A whistle of frequency 540 Hz rotates in a circle of radius 2 m at an angular speed of `15rads^(-1)`. What is the lowest and highest frequency heard by a listener a long distance away at rest with respect to centre of the circle ? Can the apparent frequecny be ever equal to the actual frequency? Take `V=330ms^(-1)`.

Explanation

The situation is shown in the figure.

Speed of source (whistle),
`v_(s)=romega=2xx15=30ms^(-1)`
Actual frequency,
`v=540Hz,`
Speed of sound,
`V=330ms^(-1)`
When the whistle (at position B) is moving away from the observer, the apparent frequency is lowest. It is given by
`v'=(V)/(V+v_(s))xxv=(330)/(330+30)xx540`
=495Hz
When the whistle (at position D) is moving towards the observer, the apparent frequency is highest. It is given by
`v''=(V)/(V-v_(s))xxv=(330)/(330-30)xx540`
=594 Hz.
When the whistle is at A (or) C, its speed along. `OL=v_(s)cos09^(@)=0`
`:.` Apparent frequency= Actual frequency.