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Question
A train standing at the outer signal of a railway station blows a whistle of frequency 400 Hz still air. The train begins to move with a speed of 10 ms–1 towards the platform. What is the frequency of the sound for an observer standing on the platform? (sound velocity in air = 330 ms–1)
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Solution
Frequency of train standing at the outer signal, vo = 400 Hz
Speed of train moving towards the platform, vs = 10 ms–1
The velocity of sound in air, va = 300 ms–1
Apparent frequency of the sound for an observer standing on the platform,
⇒ v' = `v_a/((v_a - v_s)) v_o`
⇒ v' = `(330 xx 400)/((330 - 10))` Hz
⇒ v' = `(330 xx 400)/320` Hz
⇒ v' = `825/2` Hz
⇒ v' = 412.5 Hz
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