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A whistle of frequency 385 Hz rotates in a horizontal circle of radius 50 cm at an angular speed of 20 radians s⁻¹. The lowest frequency heard by a listener a long distance away at rest with respect to the centre of the circle, given velocity of sound equal to 340 ms⁻¹, is

1. 396 Hz
2. 363 Hz
3. 374 Hz
4. 385 Hz

Correct answer: 363 Hz

Solution

The lowest frequency is heard when the source moves away from the listener at maximum speed. The speed of the source is v_s = rω = 0.5 × 20 = 10 m/s. Using the Doppler effect formula for a source moving away, f' = f(v / (v + v_s)), we get f' = 385 × (340 / (340 + 10)) = 363 Hz.

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