Intensity of a Progressive Wave
- 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
- The unit of intensity is Watts per metre squared (W m-2)
- 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
- This means that 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 which 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?
Examiner Tip
The key takeaway here is:
Intensity has an inverse square relationship with distance (not a linear one)
This means the energy of a wave decreases very rapidly with increasing distance