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A whistle of frequency 540 H(Z) rotates ...

A whistle of frequency `540 H_(Z)` rotates in a circle of radius `2 m`at a linear speed of `30 m//s` . What is the lowest and highest frequency heard by an observer a long distance away at rest with respect to the centre of circle ? Take speed of sound of sound in air as `330 m//s`. Can the apparent frequency be ever equal to actual ?

Text Solution

Verified by Experts

Apparent frequency will be minimum when the sorce is at `N` and moving away from the observer.
`f_(min) =((nu)/(nu + nu_(s))) f`
= `(330/(330 + 30)) (540) = 495 H_(Z)`
frequency will be maximum when source is at `L` and approaching the observer.
`f_(max) = ((nu)/(nu -nu_(s))) f = ((330)/(330 - 30)) (540)`
= `594 H_(Z)`

Further, when the source is at `M` and `K` , angle between velocity of sorce and line joining source and observer is `90^(@)` or `nu_(s) cos theta = nu_(s) cos 90^(@) = 0` . So, will be no change in the apparent frequency.
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