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 624-Hz source of sound. The microphone vibrates up and down in simple harmonic motion with a period of 2.31 s. The difference between the maximum and minimum sound frequencies detected by the microphone is 2.26 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.

Answer 1

the Doppler shift is half of the frequency difference
... higher freq going down, lower going up

the speed indicated by the Doppler shift is the velocity of the microphone at the midpoint of its travel

using the period and max velocity, find the amplitude