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Math Help - Decibel work.

  1. #1
    Newbie
    Joined
    Jan 2009
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    6

    Decibel work.

    I got through 3 problems involving decibels, and now it asks me this: "How many times more intensity does a sound of 47dB have than a sound of 42dB?"
    The decibel equation is: D = 10 log(I/10^-16) where I is intensity( W/cm^2) and D is decibels. And I might mention, intensity is in 10^-n and n is a number lower than 16
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
    Posts
    1,458
    Hi

    Let I1 be the intensity for D1 = 47 dB
    Let I2 be the intensity for D2 = 42 dB

    D_1 = 10 \log \frac{I_1}{I_0}

    D_2 = 10 \log \frac{I_2}{I_0}

    D_1 - D_2 = 10 \log \frac{I_1}{I_0} - 10 \log \frac{I_2}{I_0}

    D_1 - D_2 = 10 \,(\log \frac{I_1}{I_0} - \log \frac{I_2}{I_0})

    D_1 - D_2 = 10 \,\log \frac{\frac{I_1}{I_0}} {\frac{I_2}{I_0}}

    D_1 - D_2 = 10 \,\log \frac{I_1}{I_2}

    \frac{I_1}{I_2} = 10^{\frac{D_1 - D_2}{10}}
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