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Loudspeaker Question (Sound and Intensity)

  • #1
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Homework Statement


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?

Homework Equations


[/B]
I = P/A

I ∝ A^2 (According to my TA)

The Attempt at a Solution


[/B]
Part A:

I = P/A

I = 10/4π(3.0)^2 = 0.0884 W/m^2

Part B:

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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Answers and Replies

  • #2
berkeman
Mentor
57,486
7,510

Homework Statement


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?

Homework Equations


[/B]
I = P/A

I ∝ A^2 (According to my TA)

The Attempt at a Solution


[/B]
Part A:

I = P/A

I = 10/4π(3.0)^2 = 0.0884 W/m^2

Part B:

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.
You are already given the power, so you only need to figure out what the surface areas are at the different radii to get the Intensity in W/m^2.

Intensity may be proportional to the amplitude of the sound pressure wave squared, but you don't need that in this problem.
 

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