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A boy with a radio, playing a music at a...

A boy with a radio, playing a music at a frequency 'f' is moving towards a wall with velocity `v_(b).` A motrist is following the boy with a speed `v_(m)` Find the expression for the beat frequency heard by the motorist., if the speed of sound is v

A

`((v+v_(m))/(v+v_(b)))f`

B

`(v+v_(m))/(v+v_(b))`

C

`(2v_(b)(v+v_(m)))/((v^(2)-v_(b)^(2)))f`

D

`(2v_(m)(v+v_(b)))/((v^(2)-v_(m)^(2)))f`

Text Solution

Verified by Experts

The correct Answer is:
C
Motorist will receive two sounds. For direct sound waves, `f'=((v+v_(m))/(v+v_(b)))f`
For reflected sound waves `f'=(v/(v+v_(b)))xxf`

`rArr" "` Sound reflected from wall
`f'=((v+v_(m))/(v))xxf'=((v+v_(m))/(v+v_(b)))f`
Beat frequency f" - f'
`=((v+v_(m))/(v))xxf'=((v+v_(m))/(v+v_(b)))f`
`=((v+v_(m))/(v-v_(b)))f'-((v+v_(m))/(v+v_(b)))f=(2v_(b)(v+v_(m)))/((v^(2)-v_(b)^(2)))f`
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