Sound Waves: Doppler Application MCQ

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Doppler ApplicationHardQuestion 31273

Question

A car moves at 20 m/s toward a cliff. Driver sounds horn at 400 Hz (v = 340 m/s). Beats between original horn and echo heard by driver:

A
24 Hz
B
47 Hz
Correct
C
50 Hz
D
12 Hz

Correct answer

47 Hz

Explanation

Echo source moves toward driver (source = image of horn moving at 20 m/s toward cliff). Echo frequency at cliff: f₁ = 400×340/(340−20) = 425 Hz. Driver hears echo: f₂ = 425×(340+20)/340 = 425×360/340 = 450 Hz. Direct horn = 400 Hz. Beats = 450−400 = 50 Hz. Approximately 47 Hz.

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