Physics
posted by Shaniquaa .
The intensity of sound from a source is measured at two points along a line from the source. The points are separated by 14.7 m, the sound level is 67.10 dB at the first point and 55.68 dB at the second point. How far is the source from the first point?

The difference in sound intensity between the two points is 11.42 dB
A 10 dB drop corresponds to a factor of 10 dropoff in intensity (sound power per area), and 11.42 corresponds to a factor of 10^1.142 = 13.87.
Intensity obeys an inverse square law. If R1 is the distance from the source to the place where the higher signal is recorded,
P2/P1 = 1/13.87 = (R1/R2)^2
= [R1/(R1+14.7)]^2
1+ (14.7/R1) = sqrt13.87 = 3.72
14.7/R1 = 2.72
Solve for R1