A block with a speaker bolted to it is connected to a spring

A block with a speaker bolted to it is connected to a spring having spring constant k = 17.0 N/m and oscillates as shown in the figure below. The total mass of the block and speaker is 4.00 kg, and the amplitude of this unit\'s motion is 0.500 m. The speaker emits sound waves of frequency 460 Hz.

(a) Determine the highest frequencies heard by the person to the right of the speaker. (Give your answer correct to 1 Hz.) Hz

(b) Determine the lowest frequencies heard by the person to the right of the speaker. (Give your answer correct to 1 Hz.) Hz

(c) If the maximum sound level heard by the person is 62.0 dB when the speaker is at its closest distance d = 1.00 m from him, what is the minimum sound level heard by the observer? dB

Solution

The speed v_max is the maximum speed of the oscillator and it is given by

v_max = w A

w = sqrt [k/m] = sqrt [17/4] = 2.06

v_max = 2.06 * 0.5 = 1.03

f\' = v_s / v_s - vpolice f = [343 / 343 - 1.03] * 460

= 461.39 Hz

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f\' = [v_s / v_s + v_police ] f = [343 / 343 + 1.03] * 460

= 458.62 Hz