Thanks for the analogy.

One can mathematically and conceptually conceive two opposite-traveling
waves that add up to the observed standing wave, and that's fine. The
problem comes with assigning power or energy to the waves. Then you run
into the problem of how one wave got the energy over the barrier into
the pocket and the other wave took the same amount back out, without
transfering any air molecules across the barrier in the process.

The average power analysis looks to me something like this. Suppose you
have two batteries each with exactly 2 volts potential and zero internal
resistance, with a 2 ohm resistor connected between their positive
terminals. The negative terminals are connected together. You replace
the battery on the left with a short (turning it off), and observe that
the current through the resistor is one amp to the left. Then you hook
the left hand battery back up and turn the right hand battery "off" by
replacing it with a short. You observe that there's one amp now flowing
through the resistor to the right. Finally, turn both batteries "on" by
putting them both in place. You can use superposition to conclude,
correctly, that there's zero current flowing in the resistor.

But it's silly to insist that there's a forward two watt "power wave"
flowing to the right, and another two watt wave flowing to the left. You
subtract one from the other and, sure enough, get zero. But are the
"power waves" real? Studying and analyzing these imaginary waves is
surely a lot more interesting than simply looking at the circuit and
noting that the "boring" (as Cecil calls it) net power is zero. But
aren't you studying ghosts?

Even more risky is adding the things. This time hook two one volt
batteries in series with the 2 ohm resistor and energize one at a time.
With the upper one on and the lower one "off" (replaced with a short)
you get 1/2 amp. You've got a "power wave" of I^2 * R = 1/2 watt. Turn
the lower one on and the upper one "off", and you get another "power
wave" of 1/2 watt, in the same direction. Turn them both on, and you
have a power flow of, um, 2 watts. Welcome to the new math.

Roy Lewallen, W7EL

Jack Smith wrote:

Roy:

Interesting point and I don't recall reading or hearing it elsewhere.

The following is dashed off without fully thinking it through, so no
warranty on its accuracy.

If you think of a sound wave (longitudinal transmission, of course) in
a lossless acoustic transmission line terminated with a short, the
individual air molecules within each 1/4 wave section are likewise
trapped since at the 1/4 wave points there is zero sound pressure.
This may be a useful analogy for the electromagnetic transverse
propagating T-line.

Jack K8ZOA