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

Question

A block with a speaker bolted to it is connected to a spring having spring constant k = 33.0 N/m as shown in the figure below. The total mass of the block and speaker is 5.00 kg, and the amplitude of this unit's motion is 0.610 m. If the speaker emits sound waves of frequency 440 Hz, determine the lowest and highest frequencies heard by the person to the right of the speaker. (Enter your answer to three significant figures.)

lowest frequency     Hz highest frequency     Hz A block with a speaker bolted to it is connected to a spring having spring constant k = 33.0 N/m as shown in the figure below. The total mass of the block and speaker is 5.00 kg, and the amplitude of this unit's motion is 0.610 m. If the speaker emits sound waves of frequency 440 Hz, determine the lowest and highest frequencies heard by the person to the right of the speaker. (Enter your answer to three significant figures.)

Explanation / Answer

w = sqrt [k / m]

= sqrt [33.0 / 5.00] = 2.57 s^-1

Maximum speed of the speaker Vmax = w A

= (2.57 s^-1) (0.610) = 1.57 m/s

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When the speaker is moving at maximum speed toward the person he hears a

frequency f' = [v / v - vs] f

= [343 / 343 - 1.57] 440

= 442 Hz

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When the speaker is moving at maximum speed away from the person he hears a

frequency f' = [v / v + vs] f

= [343 / 343 + 1.57] 440

= 437.99 Hz

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