Editing Wave interference (section)

=== Multiple beams ===
Interference occurs when several waves are added together provided that the phase differences between them remain constant over the observation time.

It is sometimes desirable for several waves of the same frequency and amplitude to sum to zero (that is, interfere destructively, cancel). This is the principle behind, for example, [[three-phase electric power|3-phase power]] and the [[diffraction grating]].  In both of these cases, the result is achieved by uniform spacing of the phases.

It is easy to see that a set of waves will cancel if they have the same amplitude and their phases are spaced equally in angle.  Using [[phasor]]s, each wave can be represented as <math>A e^{i \varphi_n}</math> for <math>N</math> waves from <math>n=0</math> to <math>n = N-1</math>, where
<math display="block">\varphi_n - \varphi_{n-1} = \frac{2\pi}{N}.</math>

To show that
<math display="block">\sum_{n=0}^{N-1} A e^{i \varphi_n} = 0</math>

one merely assumes the converse, then multiplies both sides by <math> e^{i \frac{2\pi}{N}}.</math>

The [[Fabry–Pérot interferometer]] uses interference between multiple reflections.

A [[diffraction grating]] can be considered to be a multiple-beam interferometer; since the peaks which it produces are generated by interference between the light transmitted by each of the elements in the grating; see [[interference vs. diffraction]] for further discussion.