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Intensity : Log

  1. Nov 20, 2007 #1
    1. The problem statement, all variables and given/known data

    A hearing aid increases the sound intensity level, thereby allowing a person to hear better. For the following decibel increases, by how much does the intensity of sound increase?

    a)30dB
    b) 22dB

    2. Relevant equations

    [tex]\beta=10log (I/Io)[/tex]


    3. The attempt at a solution
    I substitute 30 in for the beta, and 1x10^-12 for the Io, but i can't seem to solve for the correct answer. Can anyone lend a hand?

    I really have trouble with bringng to log to the other side. Thanks
     
  2. jcsd
  3. Nov 21, 2007 #2

    Gib Z

    User Avatar
    Homework Helper

    [tex]\frac{\beta}{10} = \log_{10} (I/I_0)[/tex]

    By the definition of the logarithm, [tex]I/I_0 = 10^{\frac{\beta}{10}}[/tex]

    So [tex]I = I_0 \cdot 10^{\frac{\beta}{10}}[/tex]
     
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