A whistle of frequency 540 Hz 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 in air as 330 m/s. Can the apparent frequency be ever equal to actual?

Explanation

Apparentfrequency will be minimum when the source is at N and moving away from the observer.

`f_("min") + (v/(v +v_s)) f =(330/(330 +30)) xx 540 = 495 Hz`
Frequency will be maximum when source is at L and approachign the observer.
`f_(max) =(v/(v-v_s)) f = (330/(330 -30)) (540) = 594 Hz`
Further when source is at M and K, angle between velocity of source and line joining source and observer is `90^@" or " v_s cos theta =v_s cos 90^@ =0`. So, there will be no change in the apparent frequency. i.e., no Doppler effect.