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A policeman blos a whistle of frequency ...

A policeman blos a whistle of frequency 400Hz as a car speeds past him with a velocity of `54km h^(-1)`. Find the cahnge in frequency as heard by the driver of the car just as he passes the policeman. Velocity of sound in air is `350ms^(-1)`

Text Solution

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`v=400Hz,`
`upsilon_(L)=54kmh^(-1)=15ms^(-1),upsilon=350ms^(-1)`
Case (i) When the car approaches the policeman i.e. the observer (driver of the car) is approaching the source (policeman) at rest.
Therefore,
`upsilon_(L)=-15ms^(-1),upsilon_(s)=0`
The observed frequency `(v^('))` is given by,
`v^(')=((upsilon-upsilon_(L))/(upsilon))xxv=(350-(-15))/(350)xx400`
Case (ii) When the car has crossed the policeman i.e., the observer is moving away from the source at rest, then `upsilon_(L)=15ms^(-1),upsilon=0`
The observed frequency `(v^(''))` is given by,
`v^('')=((upsilon-upsilon_(L))/(upsilon))v=(350-15)/(350)xx400=382.8Hz`
Hence, change in frequency just as the car passes the policeman `=v^(')-v^('')=417.1-383.8`
`=34.3Hz`
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