answer 1

The correct option is A $6$

For first train (leaving) ,
$v_s=4{\text{ms}}^{-1}$, $v_o=0{\text{ms}}^{-1}$, $V=320{\text{ms}}^{-1}$
From Doppler's effect in sound waves,
$f_1=\frac{320}{320+4}\times 240=\frac{320}{324}\times 240=237\text{Hz}$
in second train comming towards observer,
$v_s=4{ms}^{-1}.v_o=0{\text{ms}}^{-1},$
From Doppler's effect in sound waves,
$f_2=\frac{320}{320-4}240=\left(\frac{320}{316}\right)\times 240=243\text{Hz}$
therefore,
$f_2-f_1=(243-237)\text{Hz}=6\text{Hz}$
Option "A" is correct.