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Do 2 superimposed waves have to be 180/0 degree apart to form a standing wave? It seems to be the necessity for forming nodes of 0 displacement (taken that their amplitudes are the same) but can they form a standing wave with minimum displacement nodes if the phase is NOT 180 or 0 degrees? As in a situation that is NOT the case of incident and it's reflected wave interfering but simply two waves of opposing directions, same frequencies and amplitudes but phases that are anything but 2 π or 1 π apart. I have trouble visualizing it and could not find a simulator that would let me change the phase of opposing waves.

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2 Answers 2

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For two waves moving in the same direction (and with the same frequency), we find their phase difference is the same at all points. If you move to a point a small distance away, the phase of both waves has advanced by the same amount. So it makes sense to ascribe a phase difference to the waves themselves.

But for waves moving in opposite directions, this isn't true. Moving a small distance will find one phase has advanced while the other has retarded. So you can't say that the waves themselves have any defined difference. Only that they have a difference at a given point.

Assuming they have the same amplitude and frequency, you will always be able to find some points where the phase difference is $\pi$ and some where the phase difference is zero. These will form the nodes and the anti-nodes. Changing the phase of one of the waves at its emission point will shift the location of the nodes, but cannot remove them.

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  • $\begingroup$ "Changing the phase of one of the waves at its emission point will shift the location of the nodes, but cannot remove them." That is a good point. Basically what I failed to notice is that the phase is opposite only at the point of the nodes, and whether the displacement is 0 or not depends only on whether the amplitudes are the same at that position, right? And the peak of one and the valley of the other are bound to meet somewhere where, seeing how the periods/wavelengths are the same, the node will be formed from then on. The phase as you say only dictates the postion of the nodes in space $\endgroup$
    – Dimitri
    Sep 26, 2022 at 8:40
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Consider two waves of equal amplitude, frequency and speed moving in opposite directions and overlapping.

There will be positions where the waves are exactly in phase, ie the displacements of the two waves are equal at all times thus at these position antinodes are formed whereas if the displacements are equal in magnitude but opposite in direction then nodes are formed.

One way to form a standing wave is by reflection and one can then think of waves from a source and waves from the virtual image of the source overlapping and forming a standing wave.
If there no phase change on reflection then standing waves are produced which have nodes and antimonides at different positions than those if there was a $\pi$ phase change on reflection.
This is equivalent to changing the phase of the virtual source relative to the actual source by $\pi$.
This simulation illustrates this point.
Changing the separation of two sources is equivalent to keep the separation of the two sources the same and changing the phase of one relative to the other.

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  • $\begingroup$ Thanks. That is an awesome website btw, a bunch of cool stuff. :) $\endgroup$
    – Dimitri
    Sep 26, 2022 at 9:32

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