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A policeman on duty detects a drop dete...

A policeman on duty detects a drop detects a drop of `15%` in the pitch of the horn of a motor car as it crossed him. If the velocity of sound is `330metre //sec`., calculate speed of the car.

Text Solution

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Before crossing the policeman, source is moving towards listener,
`:. v^(')=(upsilonv)/(upsilon-upsilon_(s))` ..(i)
After crossing the policman, source is moving away from listener,
`:. v^('')=(upsilonv)/(upsilon+upsilon_(s))` …(ii)
Dividing (ii) by (i), we get, ` (v^(''))/(v^('))=(upsilon-upsilon_(s))/(upsilon+upsilon_(s))` ...(iii)
Drop of `15%` means ` (v^(''))/(v^('))=(85)/(100)` `:.` From (iii), `(85)/(100)=(330-upsilon_(s))/(330+upsilon_(s))`
Solve to get `upsilon_(s)=26.7m//s`
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