A whistle emitting a sound of frequency `440 H`z is tied to string of `1.5 m` length and rotated with an angular velocity of `20 rad//sec` in the horizontal plane. Then the range of frequencies heard by an observer stationed at a large distance from the whistle will `(v=330 m//s)`

Answer

`f_(max) = 484 Hz , f_(min) = 403.3 Hz`

Explanation

`V_(S) =` Speed of source(whistle)
`= R_(omega)`
`= (1.5)(20)m//s`
`V_(s) = 30 m//s`

Maximum frequency will be heard by the observer `O` in position `P` of whistle and minimum in position `Q` of whistle. Now-
`f_(max) = f((V)/(V - V_(S)))` where `V =` Speed of sound in air
`= (440)((330)/(330 - 30)) Hz`
`f_(max) = 484 Hz`
and `f_(min) = f((V)/(V + V_(S)))`
`= (440)((330)/(330 + 30))`
`f_(min) = 403.33 Hz`
Therefore, range of frequencies heard by observer is form `403.33 Hz` to `484 Hz`.