Cecil Moore wrote:
John Popelish wrote:

Cecil Moore wrote:

That is not what the formula says. Pick and X and you get a constant
phase angle with respect to the zero degree reference.

But that phase angle is not zero as it is for standing waves.
You seem to be talking in circles. How can the phase shift
between the traveling wave and the source reference ever be
zero at a point 90 degrees away from the source?

I said the phase was was fixed, not zero, at a given position.

If it cannot,
then you have evidence that the traveling wave is NOT identical
to the standing wave as evidenced by their different equations.

I agreed that the pattern of amplitude and phase is different along a
line for traveling and standing waves. But at any given point, there
is a very similar kind of phasor ( one with an amplitude value and a
phase value) that describes what is happening at that point. That
difference in amplitude distribution and phase shift with respect to
position is what the two functions describe.

You keep claiming that there is something fundamentally different
about the kind of phasor describing a single point (rotating versus
non rotating), depending on whether the phasor is describing a point
on a standing or traveling wave. That is where we disagree.

Let's cut to the bottom line. You seem to believe that standing wave
current is identical to traveling wave current.

At a point, it certainly can be. How current varies (amplitude and
phase) over length is what is different.

If that's your point, just say so.

I have said so as emphatically as I can, at least a half dozen times.
You keep saying I am wrong and refer to rotating phasors and non
rotating phasors. The only rotating phasor I know if is when a
different (from the reference frequency and phase) frequency is
described by phasor notation. That phasor rotates.

Otherwise, please tell us the difference between the
standing wave current and the traveling wave current which seems
obvious to me from the equations.

I have, already. But here goes once again. A current produced by a
traveling wave has a constant (RMS) amplitude along the line. The
phase of the current (relative to some arbitrary phase reference)
varies linearly along the line. If the line is a wavelength or more
long, you can find any relative phase you want, just by moving along
the line. There is energy moving along the line during this process,
but no net (averaged over a cycle) current moving along the line.
this is similar to how wave energy moves along the surface of water,
without the water traveling along with the wave. The water just moves
up and down as the wave passes along its surface. Likewise, charge
moves back and forth, locally, within a half wavelength of the line as
the wave passes, and the local current is a measure of the rate of
this charge movement.

In the case of a pure standing wave, you have the super position of
two equal and opposite traveling waves. The current (RMS) magnitude
can vary anywhere from zero to twice the (RMS) magnitude of that
produced by either of the two traveling waves. The RMS amplitude
envelope will vary in a [absolute value of sine] way along the line.
The relative phase of the current will have one of two values (the
actual angle depending on what phase is chosen as the reference) that
are 180 degrees apart. The phase switches between these two values
each time you pass through a node in the amplitude distribution.
There is no net energy movement, since the movement in one direction
is canceled by energy movement in the other direction. There is,
however, energy storage on the line.

Since the charge movement in a standing wave is the superposition of
the charge movement of two traveling waves, in a standing wave, charge
also moves back and forth only within a half wavelength interval of
the line. And the standing wave current is the measure of the rate of
change in this charge movement as it sloshes back and forth within
that half wavelength.

If you have any corrections to any of this, please quote enough of
what you what you are correcting for the context to be clear, and have
at it. I want to get this right.