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A source of sound is moving along a circular orbit of radius 3 meters with an angular velocity of 10 rad /s. A sound detector far away from the source is executing linear simple harmonic motion along the line BD with an amplitude BC = CD = 6 meters. The frequency of oscillation of the detector is 5/π per second. The source is at the point A when the detector is at the point B. If the source emits a continuous sound wave of frequency 340 Hz, find the maximum and the minimum frequencies recorded by the detector.

A source of sound is moving along a circular orbit of radius 3 meters with an angular velocity of 10 rad /s. A sound detector far away from the source is executing linear simple harmonic motion along the line BD with an amplitude BC = CD = 6 meters. The frequency of oscillation of the detector is 5/π  per second. The source is at the point A when the detector is at the point B. If  the source emits a continuous sound wave of frequency 340 Hz, find the maximum and the minimum frequencies recorded by the detector.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
Hello Student,
Please find the answer to your question
The angular frequency of the detector = 2πv
= 2π x 5/π = 10 rad/s
The angular frequency of the detector matches with that of the source.
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⇒ When the detector is at C moving towards D, the source is at A1 moving leftwards. It is in this situation that the frequency heard is minimum
v’ = v [v – v 0/v + vs] = 340 x (340 – 60)/(340 + 30) = 257.3 Hz
Again when the detector is at C moving towards B, the source is at A3­ moving rightward. It is in this situation that the frequency heard is maximum.
v” = v[ v + v0/v – vs] = 340 x (340 + 60)/(340 – 30)= 438.7 Hz

Thanks
Aditi Chauhan
askIITians Faculty

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