1.

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

Answer»

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

Solution :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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