Interference between different eigenmodes of the wave equation

[Demidov]

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?

 

[Gonzolo]

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.