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Question

# A train approaching a railway crossing at a speed of 120 kmh−1 sounds a short whistle at frequency 640 Hz, when it is 300 m away from the crossing. The speed of sound in air is 340 ms−1. What will be frequency heard by a person standing on a road perpendicular to the track through the crossing at a distance of 400 m from the crossing ?

A
660 Hz
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B
680 Hz
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C
700 Hz
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D
720 Hz
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Solution

## The correct option is B 680 Hz Given that, the speed of the source, vs=120 kmh−1=120×518=1003 ms−1 Original Frequency of the source fo=640 Hz Speed of sound, v=340 ms−1 From the diagram it is clear, the person receives the sound of the whistle in a direction BA making an angle θ with the track. cosθ=300AB AB=√(300)2+(400)2=500 cosθ=300500=35 The component of velocity of the source (the train) along direction AB is vscosθ=1003×35=20 ms−1 The source is approaching the person with this speed component, the frequency heard by the observer is given by, f=fo(v+v0v−vscosθ) Since observer (person) is at rest, v0=0 ⇒f=640(340340−20) ∴f=680 Hz Hence, option (B) is correct.

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