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A band playing music at a frequency f is...

A band playing music at a frequency `f` is moving towards a wall at a speed `v_(b)`. A motorist is following the band with a speed `v_(m)`. If `v` is the speed of sound, obtain an expression for the beat frequency heard by the motorist.

Text Solution

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The correct Answer is:
`[n_(0)[[(v +v_(m))(2v_(b)))/((v^(2) - v_(b)^(2))]]]`

Apparent frequency received bymotorist directly from ban is
`n_(1) = n_(0)((v + v_(m))/(v + v_(b)))`
Apparent frequency received by motorist from reflected sound by wall is
`n_(1) = n_(0)((v + v_(m))/(v - v_(b)))`
Beat frequency
`n_(B) = n_(2) - n_(1)`
`(v + v_(m))((1)/(v - v_(b)) - (1)/(v+ v_(b)))`
`(2v_(b) (v + v_(m)))/((v^(2) - v_(b)^(2)) )n_(0)`
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