Relation between intensity and amplitude

  • #1
When superposing waves in say double slit interference from two slits, I seem to have come across two approaches:
1. Sum the two waves in complex form to get the resultant amplitude, take the real part, and square to get the intensity, i.e I=[Re(A)]2
2. Sum the two waves in complex form to get the resultant complex amplitude. Then take the modulus squared to get the intensity, i.e I=AA*.
What is it that makes these two approaches give the same result. Mathematically they seem to be different to me. Also, where does the second come from? I know I=cε0E2 but this doesn't involve the modulus does it?
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  • #2
If you think of the complex A in the exponential form, ## A = r e^{i \theta} ##, then ## [Re(A)]^2 =( r \cos \theta) ^2##.
Also, ## AA^* = r e^{i \theta}r e^{-i \theta} =r^2##, therefore these are mathematically the same only when you are approaching head on (angle = 0 or pi).

What is the difference between intensity and amplitude?

Intensity refers to the amount of energy per unit area, while amplitude refers to the maximum displacement of a wave from its equilibrium position.

How are intensity and amplitude related?

Intensity and amplitude are directly proportional to each other. As the amplitude of a wave increases, the intensity also increases.

How can intensity and amplitude affect the properties of a wave?

The intensity and amplitude of a wave can affect its speed, frequency, and wavelength. A higher intensity and amplitude can lead to a faster wave with a higher frequency and shorter wavelength.

What units are used to measure intensity and amplitude?

The SI unit for intensity is watts per square meter (W/m^2), while the SI unit for amplitude is meters (m).

Can intensity and amplitude be changed?

Yes, intensity and amplitude can be changed by altering the energy or force behind the wave. For example, changing the source of the wave, such as increasing the amplitude of a guitar string, can change the intensity and amplitude of the resulting sound wave.

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