First slide

Doppler

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 while the train approaches the siren. During his retum joumey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train.B to that of train l is

Moderate

A

$\frac{242}{252}$
B

2
C

$\frac{5}{6}$
D

$\frac{11}{6}$

Solution

In both the cases observer is moving towards the source. Hence by using $n^{'} = n (\frac{v + v_{0}}{v})$
When passenger is sitting in train A, then
5.5 = $5 (\frac{v + v_{A}}{v})$ ----------------(i)
when passenger is sitting in train B, then
$6 = 5 (\frac{v + v_{B}}{v})$ --------------(ii)
On solving equation (i) and (ii) we get $\frac{v_{B}}{v_{A}} = 2$

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