Wave intensity
- 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
- Where
- I is intensity in W m−2
- P is power in W
- A is area in m2
- 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
- Where
- A is amplitude in m
- f is frequency in Hz
- Recall that ∝ means "proportional to"
- 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:
Inverse square law for intensity
Intensity is proportional to the amplitude squared
- Assuming none of the wave energy is absorbed, the intensity I decreases with increasing distance from the source
- The inverse square law states that
-
- The inverse square law means when the source is twice as far away, the intensity is 4 times smaller
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?
Answer:
Step 1: Compare waves Q and P:
- The amplitude of wave Q is twice the amplitude of wave P
- The frequency of wave P is double the frequency of wave Q
Step 2: Evaluate how amplitude affects the intensities:
- Q has twice the amplitude of P
- The ratio of amplitudes squared is equal to the ratio of intensities, because intensity and amplitude squared are proportional
- So Q's larger amplitude increases its intensity by a factor of 4
Step 3: Evaluate how frequency affects the intensities:
- Q has half the frequency of P
- The ratio of frequencies squared is equal to the ratio of intensities because intensity and frequency squared are proportional
- So Q's lower frequency decreases its intensity by a factor of 4
Step 4: Determine the intensity of wave P in terms of I0 :
- P has a lower amplitude which reduces its intensity by a factor of 4 compared to Q
- However, P has a higher frequency which increases its intensity by a factor of 4 compared to Q
- These effects cancel out, so wave P has an intensity of I0 , which is equal to that of wave Q
Examiner 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