John Popelish wrote:
. . .
The real revelation for me, from this discussion is how the concept of
"phase" takes a dimensional jump (from time to position) when you change
from taking about a traveling wave to the standing wave that results
from the superposition of a pair of oppositely traveling waves of the
same frequency.

Of course, we can speak of the phase (temporal or spacial) of any
periodic waveform. But it might be important to keep in mind that the
spacial amplitude distribution of a standing wave isn't generally
sinusoidal. When the forward and reverse traveling waves are equal in
magnitude, the amplitude distribution -- that is, the "waveform" if you
plot magnitude versus position -- is the absolute value of a sine
function. For all other cases, it's described by hyperbolic trig
functions. So the "jump" from time to position involves more than phase;
it also involves a change in waveshape.

Roy Lewallen, W7EL