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 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

$n^{'} = n (\frac{V}{V - V_{s}}) or 5 \cdot 5 = 5 (\frac{v}{v - v_{1}}) or v - v_{1} = \frac{10 v}{11} or v_{1} = (v / 11) Again, 6 = 5 (\frac{V}{V - V_{s}}) = 5 (\frac{V}{V - V_{2}}) or 6 (v - v_{2}) = 5 v or v_{2} = \frac{v}{6} From eqs . (1) ard (2), \frac{V_{2}}{V_{1}} = \frac{11}{6}$

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