Question

A person is seeing two trains one of there is coming with speed of 4$m/s$ and another is going with same speed. If two trains blowing a whistle with frequency 243$Hz$ . The beat frequency heard by stationary person will be (speed of sound in air $=320m/s)$

• A. $0.01Hz$
• B. $3Hz$
• C. $6Hz$
• D. $12Hz$

Answer 1

The correct option is A $0.01Hz$

$v_s=velocityoftrian=4m/s$

$v=velocityofsound=320m/s$

when train is approaching the observer$,$ apparent frequency is given by$:$

$f_1=\frac{vd}{v-v_s}{f}_0$

when train is moving away from the observer

$f_2=\frac{v}{v+v_s}{f}_0$

$f_1-f_2=$ beat frequency

$=\frac{v}{v-v_s}{f}_0-\frac{v}{v+v_s}{f}_0$

$=\frac{2v_s}{v^2-{v_s}^2}{f}_0$

$=\frac{2\times 4}{{\left(320\right)}^2-16}\times 243$

$=0.01Hz$

Hence,

option $\left(A\right)$ is correct answer.