A microphone is attached to a spring that is suspended from the ceiling, as the

Question

A microphone is attached to a spring that is suspended from the ceiling, as the drawing indicates. Directly below on the floor is a stationary 618-Hz source of sound. The microphone vibrates up and down in simple harmonic motion with a period of 2.05 s. The difference between the maximum and minimum sound frequencies detected by the microphone is 2.15 Hz. Ignoring any reflections of sound in the room and using 343 m/s for the speed of sound, determine the amplitude (in m) of the simple harmonic motion.

Explanation / Answer

using doppler effect f'/f = (c+vr)/(c+vs) here vs=0 maximumf1 and minimumf2 sound freq will be detected at the mean position of oscillation when vr is max (-ve when going up and vice-versa) f1-f2/f = 2vr/c vr = 0.596m/s T = 2.05s = 2pi*sqrt(m/k) 0.5 kA^2 = 0.5mV^2 A = V * sqrt(m/k) = 0.194 m

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