Superposition of waves in different planes

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Darkseid807
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If you have two travelling waves one is traveling in the x-y plane to the left the other is traveling in the x-z plane towards the other wave in right direction what happens when they combine? How will they superpose each other?
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Joinedup
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I think you'd get various Lissajous curves depending on the phase difference. :unsure:
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Eimmanuel
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(Original post by Darkseid807)
If you have two travelling waves one is traveling in the x-y plane to the left the other is traveling in the x-z plane towards the other wave in right direction what happens when they combine? How will they superpose each other?
See the following nice animation that demonstrates the superposition.
https://www.youtube.com/watch?v=aUi8...OlegPashkovsky
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Stonebridge
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Eimmanuel Joinedup

This is an interesting question and i suspect it's the answer the OP was looking for.
But in the question he/she asks about 2 waves in different planes, the xy and the xz.
The Lissajous figures and the animations show 2 waves in the same plane (the xy) meeting at right angles.
I'm not sure right now, what the result (with 2 different planes) is, other than to ask under what possible conditions it could be observed.
The result could only be observed at the intersection of the 2 planes.
Maybe it's food for a bit more thought. My brain already hurts.
But would I be correct in suspecting that the result is the same anyway?
Last edited by Stonebridge; 1 month ago
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Callicious
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(Original post by Darkseid807)
If you have two travelling waves one is traveling in the x-y plane to the left the other is traveling in the x-z plane towards the other wave in right direction what happens when they combine? How will they superpose each other?
In this case, it seems (I am just guessing) that you're implying that you have a wave travelling down the x-axis (parallel to x) with its amplitude parallel to y, i.e. you're specifying something along the lines of y(x,t) for that plane such as

y(x,t) = a_1\sin(k_1{x} - \omega_1{t} + \delta_1)

For the second wave, you're having one coming along the x-z plane, for example specifying (right down parallel to the x-axis, same as for y) z(x,t) to be interpreted as the wave amplitude, and opposite angular frequency (with some multiplier possible) i.e.

z(x,t) = a_2\sin(k_2{x} - \omega_2{t} + \delta_2)

For both the above I've included the option to have a phase (as wikipedia implies) and also differing angular frequencies, plus the standard wavenumber that you have to add for waves that propagate (to define wavelength.)

If you then consider the intersection of these two in a plane at the origin (which is what is implied based on the rest of this thread), you'll get a standard Lissajous curve in the y-z plane at the origin (given that your wave propagates parallel to the x-axis.)

To show this, here's an animation I just made- note that the red curve is the wave in the x-y plane, the blue in the y-z plane, and the green curve the linear sum of the two. I've done it for the example parameters shown here and have set the wavenumber to unity (and the amplitudes to unity, also.) Note that the waves here propagate in the same direction, but with a factor of two in their frequency ratio. Note that you get more interesting curves at different values of x- anyway.



I have to note that the form of the curve formed may well depend on the place you cut your plane through the waves: I just chose the origin because that's what Wikipedia uses. If you don't, you actually get more esoteric curves (at least in practice- that's what I saw.)
Last edited by Callicious; 1 month ago
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