Intensity

This lesson covers: 

  1. Definition of intensity and its relation to wave energy
  2. Calculating intensity using its units and equation
  3. Relationship between intensity, amplitude, and energy transport in waves

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.


I = AP​


Where:

I = intensity (W m−2)

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

A = Area (m2) - 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

I = AP​


Step 2: Substitution and correct evaluation

I = AP​=420​=5 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.


Intensity (I)∝Amplitude2


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 W m−2×4=40 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.