The intensity of a wave decreases as the distance from the source increases. This is because the wave spreads out as it travels, so the energy is distributed over a larger area. The relationship between intensity and distance is given by the inverse square law, which states that the intensity is inversely proportional to the square of the distance from the source. This means that if the distance from the source is doubled, the intensity will be reduced by a factor of four.

Here is a mathematical representation of the inverse square law:

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

Where:

* I is the intensity in watts per square meter (W/m^2)

* P is the power of the source in watts (W)

* r is the distance from the source in meters (m)

The inverse square law applies to all types of waves, including sound waves, light waves, and water waves.