One train is approaching an observer at rest and another train is receding from

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One train is approaching an observer at rest and another train is receding from him with the same velocity 4 m/s. Both the trains blow whistles of same frequency of 243 Hz. The beat frequency in Hz as heard by the observer is (speed of sound in air is 320 m/s)

Options:

A . 10

B . 6

C . 4

D . 1

Answer: Option B
:
B
When the train is approaching,

n_{1} = \frac{v}{v - v_{s}} \times n = \frac{320}{320 - 4} \times 243 = \frac{80}{79} \times 243

When the train is receding,

n_{2} = \frac{v}{v + v_{s}} \times n = \frac{320}{324} \times 243 = \frac{80}{81} \times 243

Beat frequency is

n = n_{1} - n_{2} = 80 \times 243 (\frac{1}{79} - \frac{1}{81}) = 6 H z

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