A question about wave interference.

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SUMMARY

The discussion centers on wave interference, specifically regarding the interference of multiple solutions to the wave equation characterized by eigenvalues and eigenfunctions. Two primary methods are proposed for analyzing this interference: using the analytic sum of functions to calculate the interference of plane waves with varying amplitudes and wavelengths, and directly summing the solutions while considering the phase difference between eigenmodes. It is concluded that the phase difference is crucial and should be determined by boundary conditions, as adding solutions inherently leads to interference.

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  • Understanding of wave equations and eigenvalues
  • Familiarity with eigenfunctions and their properties
  • Knowledge of wave interference principles
  • Basic skills in mathematical analysis of functions
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Demidov
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Hello All!
My question is about the interference if the waves.

For example, I have SEVERAL solutions of the wave equation in some area (several eigenvalues and corresponding eigenfunctions). I want to see if the would be an interference between these solutions.

What should I do?

I see the 2 ways:

1) use analytic sum of this functions.
by this I mean to calculate the interference of the two plain waves of different amlitudes and wavelength. How can I do this?

2) sum directly two my solutions.
BUT a question arises: can I suppose that the difference in phase between my two solutions of the wave equation is what I need?
Can I state that the phase difference between the 2 eigenmodes of the equation is the real phase difference between these two field distributions?
 
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Seems to me you have to add all your solutions to get the unique, general solution. Adding them inherently means they interfere. Not sure I see any difference between your 1) and 2). The phase should be determined by boundary conditions.
 

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