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Question

A train approaching a railway crossing at a speed of 120 kmh1 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 ms1. 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 kmh1=120×518=1003 ms1

Original Frequency of the source fo=640 Hz

Speed of sound, v=340 ms1

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 ms1

The source is approaching the person with this speed component,

the frequency heard by the observer is given by,

f=fo(v+v0vvscosθ)

Since observer (person) is at rest, v0=0

f=640(34034020)

f=680 Hz

Hence, option (B) is correct.

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