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  1. #1
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    Need Some Help

    A loudspeaker is placed between two observers who are 120 m apart, along the line connecting them. If one observer records a sound level of 60.0 dB and the other records a sound level of 90 dB, how far is the speaker from each observer?


    3.7,116.3

    4.3,115.7

    6.2,113.8

    8.6,111.4
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  2. #2
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    Quote Originally Posted by jaycas21 View Post
    A loudspeaker is placed between two observers who are 120 m apart, along the line connecting them. If one observer records a sound level of 60.0 dB and the other records a sound level of 90 dB, how far is the speaker from each observer?


    3.7,116.3

    4.3,115.7

    6.2,113.8

    8.6,111.4
    Let the distance to each observer be $\displaystyle d_1$ and $\displaystyle d_2$ respectivly, and the source level of the speaker be $\displaystyle SL$ then the sound level at the two observers are:

    $\displaystyle SL-20\log_{10}(d_1)=60 \mbox{ dB}\ \ \ \ ...(1)$

    and:

    $\displaystyle SL-20\log_{10}(d_2)=90 \mbox{ dB}\ \ \ \ ..(2)$

    Also:

    $\displaystyle d_1+d_2=120 \mbox{ m}\ \ \ \ ...(3)$.

    Subtract the first from the second equation:

    $\displaystyle
    20 \log_{10}(d_1) - 20 \log_{10}(d_2) = 20 \log_{10}(d_1/d_2) =30
    $

    so:

    $\displaystyle
    d_1/d_2 = 10^{3/2} \ \ \ \ ...(4)
    $

    Now solve the pair of simultaneous equations $\displaystyle (3)$ and $\displaystyle (4)$ in two variables $\displaystyle d_1$ and $\displaystyle d_2$

    (Just trying the given solutions, it looks to me as though the first answer is the one you want)

    RonL
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