An electric buzzer with a mass of 200 g is attached to a light weight spring. Th

Question

An electric buzzer with a mass of 200 g is attached to a light weight spring. The buzzer is bouncing back and forth in simple harmonicmotion. A microphone which is at rest records the sound from the buzzer as itbounces. Using the recording from the microphone, the frequency of the buzzeris found to vary from 860 Hz to 878 Hz.

a) Determine the maximum magnitude of the velocity of the motion.

b) Determine the total energy in the oscillating buzzer.

c) The amplitude of the motion is 30cm, then find the spring constant, k.

Explanation / Answer

(a) using doppler's effect:
maximum frequency is observed when buzzer is coming toward the microphone with maximum velocity and minimum is when buzzer is going away with maximum velocity.

suppose maximum velocity is v. then applying doppler's effect:

f = Vsound f0 / (Vsound + v )

when coming toward (v will be negative)

878 = 343 f0 / (343 - v )

whn gooing away (v will be +ve)

869 = 343f0 / (343 + v)

dividing,

878/869 = (343 f0 (343 + v)) / (343f0 (343 - v))

346.55 - 1.01v = 343 + v

v = 1.77 m/s ............Maximum velocity.

(B) total energgy = m Vmax^2 /2

= 0.200x 1.77^2 /2 = 0.312 J

(C) total energy = k A^2 /2

0.312 = k (0.30^2) /2

k =6.94 N/m

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