What is wave intensity?

Wave intensity is a measure of the energy a wave conveys through a unit area perpendicular to its direction of travel per second. It is commonly referred to in terms of the 'brightness' of light or the 'loudness' of sound.

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

Where:

I = intensity (W m${}^{-2}$)

P = Power (W) - The rate of energy transported by the wave.

A = Area (m${}^2$) - The surface area through which the wave travels.

A higher intensity indicates a wave that is brighter or louder.

Worked example - Calculating the intensity of a wave

Calculate the intensity of a wave which has a power of 20 W and passes through an area of 4 m².

Step 1: Formula

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

Step 2: Substitution and correct evaluation

$\text{ I = }\frac{P}{A}=\frac{20}{4}=5{\text{ W m}}^{-2}$

Intensity and amplitude

Intensity is directly proportional to the square of the amplitude. This relation is because the energy of a wave is directly proportional to the square of its amplitude.

$\text{Intensity (I) }\propto {\text{ Amplitude}}^2$

If the amplitude of a wave is doubled, the intensity is quadrupled. For instance, if a wave with an amplitude of 2 units has an intensity of 10 W m^-2, a wave with an amplitude of 4 units (double the original) will have an intensity of:

$10{\text{ W m}}^{-2}\times 4=40{\text{ W m}}^{-2}$

This demonstrates how a small increase in amplitude can lead to a significant increase in intensity.

This principle means that sound intensity follows the inverse square law, decreasing rapidly with increasing distance from the source.