First slide

Doppler

Question

A source of sound of frequency 256Hz is moving rapidly towards a wall with a velocity of 5m/s. The speed of sound is 330 m/s. If the observer is between the wall and the source, then beats per second heard will be

Difficult

A

7.8 Hz
B

6.7 Hz
C

3.9 Hz
D

Zero

Solution

The observer will hear two sounds, one directly from source and other from reflected image of sound.
Hence number of beats heard per second
= $(\frac{v}{v - v_{S}}) n - (\frac{v}{v + v_{S}}) n$
= $\frac{2 {nvv}_{S}}{v^{2} - v_{S}^{2}} = \frac{2 \times 256 \times 330 \times 5}{335 \times 325} = 7.8 Hz$

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