Question

A man is standing on a platform and watching two trains, one leaving and the other coming with equal speeds $4m/sec$. If the trains sound the whistles each of frequency $240Hz$ find the number of beats heard by the person. (Given the velocity of sound $=320m/sec$).

• A. 4
• B. 5
• C. 6
• D. 2

Answer 1

Answer: (C)

6

Let $v=320$ velocity of sound

Let $v_s=$ velocity of source

Apparent frequency n when both source and listener are moving in the same direction is given by

$n^{\prime \prime }=n\left(\frac{v}{v-v_s}\right)$

Given, $n=240$

$n^{\prime }=240\ast \frac{320}{320+4}$

$n^{\prime \prime }=240\ast \frac{320}{320-4}$

No of beats per sec is $n_{beats}=n"-n^{\prime }=\frac{240\ast 320\ast 8}{324\ast 316}=6$