Intensity of sound and finding distance from sound source

[leinad0213]

The intensity of the sound from a certain source is measured at two points along a line from the source. The points are separated by 11.8 m, the sound level is 68.10 dB at the first point and 60.31 dB at the second point. How far is the source from the first point?


Know:
I = P/A = Ps/(4*pi*r^2)
SL = 10log(I/Io)

Io = 1*10^-12 W/m^2

Using these equations I found both I(1) and I(2) which turned out to be I(1) = 6.46 * 10^-6 and I(2) = 1.07 * 10^-6. Each of these equal P/(4*pi*r^2) except for I(2), r = r1+d where d=11.8m. I put I(1)/I(2) which canceled out P and made it [(r1+1.8)^2]/(r1^2). When I expand and solve, the answer I get is incorrect. Am I missing some detail for solving this problem?

 

[jbsteele]

The correct answer is 8.48 meters from the first point. To solve this problem, you need to use the fact that sound intensity is inversely proportional to the square of the distance from the source. In other words, the sound intensity at a certain point will be inversely proportional to the square of the distance from the source. Therefore, you can set up the following equation: I1/I2 = (r1+d)^2/r1^2 Where I1 is the sound intensity at the first point, I2 is the sound intensity at the second point, r1 is the distance from the source to the first point, and d is the distance between the two points. Solving this equation for r1 will give you the answer.