A whistle emitting a sound of frequency `440 Hz` is tied to a string of `1.5 m` length and roated with an angular velocity of `20 rad//s` in the horizontal plane. Calculate the range of frequencies heard by an observer stationed at a larger distance from the whistle .(Speed of sound =`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

D

Explanation

Frequency heard by the observes will be maxmum 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 larger distance.)
`n_(max)=(v)/(v-v_S)n`
`=(330xx440)/(330-1.5xx20)`
`=484Hz`
Similarly, frequency heard by the observer will be minimum when the source reaches at position B. Now, the source will be moving away from the observer.
`n_(min)=(v)/(v+v_S)xxn=(330)/(330+1.5xx20)xx440`
`=(330xx440)/(360)=403.3Hz`