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).

A whistle of frequency 540 Hz rotates in a circle of radius 2 m at an

1.	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).
Answer» Solution :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.