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  1. #1
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    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?


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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 d_1 and d_2 respectivly, and the source level of the speaker be SL then the sound level at the two observers are:

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

    and:

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

    Also:

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

    Subtract the first from the second equation:

    <br />
20 \log_{10}(d_1) - 20 \log_{10}(d_2) = 20 \log_{10}(d_1/d_2) =30<br />

    so:

    <br />
d_1/d_2 = 10^{3/2} \ \ \ \ ...(4)<br />

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