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Homework Help: Sound Energy & Intensity

  1. Feb 11, 2010 #1
    1. The problem statement, all variables and given/known data

    a)A sound wave with an intensity level of 80.1 dB is incident on an eardrum of area 0.600 10-4 m2. Calculate the energy is absorbed by the eardrum in 4.00 minutes in microJ

    b)The sound level 25.0 m from a loudspeaker is 69.0 dB. Calculate the rate at which sound energy is produced by the loudspeaker, assuming it to be an isotropic source.


    2. Relevant equations



    3. The attempt at a solution

    We know tha the refernece intensity (I0) = 10-12W/m2
    We know that sound intensity level is
    β = 10dB log (I/Io)
    Then 80.1dB = 10dB log (I/Io)
    8.01 = log (I/Io)
    Now finding I then substitue in the equation
    I =P/A
    = E/AΔt
    Then the area covered by the sound is
    A = 0.600 10-4 m2.
    Then energy is absorbed by the eardrum in 4.00 minutes ( i.e 4*60s = 240s) in μJ.
    E = IAΔt

    I got 1.44x10-14 (which ended up being wrong))


    b)
    We know tha the refernece intensity (I0) = 10-12W/m2
    We know that sound intensity level is
    β = 10dB log (I/Io)
    Then 69dB = 10dB log (I/Io)
    6.9 = log (I/Io)
    Now finding I then substitue in the equation
    I =P/A
    Then the area covered by the sound is
    A = 4π(25.0m)2
    = 7850m2
    Now the total power of the source is
    P = IA in W Or J/s

    I got 7.85x10-9 please help. what am I doing wrong?
     
  2. jcsd
  3. Feb 12, 2010 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Your calculation in a) looks correct, although I got 1.47... x 10-6 J. Did you round before your final answer? Also, how did you get a 10-14, are you sure you did not go from J to MJ instead of the other way around?

    I'll let you check b) again then, probably it's a similar mistake.
     
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