Cecil Moore wrote:
John Popelish wrote:

But at any point that is not a node in the standing wave pattern,
there will be an ordinary AC voltage or current at some amplitude
between double the traveling wave amplitude and zero amplitude, and
one of two phases (that switch each time you pass a node).


Please give us the equation for "ordinary AC voltage or current".

The simplest (without a reference phase) would be cos(wt). The
standing wave function contains this term, with a modifier to tell you
how amplitude varies with position. But at any point, cos(wt) times
some amplitude describes the ordinary AC voltage or current swing.

No argument. But a standing wave still represents storage of energy
in the line, as with any resonant structure, and that stored energy
shows up as magnetic fields and electric fields along the line. The big
difference is that the magnetic fields bob up and down at some areas
and the electric fields bob up and down half way in between those
areas. At any given moment, there is a fixed total energy in the
combination of all the magnetic and electric fields.


No argument, and therefore no need for the "But" in your statement.
I agree with you but it doesn't change a thing about the real
argument.

Exactly. How can you write this, but deny the capacitive current that
delivers this electric field energy twice every cycle to all
capacitance feeling this voltage swing?

I don't deny it - never have - never will. Please stop trying
to set up straw men. The discussion has *NEVER* be about what
happens during one cycle. The current measured by W8JI and W7EL
and reported by EZNEC is RMS current. Instantaneous values are
just another straw man diversion.

EZNEC must take those within a cycle currents and voltages into
account to come up with the amplitude values. The RMS value is just
the amplitude value for a cycle.

Profiles do not charge capacitance, ...

I'm glad you agree. Profiles are maximum RMS envelope values
and that is what EZNEC reports.

See? We agree on lots of stuff.

[Standing wave phase] "doesn't rotate at all, and the resultant
wave it represents doesn't progress through space - its a standing
wave."

At a given point the traveling wave phasor doesn't rotate, either.
Phasor rotation only applies to the phase change over length for a
traveling wave. The phase for standing waves has a discontinuous jump
as you pass through a node, instead of a continuous rotation over
length. I guess one might call that a form of jumpy rotation. Who
doesn't recognize these facts?

I suggest you drop talking about phasors, till you understand what
cos(wt).


Hecht and I have been a little lose with words while assuming
the readers have a certain knowledge level. For the uninitiated,
When Hecht (or I) say the phasor doesn't rotate at all, we
mean the phasor doesn't rotate at all with respect to the
source phasor.

....and within a half cycle of propagation length.

Any initiated person would know that. The phase
of the standing waves doesn't change with respect to the phase
of the source signal. Hecht assumed you would know what he meant
by that statement.

Still, it is worth saying well, once in a while.

Speaking of "... net transfer of energy, for the pure standing
wave there is none."

A standing wave does not violate conservation of energy.

Exactly my point!

I missed that point. Sorry.

Nothing violates conservation of energy. If
the RMS forward current in the coil is the same magnitude at
both ends and the RMS reflected current in the coil is the
same at both ends, the conservation of energy principle is
satisfied NO MATTER WHAT THE STANDING WAVE CURRENT TURNS
OUT TO BE. What is it about that statement that you don't
understand?

You don't add superposed RMS values to get the resultant RMS value.
You have to add instantaneous values over a cycle (so that the
relative phases of the two wave cycles are taken into account), and
take the RMS of the resultant cycle. See? We have to get inside an
individual cycle to understand what is going on. You cannot just deal
with RMS (while cycle amplitude values) and get the same answer. This
is why I (and others) keep coming back to what is happening inside a
cycle, instead of discussing RMS values, only. One cannot understand
either traveling wave mechanisms or the super position to a pair of
traveling waves (a standing wave) if you think only in RMS values.
They display the result of the process, but hide the way the process
produces that result.

Storage that must continuously be swapping back and forth from
magnetic field energy to electric field energy. When the energy
storage is all electric, that implies charges capacitance.

Again, nobody has ever been discussing what happens within a
partial cycle.

I have. You may not be, but that is your lack.

Discussion of such is obviously a diversionary
straw man. Feel free to find someone else willing to discuss it.
It is completely irrelevant to this discussion of RMS envelope
values.

There is no discussion of RMS envelope values. There is just you
repeating the same thought, over and over, while the rest of us
discuss the mechanisms that produce that resultant envelope.

You obviously understand how a phase measurement is useless to measure
phase shift within a half cycle of a purely standing wave process.

I am waiting for you to realize that you can measure the phase shift
of each of the traveling waves that superpose in a standing wave
process that includes a coil (or any other network) by using only the
RMS amplitude envelope, with no reference to phase, in an EZNEC
simulation or a real experiment. That was the whole point that began
this discussion, wasn't it?

You keep showing how the current into and out of a particular coil
does not have the same RMS value. We get it.

Now, measure the phase shift of that coil (for each of the equal
amplitude waves traveling through it) without having to change its
environment to put it into a pure traveling wave process. And don't
use a phase measurement to do it (which you know is impossible). Use
the amplitude envelope. You should be able to measure its phase shift
to within a degree or so. And you can then see how that phase shift
changes (or if it does) when you move the coil to different places in
the standing wave system.