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I need to make an animation of interfering coherent waves on the plane, that are produced by two sources. I would really appreciate if I am able to change the wavelength.

I am quite new to Wolfram, so I have completely no idea on how to make these "two" waves react to each other and show that to the user.

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    $\begingroup$ Take a look at this Wolfram Demonstration for a start: demonstrations.wolfram.com/WaveInterference. You can get the source code of the demonstration as well $\endgroup$
    – MarcoB
    Commented Jul 17, 2016 at 20:11
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    $\begingroup$ What kind of sources (points, apertures, ...), what kind of time dependence? What have you tried? $\endgroup$
    – Jens
    Commented Jul 17, 2016 at 20:17
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    $\begingroup$ Here's a starting point: ReliefImage[ Table[ Sin[Norm[{x + 4, y}]] + Sin[Norm[{x - 4, y}]], {x, -30., 30., .1}, {y, -30., 30, .1} ], ColorFunction -> "Aquamarine" ] Also look up DensityPlot. $\endgroup$
    – Szabolcs
    Commented Jul 17, 2016 at 20:23

1 Answer 1

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I guess you're looking for something like this:

wave[x_, y_, x0_, y0_, l_, t_] := 
  Sin[Sqrt[(x - x0)^2 + (y - y0)^2]/l + t];

Manipulate[
 DensityPlot[
  wave[x, y, d, 0, l1, t l1 l2] + 
   wave[x, y, -d, 0, l2, t l1 l2], {x, -100, 100}, {y, -100, 100}, 
  Mesh -> 10, PlotPoints -> 50], 
  {d, 5, 20},
  {l1, 5, 20}, 
  {l2, 5, 20}, 
  {t, 0, 1}]

d controls the distance between sources, l1 and l2 changes their wavelengths. Image of the manipulate object

Another example

Manipulate[
 ContourPlot[
  wave[x, y, d, 0, l1, t l1 l2] + 
   wave[x, y, -d, 0, l2, t l1 l2], {x, -100, 100}, {y, -100, 100}, 
  Mesh -> 10, PlotPoints -> 100, Contours -> {-0.5, 0.5}], {d, 5, 
  20}, {l1, 5, 20}, {l2, 5, 20}, {t, 0, 1}]

Another example

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  • $\begingroup$ Thanks. But I want waves to move to see the process of interferrence itself. Do I add "Dynamic" or sth of this kind? $\endgroup$
    – Michael Freimann
    Commented Jul 18, 2016 at 5:12
  • $\begingroup$ I didn't include it because it might be kind of slow. $\endgroup$
    – Lucas
    Commented Jul 18, 2016 at 15:14
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    $\begingroup$ @MichaelFreimann I've updated it, I just included a additional Manipulate field for t (with the right period). Use the + then just press play. $\endgroup$
    – Lucas
    Commented Jul 18, 2016 at 15:23
  • $\begingroup$ Thanks a lot! I now about the density plot. $\endgroup$
    – Michael Freimann
    Commented Jul 19, 2016 at 15:58
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    $\begingroup$ @MichaelFreimann see updated answer $\endgroup$
    – Lucas
    Commented Jul 19, 2016 at 22:50

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