Cecil Moore wrote:
Jim Kelley wrote:
So I'm happy to
leave it to you to explain to Cecil how waves cancel but without
anhiliating the energy "in" them.

No need for that, Jim. Florida State University has done
an excellent job of explaining how wave cancellation
"redistributes" the pre-existing wave energy in "new
directions" such as the opposite direction in a
transmission line (the only other direction possible).

"... when two waves of equal amplitude and wavelength that
are 180-degrees ... out of phase with each other meet, they
are not actually annihilated, ... All of the photon energy
present in these waves must somehow be recovered or redistributed
in a new direction, according to the law of energy conservation ...
Instead, upon meeting, the photons are redistributed to regions
that permit constructive interference, so the effect should be
considered as a redistribution of light waves and photon energy
rather than the spontaneous construction or destruction of light."

The killer is that word "somehow"... "all of the photon energy must
somehow be redistributed".

Well of course it must! Nobody denies that conservation of energy will
hold, in a system with properly defined boundaries. But the weakness of
a photon model is that it cannot provide a detailed nuts-and-bolts
explanation of the mechanism by which that energy becomes redistributed
in time and space.

A wave model will provide all of that detail - and in transmission-line
problems we can use it. If we trace what happens to forward and
reflected waves of voltage (and/or current) we can predict the
magnitudes and phases of those quantities at any location, at any
instant. That gives us a complete time-dependent map of the voltage and
current across the entire system.

From that, we can also find out where the energy is - the inputs,
outputs, losses and stored energy. Sure enough, we will find that energy
is conserved within the system boundaries... but that is no big deal, we
always knew it would. In a wave model, conservation of energy is
something you should check for, but only as an overall confirmation that
you've done the sums correctly. All the useful detail came from the
analysis of the voltage and/or current waves.



--

73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek