4.6.5 Intensity of a Wave

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?

Exam 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

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