Question

A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train $A$ records a frequency of 5.5 kHz when the train approaches the siren. During his return journey in a different train $B$ he records the frequency of 6 kHz while approaching the same siren. The ratio of velocity of train $B$ to train $A$ is :

• A. $\frac{242}{252}$
• B. $\frac{5}{6}$
• C. $2$
• D. $\frac{11}{6}$

Answer 1

The correct option is C $2$

Original frequency of the siren $f_o=5kHz$
Let the speed of train A and B be $V_A$ and $V_B$, respectively.
Doppler effect when an observer moves towards the stationary source :
Apparent frequency heard $f=f_o[\frac{v_{sound}+v_{observer}}{v_{sound}}]$
For train A : $f=5.5kHz$
$\therefore$ $5.5=5[\frac{330+V_A}{330}]$
$⟹V_A=33m/s$
For train B : $f=6kHz$
$\therefore$ $6=5[\frac{330+V_B}{330}]$
$⟹V_B=66m/s$
Thus we get $\frac{V_B}{V_A}=\frac{66}{33}=2$