Conjecture on superposition: please help! simple concept, complex math!

  • Thread starter elegysix
  • Start date
406
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I have conjectured that two different waves in the same region, will not exactly result in the superposition, or addition of both waves independently.

The logic: Every point in a region which a wave propagates has a position, and an acceleration which partially, if not totally, depends on the position of the local points around it. (due to cohesion) The positions of those local points depend on all present waves. As such, including this term in acceleration changes the sum of distinct wave functions over time and space into a new, single wave function.
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As proof of this idea:
- consider when we have two independent wave sources in water. At distances relative to the separation between them, we see what appears to be two independent waves, superimposing, simply added together. Yet at much larger distances, the wave appears to originate from a single source. Thus, the wave function must have changed. -

-I believe this explains why diffraction occurs, and we do not find discontinuity after passing a wave through a barrier. Instead, we find a new wave function, even though it is the sum of two waves, a flat on one side of a barrier, and a sine on the other. Adding a region of sine wave to a larger space of a flat wave causes it to diverge about the opening, due to the cohesion between particles. -
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The Plan:
In 2 dimensions, I would like to model a transverse plane wave propagating through a region in which another transverse wave is generated from a point. (infinite regions, no boundaries) The usual wave equation can be used for the independent waves, but a derivation of forces depending on cohesion and the local regions about a point, is needed to find the resulting acceleration.

I expect to see the resulting net forces on a point are not merely the sum of the forces in the independent waves, but include a term dependent on cohesion and the angle and phase between their directions of propagation. I expect to find that the plane wave exerts a force on the other wave in the direction of from which it came.


Any help with this would be much appreciated. Also, any criticism is welcomed, as I believe the logic behind it is very solid.

Thanks,
austin
 
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