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Question

A source emitting sound at frequency 3000 Hz, is moving along positive y axis with a speed 35 m/s. A listener is situated on the ground at the position (670 m,0). Find the frequency of the sound received by the listener at the instant the source crosses the origin. Speed of sound in air is 335 m/s

A
3350 Hz
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B
3033 Hz
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C
3000 Hz
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D
2568 Hz
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Solution

The correct option is B 3033 Hz


Given that,
Speed of sound in stationary medium (v)=335 m/s

Actual frequency f0=3000 Hz

Velocity of source of sound (vs)=35 m/s

At t=0, source is emitting sound and after time t1 it crosses the origin.

This means sound also travelled from B to A in time t1.

BCvs=ABv

BCAB=vsv=35335

Now In ΔABC,

cosθ=BCAB=35335

From the definition of Doppler effect,

fapp=f0(v±vov±vs)

Since the listener has fixed position, we can say that, vo=0, and source is approching the listener along the line joining them.

fapp=f0(vvvscosθ)

Substituting the data given in the question,

fapp=3000×⎜ ⎜ ⎜33533535×35335⎟ ⎟ ⎟
=3000×335×33533523523033 Hz

Note:- No matter where this point is on X axis, frequency of sound heard by every point on the X axis is same when the source crosess the origin .

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