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- Thread starter gangsta316
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Also, theoretically, do the two waves have to be exactly in phase to produce a stationary wave?

And are anti-nodes in phase and nodes out of phase or are they both in-phase (otherwise we wouldn't get a stationary wave)

Finally, why is the distance between two adjacent nodes or anti-nodes half of the wavelength? Is it because

http://www.csounds.com/ezine/winter1999/beginner/sine.gif [Broken]

if we took the horizontal distance between the two peaks at y=1 and y=-1(probably easier to look at with y = |sinx| because they are adjacent) it is pi which is half of the "wavelength" (2 pi). Would a stationary wave with this look like y = sinx and y = - sinx on the same axes?

And are anti-nodes in phase and nodes out of phase or are they both in-phase (otherwise we wouldn't get a stationary wave)

Finally, why is the distance between two adjacent nodes or anti-nodes half of the wavelength? Is it because

http://www.csounds.com/ezine/winter1999/beginner/sine.gif [Broken]

if we took the horizontal distance between the two peaks at y=1 and y=-1(probably easier to look at with y = |sinx| because they are adjacent) it is pi which is half of the "wavelength" (2 pi). Would a stationary wave with this look like y = sinx and y = - sinx on the same axes?

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- #5

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Since the 2 waves are travelling in opposite directions, they will be in phase at some locations, and out of phase at other locations.Also, theoretically, do the two waves have to be exactly in phase to produce a stationary wave?

YesAnd are anti-nodes in phase and nodes out of phase

Noor are they both in-phase (otherwise we wouldn't get a stationary wave)

Moving half a wavelength means changing the phase of 1 wave byFinally, why is the distance between two adjacent nodes or anti-nodes half of the wavelength?

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No, they have the same phase at the anti-nodes and opposite phase (180 degrees diference) at the nodes. The phase difference for a given point should be constant (in time) in order to have a stationary wave.

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No, they have the same phase at the anti-nodes and opposite phase (180 degrees diference) at the nodes. The phase difference for a given point should be constant (in time) in order to have a stationary wave.

I don't get it. Don't the waves need a constant phase relationship for a stationary wave to be formed? So they are in phase and this is the constant relationship, so why will they ever be out of phase? Aren't all the points in phase? Although I guess it makes sense because they are both traveling in opposite directions, so some points will be in phase and some out of phase.

Also, when we have double slit diffraction are the minima on the interference pattern where the two waves are out of phase? But again, aren't the two waves always in phase because they are essentially the same wave through each slit? So how would the waves ever cancel each other out if they are exactly in phase?

Thank you for any help.

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Wave#1 = cos(*x+t*)

Wave#2 = cos(*x-t*)

Wave#2 = cos(

We'll look at these waves at two locations.

First, at

Wave#1 = cos(*t*)

Wave#2 = cos(*-t*) = cos(*t*) **= Wave#1**

Wave#2 = cos(

Secondly, look at the waves when

Wave#1 = cos(

Wave#2 = cos(

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If it is the same everywhere you'll have no pattern.

As Redbelly has shown already, the phase difference at x=0 is zero and it will be zero at any time.

At x=pi/2 the phase difference is 180 degrees and it will be 180 degrees at any time.

However the phase difference at x=0 is not the same as the phase difference at pi/2.

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Thank you. So what does "constant phase difference" mean?

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Thank you. So what does "constant phase difference" mean?

Can you provide some context? How have you seen/heard that phrase used?

It

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