Two waves moving at right angles go in circles?

In summary: One is about position and one is not. You can't mix them up because they are different. In summary, Lissajous figures, which are the result of adding time varying signals, can produce a circular motion when the signals are out of phase by 90 degrees. This can be seen in experiments involving pendulums or sound waves. When the signals are in phase, the resulting motion will be linear, such as a diagonal line. It is important to distinguish between oscillations and waves, as they involve different equations and principles.
  • #1
Vriska
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ylet x = Asinx, y = Acosx, apparently x^2 + y^2 = A^2 so this combination goes in circles. wot?

creating waves in a pool 90 degrees off and out of phase by 90 will make it move in circles? I'm skeptical, anyone have a video of an experiment that demonstrates this?
 
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  • #2
Vriska said:
ylet x = Asinx, y = Acosx, apparently x^2 + y^2 = A^2 so this combination goes in circles. wot?
SineCosine.gif

Vriska said:
creating waves in a pool 90 degrees off and out of phase by 90 will make it move in circles?
In a pool you have x,y,z not just x,y.
 

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  • #3
Vriska said:
will make it move in circles
What is it that you think will move in circles? The animation in your post just shows how two vectors which vary sinusoidally and are orthogonal in direction and phase (90°) have a resultant vector with a circular locus and the same angular frequency. That is not the same as two waves.
I can't be bothered to draw it out but the situation you are describing could be represented by a grid of horizontal lines sweeping upwards and a grid of vertical lines sweeping to the right. The resulting pattern would then be a square grid of peaks moving diagonally up and to the right, with troughs all round the peaks. (a moving waffle style of pattern). That would be the interference pattern due to two (equal amplitude and frequency) continuous waves moving at right angles to each other.
I can't think of a way to generate a wave that moves round in a circle unless you used a circular trough. (A guided wave)
 
  • #4
A.T. said:
View attachment 215906

In a pool you have x,y,z not just x,y.
That's interesting, but now I'm wondering how on Earth do you get a straight line when the lines are in phase but perpendicular. Any insights on that?

thanks
 
  • #5
Look for videos about Lissajous figures .
 
  • #6
sophiecentaur said:
What is it that you think will move in circles? The animation in your post just shows how two vectors which vary sinusoidally and are orthogonal in direction and phase (90°) have a resultant vector with a circular locus and the same angular frequency. That is not the same as two waves.
I can't be bothered to draw it out but the situation you are describing could be represented by a grid of horizontal lines sweeping upwards and a grid of vertical lines sweeping to the right. The resulting pattern would then be a square grid of peaks moving diagonally up and to the right, with troughs all round the peaks. (a moving waffle style of pattern). That would be the interference pattern due to two (equal amplitude and frequency) continuous waves moving at right angles to each other.
I can't think of a way to generate a wave that moves round in a circle unless you used a circular trough. (A guided wave)

That looks like the result when the waves are in phase ? these are out of phase, my equation and AT's gif suggest a circle i guess because x2+y^2 = a^2 thing

Perhaps two speakers spaced 90 to each other playing a sound out of phase would give you some circular droning maybe
 
  • #7
Nidum said:
Look for videos about Lissajous figures .
Nidum said:
Look for videos about Lissajous figures .

thank you so much! this is exactly what I was looking for, the pendulum experiment is particularly beautiful, I'm now completely convinced of the circle thing.

@sophiecentaur look at this!
 
  • #8
Nice video on Lissajous figures..
 
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  • #9
Vriska said:
That's interesting, but now I'm wondering how on Earth do you get a straight line when the lines are in phase but perpendicular. Any insights on that?
When they are in phase then x=y which is obviously a 45° line.
 
  • #10
Vriska said:
That's interesting, but now I'm wondering how on Earth do you get a straight line when the lines are in phase but perpendicular. Any insights on that?

thanks
I suggest 'one thing at a time'.
Your question has to be either about Waves (which vary in time and space) or simple signals which vary in time; you should choose which you want to talk about. Lissajous Figures are not a Wave phenomenon - they are the result of adding time varying signals and the result is a time varying signal.
Two linear waves on a tank (as above), at right angles and in phase will produce a linear wave that travels diagonally. Two sinusoids, in quadrature, applied to the X and Y inputs of an oscilloscope will produce a circle (ellipse in the general case). If they are in phase, they will produce a diagonal line.
A simple Oscillation can be written Vt = V0 Cos(ωt)
There is no mention of position.
A simple wave, traveling along the x-axis can be written as
Vt,x = V0 Cos(ωt- kx)
See the difference?
 
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Related to Two waves moving at right angles go in circles?

1. How do two waves moving at right angles go in circles?

When two waves intersect at right angles, they create a circular pattern as they interfere with each other. This is known as a circularly polarized wave.

2. What causes two waves to move at right angles?

Two waves can move at right angles if they are of different frequencies or if they are traveling in different directions. This is known as cross-polarization.

3. Can two waves moving at right angles create interference patterns?

Yes, when two waves intersect at right angles, they can create interference patterns that appear as circular or spiral shapes.

4. How does the amplitude of the two waves affect the circular pattern?

The amplitude of the two waves does not affect the circular pattern itself, but it can affect the size and intensity of the interference pattern created.

5. Are there real-world applications of two waves moving at right angles in circles?

Yes, circularly polarized waves are commonly used in technologies such as satellite communication, radar, and 3D glasses. They are also studied in the field of optics and electromagnetic waves.

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