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 $\displaystyle d_1$ 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