When a sound is made, the particles that transmit the sound do so in an outward manner, sometimes for great distances depending on the initial energy that made the sound.

If a gun goes off, people could hear it no matter what direction they were in relation to it.  Since there is no new source of energy for the sound wave, as it travels and spreads out, it gets weaker.


 
shortly after the
sound is made, the
energy is represented 
by the surface of this
sphere
after twice as long,
the sound has moved
outward, and now the
same amount of energy
occupies more area,
so the sound must be weaker

QUESTION: How much bigger is the second sphere than the first one?
SAME QUESTION: How much weaker has the sound gotten from the first one to the second one?

The surface area of a sphere is given by 4pr2.
All we need to do is solve two problems, one with radius of 1, and another with r=2....

4pr2
=
12.6
 4pr2
=
50.3
The sound has gotten 4X weaker.
Written another way, Iold / Inew=rnew2 / rold2
where "I" is Intensity, and is often measured in watts/m2