Question:
An observer measures an intensity of 
at an unknown distance
from a source of spherical waves whose power output is also unknown.
The observer walks 
closer to the source and measures an
intensity of 
at this new location.
Calculate the power output of the source.
Solution:
Lets call the intensity and separation from the source at location 1, 
and 
respectively and the similarly at location 2 we have 
and 
respectively.
The intensity at any location is related to the power output of the source, P, by
for spherical waves, and therefore, taking the ratio at the
two locations we find
.
Now setting 
, we find that
.
We therefore find 
, and the 
.