# Wave intensity

The intensity $$(I)$$ of a wave is a physical quantity measuring how "concentrated" (or "dense") a wave is within a particular area. It depends on both the properties of the wave itself as well as the area over which it is spread.

Light from a light bulb (low intensity) can only brighten a dark room. Light from a laser (high intensity), on the other hand, can cut through steel.

More precisely, the intensity is **the energy flux, or the power of the wave per unit area** normal to the direction of motion of the wave (or the energy per unit time per unit area). It is given by: $$$I=\frac{P}{A}$$$ $$P$$ is the power (energy per unit time) of the wave and $$A$$ is the area normal (i.e. whose surface is perpendicular) to the direction of wave motion.

Intensity is proportional to the square of the amplitude of the wave (i.e. $$I\propto x_{0}^{2}$$)

The SI unit for intensity is watts per metre squared $$(\text{W m}^{-2})$$.

The intensity is a measure of the loudness of a sound in a particular area or of the brightness of light.

A uniformly radiating point source is an idealised source of waveforms that has no physical dimensions and which radiates energy in all directions equally.

An approximation of a uniformly radiating source is a small pebble dropped into the middle of a big pond of water. The waves caused by the pebble will form an almost perfect circle.

The **intensity of waves** produced by a uniformly radiating point source at a distance $$r$$ from the source is given by: $$$I=\frac{P_{\text{S}}}{4\pi r^{2}}$$$ The intensity of waves produced by a uniformly radiating point source is equivalent to that of a normal wave passing through a surface of area $$4\pi r^{2}$$ (i.e. the surface area of a sphere).

This equation assumes that the wave **does not lose energy** as it travels from the source.

$$P_{\text{S}}=$$ power of the source; $$x_{0}=$$wave amplitude.