# 2.12 Equation for the Intensity of Radiation

## Equation for the Intensity of Radiation

• Progressive waves transfer energy
• The amount of energy passing through a unit area per unit time is the intensity of the wave
• Therefore, the intensity is defined as power per unit area Intensity is equal to the power per unit area

• The area the wave passes through is perpendicular to the direction of its velocity
• The intensity of a progressive wave is also proportional to its amplitude squared and frequency squared Intensity is proportional to the amplitude2 and frequency2

• This means, if the frequency or the amplitude is doubled, the intensity increases by a factor of 4 (22)

#### Spherical Waves

• A spherical wave is a wave from a point source that spreads out equally in all directions
• The area the wave passes through is the surface area of a sphere: 4πr2
• As the wave travels further from the source, the energy it carries passes through increasingly larger areas as shown in the diagram below: Intensity is proportional to the amplitude squared

• Assuming there’s no absorption of the wave energy, the intensity I decreases with increasing distance from the source
• Note the intensity is proportional to 1/r2
• This means when the source is twice as far away, the intensity is 4 times less

• The 1/r2 relationship is known in physics as the inverse square law

#### Worked example

The intensity of a progressive wave is proportional to the square of the amplitude of the wave. It is also proportional to the square of the frequency. The variation with time t of displacement x of particles when two progressive waves Q and P pass separately through a medium are shown on the graphs The intensity of wave Q is I0. What is the intensity of wave P?  #### Exam Tip

The key concept with intensity is that it has an inverse square relationship with distance (not a linear one). This means the energy of a wave decreases very rapidly with increasing distance ### Get unlimited access

to absolutely everything:

• Unlimited Revision Notes
• Topic Questions
• Past Papers 