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A car moving at a speed of 72km/hr sound...

A car moving at a speed of 72km/hr sounds its whistle which has a frequency of 550Hz, Find the frequencies heard by a stationary observer as the car approaches and then recedes from the observer, velocity of sound =340m/s.

Text Solution

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Original frequency =v=550Hz
Velocity of sound `=V=340ms^(-1)`
Velocity of listner `=V_(i)=0`
Velocity of source `=V_s="72km/hr=20m/s"`
`v.=[(V-V_(1))/(V-V_(s))]v`
The direction in which sound travels to reach the listner is positive,
(a) The car is approaching the listener. So `V_s` is +ve.
`v.=(v V)/(V-V_(s))`
`=(400 xx 340)/(340-20)`
=432Hz.
(b) When the car receds from the listener, `V_s` is negative.
`v.=(vV)/(V+V_(s))`
`v.=(vV)/(V+V_(s))`
`=(400 xx 340)/(340+20)`
=377.78Hz
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