1. ## 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

2. Originally Posted by jaycas21
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:

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

so:

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

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