A storm warning siren emits sound uniformly in all direction

A storm warning siren emits sound uniformly in all directions. Along a line that is drawn radially outward from the sound source (the siren) determine the positions of two points, 0.77 m apart, such that the intensity level at one point is 4.12 dB greater than the intensity level at the other.

point closer to siren: m

point farther from siren: m

Solution

Power of source = P

INtensity at r1 = I1 = P/4*pi*(r1)^2

Intensity at r2 = I2 = P/4*pi*(r2)^2

Now, 10log(I1/I2) = 4.12

20log(r2/r1) = 4.12

r2/r1 = 1.606

but r2 - r1 = 0.77

so r2 = 1.606(r2 - 0.77) = 1.606 r2 - 1.2366

r2 = 2.04 m

r1 = 1.27 m