Q: 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 (velocity of sound ,v = 330 m/s )

(a) 242/252

(b) 2

(c) 5/6

(d) 11/6

Ans: (b)

Sol: Using formula ,

$\large f’ = \frac{V-V_L}{V-V_S} \times f$

Here Source is at rest , but listener is moving towards source

$\large f’ = \frac{V+V_L}{V} \times f$

In first case,

$\large 5.5 = \frac{V + V_A}{V} \times 5 $ …(i)

In second case ,

$\large 6 = \frac{V + V_B}{V} \times 5 $ …(ii)

On solving (i) by (ii)

$\large \frac{V_B}{V_A} = 2 $