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Do they need to have the same frequency or amplitude? Should they pass through a given space at the same time? Should they have the same sources?

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For two waves to interfere (by which I mean that they produce a stable interference pattern on a screen) they must be coherent i.e., they must maintain a constant phase difference and have same frequency.

However, the explanation above is naive because the real situation is a bit more complicated due to the fact that no source emits perfectly monochromatic waves. I'll try to give a more detailed answer.

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    $\begingroup$ Depends on what you mean by "interfere." Even incoherent waves can interfere; the result of the interference will change over time and/or space, but I'd still call it the same thing. Interference of incoherent waves is part of our justification for the Fourier transform of the Dirac delta function. $\endgroup$ – probably_someone Mar 29 '18 at 10:50
  • $\begingroup$ There was no indication that the OP was referring specifically to interference on a screen. $\endgroup$ – probably_someone Mar 29 '18 at 10:52
  • $\begingroup$ @probably_someone edited! $\endgroup$ – SRS Mar 29 '18 at 10:57
  • $\begingroup$ What I meant by interference was not constant interference. What would happen if Red light and Blue light from different sources were to pass through some space at the same time? Would the disturbance in the electric and magnetic field at that point in space be the "interfered" disturbance of the red light and the blue light? $\endgroup$ – user190174 Mar 29 '18 at 12:01
  • $\begingroup$ What happens when you superpose two monochromatic waves of different frequencies? $\endgroup$ – SRS Mar 29 '18 at 12:08

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