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

Question

A block with a speaker bolted to it is connected to a springhaving spring constant k = 20.0 N/m. The total mass of the block and speakeris 5.00 kg, and the amplitude of thisunit's motion is 0.500 m. Assume that the speed of sound is 343 m/s.

(a) If the speaker emits sound waves offrequency 440 Hz, determine the highest and lowest frequencies heard by the person to the right of the speaker.

(b) If the maximum sound level heard by the person is 60.0 dB when he is closest to the speaker, 1.00 m away; what is the minimum sound level heard by the observer?

Show/Explain all work.

Explanation / Answer

a)

m = mass of block = 5 kg

A = amplitude = 0.5 m

using conservation of energy

maximum KE = maximum spring energy

(0.5) m v2 = (0.5) k A2

5 v2 = 20 (0.5)2

Vmax = 1 m/s

minimum speed = Vmin = 0 m/s

V = speed of sound = 343 m/s

observed frequency when the speaker is coming towards the listener at maximum speed given as

f' = V f / (V - Vmax) = 343 x 440 / (343 - 1) = 441.3 Hz

observed frequency when the speaker is going away from the listener at maximum speed given as

f' = V f / (V + Vmax) = 343 x 440 / (343 + 1) = 438.7 Hz

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