On Nov 2, 9:54 pm, K7ITM wrote:
On Nov 2, 3:58 pm, Cecil Moore wrote:

Do you know of any way to achieve wave
cancellation without any interaction between the
waves?

It's called "vector addition," not "interaction." But you already
clarified that, so I don't know why you are going on about it.

A bit more on the lack of "interaction" between two waves...

Consider two electromagnetic (EM) waves, originating from two distinct
sources, that share some common volume of space*. If you wish,
consider only a very narrow portion of each wave, so they might be
called "beams" much as you'd get from a laser pointer. Consider where
these beams cross each other at right angles. There is no
"interaction." The beams do not bump into each other and scatter off
in different directions as billiard balls or as streams of water would
do. The net instantaneous field strength at each point in space, for
both the electric and the magnetic field, is simply the sum of the
components from each wave. It's a vector sum, because each component
has a magnitude and a direction in space. Beyond the point of
crossing, each beam is present exactly as it would be had the other
beam not been there. At least, that is what I observe; perhaps I'm
not observing closely enough. Perhaps there is some interaction that
affects the beams in a way that I could measure if only I were
measuring with enough resolution; but sensibly there is no effect on
one beam from the presence of the other. The beams may be identically
the same frequency in any relative phase, or may be different
frequencies, or may be a complex assortment of frequencies. One could
be visible light and the other a 20kHz radio wave. It wouldn't
matter; there is still no observable effect on one beam from the
presence or absence of the other.

If I then consider beams which cross at other angles, I observe the
same (lack of) effect, one on the other. My representation of the net
field as a simple vector sum of the instantaneous fields from each
beam, for each point over all space, for each instant in time, still
accurately describes the situation.

In fact, if the beams are identical frequencies and exactly aligned in
the direction of propagation, what I observe still conforms exactly to
the description where the beams crossed; the net field at every point
in space for every instant in time is the vector sum of the fields of
the component waves. I didn't have to invent any new math to describe
the situation. To the extent that there was no interaction in the
first case considered, with crossing beams, there is also no
interaction in the case of beams exactly aligned. Nothing magical
happens, and no new concept needs to be introduced for this case.

We may indeed need to introduce new concepts if we discover that, at
high enough amplitudes or with careful enough observation, there
really is an interaction and our model of simply adding vector fields
is not sufficient. But I fail to see the need to do that in the
situation described here.

It is no "mind game"--it is an IMPORTANT concept that the fields do
not "interact;" they simply sum. There is NOTHING NEW required to
consider the case where the beams HAPPEN TO BE identical amplitudes
and exactly out of phase at every point in time and space in some
particular region.

*In all of the above, I have considered that the waves are travelling
through space containing nothing but electromagnetic waves; there are
no free electrons or ionizable molecules in this region. My
observations lead me to believe that such space is a linear medium.