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Sound wave confusion

  1. Nov 29, 2007 #1
    1. The problem statement, all variables and given/known data
    In general, if a sound has intensity of beta dB at 1 m from the source, at what distance d_0 from the source would the decibel level decrease to 0 dB? Since the limit of hearing is 1 dB this would mean you could no longer hear it.
    Express the distance in terms of beta. Be careful about your signs!

    I know that the relationship between the intensity and distance is an inverse square relationship, but i'm not sure what exactly the question is looking for. Do i have to find the distance when it goes to 0 or to 1 ? Because if that is zero, then even after 100m, the intensity wouldnt be zero ?

    im confused !
  2. jcsd
  3. Nov 29, 2007 #2
    anyone ?
  4. Nov 29, 2007 #3


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    You are right, the intensity won't fall to zero. But there is a log in the relation between dB and intensity.
  5. Nov 30, 2007 #4
    so how do i get it to zero ? i mean keep on increasing distance till log of it = 0, and how do i write it in terms of beta ? :S
  6. Nov 30, 2007 #5


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    Ok, let 'I' be the intensity at 1m and 'I0' be the intensity at 0dB. dB=10*log(I/I0) (all logs base 10). So beta=10*log(I/I0). You know at distance Rm the intensity becomes I/R^2. So 0=10*log((I/I0)/R^2). Now use a property of logs.
  7. Nov 30, 2007 #6
    Why do you say the limit of hearing is 1 dB?
  8. Nov 30, 2007 #7

    thanks a ton ! finally got it .... this one was a bugger ! thanks again...
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