Intensity

When we discuss waves, we define intensity as the power incident on an area.

$$I=\frac{P}{A}$$

From a point source of distance $x$:

$$I=\frac{P}{4\pi x^2}$$

i.e., $I\propto x^{-2}$.

The intensity at a particular point is related to the amplitude $a$ of the wave at that point, i.e., $I\propto A^2$. What this means is that, for example, doubling the amplitude of a wave increases the energy carried by a factor of 4. And so on.