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Loudspeaker Question (Sound and Intensity)

  1. Feb 9, 2017 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations

    I = P/A

    I ∝ A^2 (According to my TA)

    3. The attempt at a solution

    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.
     
    Last edited by a moderator: Feb 9, 2017
  2. jcsd
  3. Feb 9, 2017 #2

    berkeman

    User Avatar

    Staff: Mentor

    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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