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)`

Options

A. 400.0 Hz to 484.0 Hz
B. 403.3 Hz to 480.0 Hz
C. 400.0 Hz to 480.0 Hz
D. 403.3 Hz to 484.0 Hz

Answer

C

Explanation

Frequency heard by the observer will be maximum when the source is in position D. In this case, source will be approaching towards the stationary observer, almost along the line of sight (as observer is stationed at a large distance).
`therefore upsilon_(max)=(v)/(v-v_(s))xxupsilon=(330)/(330-1.5xx20)xx440=484Hz`
Similary, frequency heard by the observer will be minimum when the source reaches at the position B, Now, the source will be moving away from the observer.
`therefore upsilon_(min)=(v)/(v+v_(s))xxupsilon=(330)/(330+1.5xx20)xx440`
`=(330xx440)/(360)=403.3Hz`