First slide

Doppler's effect

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 return journey 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 A is

Moderate

A

242/252
B

2
C

5/6
D

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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