Question

An intensity of a sound wave is measured to be 1.87×104 W/m2 at position A, 120 m away from the source of this sound. A worker at position B, 308 m away from the source hears the sound.

What is the sound level 120 m way from the source?

Answer 1

Given:

$I_1=1.87*10^4\:\rm W/m^2$

$r_1=120\:\rm m$

$r_2=308\:\rm m$

The intensity is inversialy proportional to the square of distance. Hence

$$I_2=I_1\frac{r_1^2}{r_2^2}=1.87*10^4*\frac{120^2}{308^2}=2839\:\rm W$$