Suppose a spherical loudspeaker emits sound isotropically at 10 W into a room with completely absorbent walls, floor, and ceiling (an anechoic chamber). (a) What is the intensity of the sound at distance d = 3.0 m from the center of the source? (b) What is the ratio of the wave amplitude at d = 4.0 m to that at d = 3.0 m?
I = P/A
I ∝ A^2 (According to my TA)
The Attempt at a Solution
I = P/A
I = 10/4π(3.0)^2 = 0.0884 W/m^2
According to my TA, Intensity is proportional to the amplitude squared. I was wondering if I could use this relationship to answer part B.
Intensity at 3.0 m = 0.0884 W/m^2
Amplitude at 3.0 m = 0.297 m
Intensity at 4.0 m = 0.0497 W/m^2
Amplitude at 4.0 m = 0.223 m
Ratio: 0.223/0.297 = 0.751
Not sure if this is the correct approach or if the relationship I ∝ A^2 is correct or not.
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