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A siren placed at a railway platform is emitting sound of 5 kHz frequency. 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 the train B to that of the train A is (a) 242 : 252 (b) 2 : 1 (c) 5 : 6 (d) 11 : 6 |
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Answer» Correct Answer is: (b) 2 : 1 When an observer approaches a stationary source, which is emitting sound of frequency ns, he hears a frequency n, given by ns = n(1 + v/V), where v = velocity of the observer and V = velocity of sound. Here, let vA and vB be the velocities of the trains A and B. For A, we have n = 5.5 kHz = (5 kHz) (1 + vA/V) or vA/V = 0.1. For B, we have n = 6 kHz = (5 kHz) (1 + vB/V) or vB/V = 0.2. ∴ vB/vA = 2 |
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