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Homework Help: Difference in radius, same power and intensity?

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data
    How much acoustic power propagates through a spherical surface (sound source in centre) with radius equal to 1.0m? with radius equal to 5.0m?

    I = 10^-2 W/m^2
    r = 1.0m or 5.0m
    f = 50kHz
    t = 2.0*10^-3s
    IL = 100dB

    2. Relevant equations
    I = P/4∏r^2

    3. The attempt at a solution
    i figured out that when r = 1.0, power must be 1.3*10^-1W. However, when I work out the intensity when r = 5.0, i get:

    10^-2 = P/4*∏*25
    (10^-2)(4*∏*25) = P
    3.1W = P

    However, the answer states that the power for both spheres is 0.12W... What concept am I not understanding?
  2. jcsd
  3. Oct 9, 2011 #2


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    Homework Helper

    It is the same sound source which produces I = 10^-2 W/m^2 at unit distance, so its power is 0.13 W. The same power propagates through any concentric spherical surface, with less and less intensity.

  4. Oct 9, 2011 #3
    ooh, i see. so basically the power stays the same because it's the same sound source (a bat, in this case), but the intensity becomes a lot less in distance. i understand now, thanks!
  5. Oct 9, 2011 #4


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    Homework Helper

    You understood it quick:smile: You are welcome.

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