Keith Dysart wrote:
Cecil does all of this analysis using average powers.

That's because the power density/irradiance/interference
equation only works for average powers. One condition
for valid use of that equation is that the powers must
have been averaged over one complete cycle and usually
over many, many cycles. How many cycles does it take
for a bright interference ring to register on the human
retina?

My example is set up such that the average interference
is zero over each complete cycle. I cannot think of a
way to eliminate interference internal to a cycle. Both
destructive and constructive interference occur during a
cycle, which is what you are seeing, but interference
averages out to zero over each complete cycle.

In other words, not only should Z.average = X.average + Y.average,
but Z.instantaneous should equal X.instantaneous + Y.instantaneous
for if the dissipation in the source resistor is not tracking the
energy in the reflected wave, it can not be the energy in the
reflected wave that is heating the resistor.

Destructive interference from one part of the cycle is
being delivered as constructive interference in another
part of the cycle. That is completely normal.

The same thing happens with an ideal standing wave. The
average power in a standing wave equals zero although
some instantaneous power can be calculated as existing
in the standing wave. You have discovered why Eugene
Hecht says that instantaneous power is "of limited utility".

In fact, what we are dealing with in the example is a
standing wave because the forward wave and reflected
wave are flowing in opposite directions through the
source resistor. I hope your math took that into account.

This means that the dissipation in the resistor is not happening
at the same time as the energy is being delivered by the reflected
wave, which must mean that it is not the energy from the reflected
wave that is heating the source resistor.

All it means is that there must be some localized interference
during each cycle for which you have failed to account.
In other words, you are superposing powers which is a
known invalid thing to do when interference is present.
--
73, Cecil http://www.w5dxp.com