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Apparent Frequency

A whistle of ...

Question

A whistle of frequency 540 Hz rotates in a horizontal circle of radius 2m at an angular speed of 15 rad/s. The highest frequency heard by a listener at rest with respect to the centre of circle:
(velocity of sound in air = 330ms $^{- 1}$ )

A

590Hz

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B

594Hz

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C

598Hz

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D

602Hz

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Solution

The correct option is B 594Hz
Highest frequency at rest, $f_{1} = (\frac{v}{v - v_{s}}) f$
$v_{s} = r ω = 30 m s^{- 1}$
$f_{1} = (\frac{330}{300}) 540 = 594 H z$

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