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Doppler Effect in Light Waves

A toy-car, bl...

Question

A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m/s, the frequency of the horn of the toy car is close to:

A

680 Hz

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B

510 Hz

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C

340 Hz

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D

170 Hz

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Solution

The correct option is D 170 Hz
Frequency heard by the observer directly from source
$f_{1} = f (\frac{340}{340 - 5})$ ,
Frequency heard by the observer coming after relection from wall
$f_{2} = f (\frac{340}{340 + 5})$
Beats $= (f_{1} - f_{2})$
$5 = f (\frac{340}{340 - 5} - \frac{340}{340 + 5})$
$\Rightarrow f = 170 H z$

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