Question

A train is approaching the platform with a speed of $4m{s}^{-1}$. Another train is leaving the platform with the same speed. The velocity of sound is $320m{s}^{-1}$. If both the trains sound their whistles at frequency 230 Hz, the number of beats heard per second will be :

• A. 10
• B. 8
• C. 7
• D. 6

Answer 1

The correct option is D 6

$answer:6$

using doppler's:

for train approaching at the station :

$f_1=230$$\frac{(v+0)}{(v-4)}$

for train going away from station:

$f_1=230$$\frac{(v-0)}{(v+4)}$

beats=$|f_1-f_2|$

beats=$|230\frac{(v-0)}{(v-4)}$$-$$230\frac{(v-0)}{(v+4)}|$

putting the value of $v$=320 m/s

we get

$beats=5.75$

since beats cant be in fraction or decimals we roundoff it to nearest integer value 6.

hence $beats=6$