Question

Suppose a spherical loudspeaker emits sound isotropically at $10W$ into a room with completely absorbent walls, floor, and ceiling (an anechoic chamber).
What is the intensity of the sound at distance $d=3.0m$ from the center of the source?

Answer 1

The source being isotropic means $A_{\text{sphere}}=4\pi r^2$ is used in the intensity definition $I=P/A.$
since intensity is proportional to the square of the amplitude this further implies
$\frac{I_2}{I_1}$

$={\left(\frac{s_{m2}}{s_{m1}}\right)}^2$

$=\frac{P/4\pi r_2^2}{P/4\pi r_1^2}={\left(\frac{r_1}{r_2}\right)}^2$

or $s_{m2}/s_{m1}=r_1/r_2$

$I=P/4\pi r^2=\left(10W\right)/4\pi (3.0m{)}^2=0.088W/m^2$