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A source is moving towards the observer with the speed of 40 m/s and emitting the sound of frequency 100 Hz. Find the observed frequency by standing observer if the velocity of propagation of sound is 340 m/s.
1. 89 Hz
2. 113 Hz
3. 110 Hz
4. 230 Hz

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Correct Answer - Option 2 : 113 Hz

​CONCEPT:​

  • Doppler Effect: An increase or decrease in the frequency of sound, light, or other waves that are observed by the observer due to movement of the source and observer towards (or away from) each other is known as Doppler Effect.

The apparent frequency heard by the observer is given by the formula:

\(f=f_0\left ( \frac{v\pm v_o}{v \pm v_s} \right )\)

where f is apparent frequency, f0 is the original frequency of the source, v is the speed of sound in air, vs is the speed of the source, vo is the speed of the observer.

CALCULATION:

Given that v = 340 m/s; vs = 40 m/s (-ve) moving towards; v0 = 0; f = 100 Hz

\(f=f_0\left ( \frac{v\pm v_o}{v \pm v_s} \right )\)

\(f=100\times \left ( \frac{340}{340-40} \right )\)

f = 340/3 Hz = 113 Hz

So the correct answer is option 2.

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