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
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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 $