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Question

A car approaching a crossing at a speed of 50 m/s blows a horn of frequency 500 Hz when 30 m away from the crossing. The speed of sound in air is 330 m/s. What frequency will be heard by an observer at rest at 40 m from the crossing?


A
540 Hz
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B
550 Hz
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C
560 Hz
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D
570 Hz
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Solution

The correct option is B 550 Hz
Pictorially we can depict the problem as shown below.

The frequency heard by observer,
f=f0(v+v0vvs), where f0=500 Hz,v0=0 m/s,v=330 m/s and vs=50 m/s
f=f0(v+v0vvscosθ)
[we take speed of source and observer along line joining the source and observer]
f=500×⎜ ⎜ ⎜330+033050×3050⎟ ⎟ ⎟
f=550 Hz

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