The intensity of a progressive wave is the radiant power passing through a surface per unit area.
where P is the power and A is the cross-sectional area.
The units are watts per square metre or Wm-2. When a wave travels from a point source, the energy spreads out uniformly in all directions. The power is spread out over an area which is the surface of a sphere. At a distance r from the source,
So the intensity has an inverse square relationship with the distance from the source. At a distance r from the source,
As the energy spreads out the amplitude decreases. This means the average speed decreases and the kinetic energy is less. Since the kinetic energy is proportional to the square of the speed, and the speed is proportional to the amplitude. It follows that the kinetic energy is proportional to the square of the amplitude.
so the intensity α (amplitude)2.
Intensity
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Specification: OCR Physics A (H156), AS-level, 4.4.1 Wave motion. Topic: Waves.