A question about wave interference.

[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.

 

[Graeme Robinson]

Hi there!

Your question about wave interference is a great one. It seems like you have a good understanding of the concepts involved, but just need some guidance on how to approach the problem. I would recommend using the superposition principle to analyze the interference between your solutions. This principle states that the total wave at any point is the sum of the individual waves at that point. In other words, you can add the solutions of the wave equation together to see the interference pattern.

For your first approach, using the analytic sum, you can use the equations for the superposition of two waves with different amplitudes and wavelengths. This will give you an idea of what the overall interference pattern will look like.

For your second approach, summing directly, you can assume that the phase difference between the two solutions is what you need. However, it is always best to confirm this assumption by checking the equations and making sure they are consistent with your understanding of the concept.

I hope this helps! Good luck with your analysis of wave interference.