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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 HzPictorially we can depict the problem as shown below. The frequency heard by observer, f′=f0(v+v0v−vs), where f0=500 Hz,v0=0 m/s,v=330 m/s and vs=50 m/s ⇒f′=f0(v+v0v−vscosθ) [we take speed of source and observer along line joining the source and observer] ⇒f′=500×⎛⎜ ⎜ ⎜⎝330+0330−50×3050⎞⎟ ⎟ ⎟⎠ ⇒f′=550 Hz

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