Need Some Help

**jaycas21** · June 10th 2007, 06:22 AM

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

**CaptainBlack** · June 10th 2007, 07:58 AM

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:

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

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

Thread: Need Some Help

LinkBack

Thread Tools

Display

Need Some Help