I typically do not like to "Xerox" material to support my arguments, but
I will make an exception in this case.

Very recently RRAA's very own "John Smith" included the following
comment in a message.

"I think Cecil has done an excellent job, if you have followed him (and,
I cannot claim I have COMPLETELY done so), however, he has shown there
ARE holes in what we 'believe.' And, some things don't quite 'mate-up'
and what we have taken for granted looks differently when under the
'microscope.' 'Standing Waves' is but the shining example."

Considering the source of that comment, I am not surprised. But for any
others who might have been hoodwinked by the nonsense, I will try to add
a bit of color. As some may recall BG, there has been a bit of an
ongoing discussion about the nature of energy flow, or lack thereof, in
standing waves.

In order to support his point about using phasors interchangeably with
field vectors, Cecil copied and posted a figure on his website under the
page name of "EHWave.jpg". This figure was referenced as an extract from
a book by Haznadar and Stih entitled "Electronic Fields, Waves, and
Numerical Methods."

The figure itself completely misses the point, since it is simply a
representation of an ordinary circularly polarized wave. The topic of
polarization is not particularly relevant here. It merely complicates
the arithmetic, and it adds nothing to the science of Poynting vectors
or standing waves. It is, however, interesting to note that the figure
caption in the original source is given quite clearly. On page 241, the
page containing Cecil's copied jpeg, it says,

"Figure 8.3.2 Propagation of a circularly polarized pure direct (in the
+z direction) travelling wave with phase velocity vf = c."

Whether Cecil did not see this caption, did not understand it, or was
again trying to pull a fast one remains unknown. It matters not in any case.

I must give great credit to Cecil's hidden research team for finding
this reference. It seems quite obscure. However, Cecil's groupies appear
to have neglected to turn a few pages to arrive at page 244. On this
page there is a discussion of the Poynting vector for standing waves. An
exact quote, or at least as close as possible in ASCII, is,

***********

"In a real domain, the instantaneous value of Poynting's vector for a
pure standing wave is, according to (8.3.26a,b),

NRe = (ax ExRe x ay HyRe) = -az 1/4 (Eo^2)/Z' sin^2 (2 pi
z/lambda) sin (2wt) (8.3.28b)

Using this expression, we see that the time-averaged value of Poynting's
vector in a real domain is equal to zero since the time-averaged value
of the function sin (2wt) is always equal to zero."

***********


The equation is slightly cleaner when the "Re" subscripts are removed.

N = (ax Ex X ay Hy) = -az 1/4 (Eo^2)/Z' sin^2 (2 pi z/lambda)
sin (2wt) (8.3.28b)

What is immediately observed is that the Poynting vector for an ordinary
standing wave is zero only for specific locations or for specific times.
At other locations and times the Poynting vector is non-zero. Only the
time or space *average* is zero. This is of course exactly what I and
some others have been saying. This is exactly what the traditional
science says. The colloquial expression is that the energy sloshes back
and forth.

This equation is easily derived from the standard representation of a
standing wave, but it is *so* much more authoritative when Xeroxed from
Cecil's own reference book.

The iconoclasts never give up. The 200 mpg carburetor lives on.

73,
Gene
W4SZ