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Here I found a summary about two-dimensional plane waves.

I have a maybe naive question.

The right-hand side of the first figure shows a plot of $\Re(\exp(i\theta))$ as a function of $(x,y)$ for fixed $t$ and the lines are are lines of constant phase (highs and lows).

(1) Wouldn't it be more illustrative/ intuitive to plot this with a third axis, i.e. giving each point $(x,y)$ its value $\Re(\exp(i\theta))$? Since then we can actually see the "mountain landscape" at ´fixed time $t$?

(2) Then, when evolving $t$. the "mountain landscape" would travel normal to the lines of constant phase, i.e. the whole mountain landscape would move normal to these lines?

mathfemi
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1 Answers1

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I do agree with you that we can use a 3D plot to visualize what you mentioned. Your notes in the pdf file used 2D plots, probably because they are easier to draw.

Gary Tam
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  • In case we would have such a 3D plot: Am I right that when looking at it in 2D we can only see moving lines of constant phase when t evolves? Maybe the author wanted to vizualize what happens in 2D only since it is a 2D-plane wave. – mathfemi Dec 29 '16 at 14:44
  • I agree that we can see moving lines of constant phase when t evolves. – Gary Tam Dec 29 '16 at 14:58
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    Besides 3D plot, we can also visualize such a 2D-plane wave on a 2D plot using heatmap. – Gary Tam Dec 29 '16 at 14:58