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A whistle is whirled in a circle of radi...

A whistle is whirled in a circle of radius 1m with 7rps. An observer is situated outside the circle, but in its plane. If the speed of sound is 336`m//s`, find the interval between the highest and lowest observed pitches.

Text Solution

Verified by Experts

Here, `r=1m`
`v=rps`
`upsilon=336m//s`
`upsilon_(s)=romega=rxx2piv=1xx2pixx7=44m//s`
The frequency will be highest when whistle is at B and `upsilon_(s)` is towards the observer
`v_(max)=(upsilon.v)/(upsilon-upsilon_(s))=(336v)/(336-44)=(336)/(292)v`
The frequency will be lowest, when whistle is at A and `upsilon_(s)` is away from the observer
`v_(min)=(upsilonv)/(upsilon+upsilon_(s))=(336v)/(336+44)=(336)/(380)v`
The required interval
`=(v_(max))/(v_(min))=((336//292)v)/((336//380)v)=(380)/(292)=1.3`
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