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A whistle emitting a sound of frequency 440 Hz is tied to a string of 1.5m length and rotated with an angular velocity of 20 rad s -1 in the horizontal plane. Calculate the range of frequencies heard by an observer stationed at a large distance form the whistle.

A whistle emitting a sound of frequency 440 Hz is tied to a string of 1.5m length and rotated with an angular velocity of 20 rad s-1 in the horizontal plane. Calculate the range of frequencies heard by an observer stationed at a large distance form the whistle. 

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
Hello Student,
Please find the answer to your question
The whistle which is emitting sound is being rotated in a circle.
236-215_6.png
We know that v = rω = 1.5 x 20 = 30 ms-1
When the source is instantaneously at the position A, then the frequency heard by the observer will be
v’ = v [v/v – vs] = 440 [330/330 – 30] = 484 Hz
when the source is instantaneously at the position B, then the frequency heard by the observer will be
v” = v[v / v + vs] = 440 [330/330 + 30] = 403.3 Hz
Hence the range of frequencies heard by the observer is
403.3 Hz to 484 Hz.

Thanks
Aditi Chauhan
askIITians Faculty

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