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  4. A source of sound of frequency 256 Hz is moving rapidly towards a wall with a velocity of 5 m / 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

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Q. A source of sound of frequency $256\, Hz$ is moving rapidly towards a wall with a velocity of $5\, m / s$. 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

Waves

Solution:

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