A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a

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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

Accepted Answer

Sol. fA = 5.5 KHz = $\left( \frac{\mathbf{v +}\mathbf{v}_{\mathbf{A}}}{\mathbf{v}} ight)$×5 KHz ⇒ 1.1 = 1 + $\frac{v_{A}}{v}$⇒ $\frac{v_{A}}{v}$ = 0.1fB = 6 KHz = $\left( \frac{
u + v_{B}}{
u} ight)$5KH2 ⇒ $\frac{v_{B}}{v}$ = 0.2Hence $\frac{v_{B}}{v_{A}}$ = $\frac{0.2}{0.1}$ = 2

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