A whistle of frequency of 540Hz rotates ini a circle of radius 2m at an angular speed of 15rad`//`s. What is the lowest and highest frequency heard by a listener a long distance away at rest w.r.t centre of the circle. Can the apparent frequency be ever equal to the actuall frequency ? Take `v=330m//s`

Explanation

In figure, O is the centre of circle in which the whistle (the source) rotates. L is position of listener.
Now, `v=540Hz, r=2m`
`omega=15rad//s`
`upsilon_(s)=romega=2xx15=30m//s`
`upsilon=330m//s`
Frequency will be minimum, when source is at B, moving away from listener.
`v^(')=(upsilonxxv)/(upsilon+upsilon_(s))=(330xx540)/(330+30)=495Hz`
Frequency will be maximum, when source is at D, moving towards listener.
`v^('')=(upsilonxxv)/(upsilon-upsilon_(s))=(330xx540)/(330-30)=594Hz`
When source is at A or C, speed of source along the line OL is `v_(s) cos90^(@)=` Zero.
`:. v^(''')=v=` actual frequency of source
`=540Hz`