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Sound intensity and ocean microphone

  1. Dec 10, 2003 #1
    The problem states:
    A microphone in the ocean is sensitive to sounds emitted by popoises. To produce a usable signal , sound waves striking the microphone must have an intesity of 10.6 dB. If porpoises emit sound waves with a power of 0.0502 W, how far can a porpoise be from the microphone and still be heard? Disregard ansorbtion of sound waves by water.

    I tried putting 10.6 decibels in the equation dB=10Log(I/Io)
    and I solved for intensity to be 1.148E-10W/m^2

    I then used that number in the I = P/4pi r^2 formula.
    Solving for r I got 5.89E+3m.

    But the right answer it the book is 1.87E+4
    Can anyone tell me where I went wrong??
  2. jcsd
  3. Dec 10, 2003 #2


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    Science Advisor

    10log(I/(10^-12)) = 10.6
    log(I/(10^-12)) = 1.06
    I/(10^-12) = 10^1.06
    I = 1.148e-11

    I = P/(4pi r^2)
    r^2 = P/(4pi I)
    r^2 = 0.0502/(4pi 1.148e-11)
    r^2 = 3.4797e8
    r = 18654m
    r = 1.87e4

    I think the error was in what you thought the value for I was. Your I is 10x as big as mine.
  4. Dec 11, 2003 #3
    Nice thanks
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