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# Wave intensity

## 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.

The light from the sun on the surface of the earth is of high intensity.

## Uniformly radiating point source

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.

Wave pulses created by a uniformly radiating point source.