K7ITM wrote:
So consider the case of a section of lossless uniform transmission
line of characteristic impedance R0, which I write as R instead of Z
since it of course must be real-valued, connected between two sources
S1 at end 1 and S2 at end 2. These sources each have source impedance
R0: they are perfectly matched to the characteristic impedance of the
line. The line is long enough that we can observe any standing waves
that may be on it. (For believers in directional couplers, that can
be short indeed, but it does not need to be short.) Source S1 is set
to output a sinusoidal signal of amplitude A1 into a matched load, on
frequency f1. Similarly S2 outputs a sinusoidal signal A2 into a
matched load at frequency f2, which is distinct from f1.

What you have described is a system with two sources which
are incapable of interfering with each other because they
are not coherent. Note that this example bears zero resemblance
to a system where the sources are coherent, i.e. frequency-
locked and phase-locked and therefore, capable of interference.

It is easy to show mathematically, and to measure in practice, that
the amplitude of the frequency f1 is constant along the line, and
similarly that the amplitude of the frequency f2 is constant along the
line. That is to say, there is no standing wave at either frequency.
Energy at f1 travels on the line only in the direction from S1 to S2,
and vice-versa for f2.

Obviously true for non-coherent sources.

That says to me that the energy on the line at f1 is absorbed entirely
by source S2, and the energy at f2 is absorbed entirely by S1, with no
reflection at the boundaries between S1 and the line, and the line and
S2.

Obviously true for non-coherent sources.

Unfortunately, "non-coherent sources" is not the subject of
this discussion. The rules change between non-coherent, non-inter-
fering sources and coherent, interfering sources. I suggest you
reference the "Interference" chapter in "Optics", by Hecht.
--
73, Cecil http://www.w5dxp.com