Turntable Doppler Spectrum

MediumPhysElo Quiz #9

51.Turntable Doppler Spectrum

+10

A small siren emitting a pure tone of frequency

f_0

is mounted at the rim of a horizontal turntable of radius

R

, which rotates at constant angular velocity

\omega

. A stationary microphone is placed far away in the plane of rotation, at distance

d \gg R

from the center of the turntable. Assume

R\omega \ll v_s

, where

v_s

is the speed of sound. As the turntable spins, the detected frequency oscillates between a minimum

f_{\min}

and a maximum

f_{\max}

. Over many complete rotations, a histogram of the detected frequency is recorded. Which of the following best describes its shape?

ARoughly uniform across the range

f_{\min}

f_{\max}

BA single smooth peak centered at

f_0

, falling to zero at

f_{\min}

and

f_{\max}

CTwo tall peaks near

f_{\min}

and

f_{\max}

, with a minimum near

f_0

DThree equal peaks at

f_{\min}

f_0

, and

f_{\max}

EA symmetric bell-shaped curve centered at

f_0

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