Roy:

[snip]
I thought this was only true for waves moving through a lossless medium
or in a lossless transmission line that supports TEM waves. Either the
electric or magnetic field isn't transverse in a hollow waveguide, and
either or both can be non-transverse in a lossy medium.

Or am I mistaken about this?

Roy Lewallen, W7EL
[snip]

Compressive-dillutive waves occur only in media that is compressible, like
the earth or the air, or springs, etc... With compressive-dillutive waves
the "vibrations" occur in the effective density of the medium.

Electromagnetic waves propagate with transversal vibrations of the E and H
fields, viz. Side to side vibrations, not shortening and lenghtening
vibrations. If an electromagnetic wave is supported in the Transverse
Electromagnetic or TEM mode then [theoretically] the E and H fields are at
right angles to each other and to the direction of propagation, in the
terminology of TEM, the term transverse referes to the orientation of the
wave with respect to it's guides, and not to it's vibration mode in the
longitudinal - transverse sense.

Visualize a long "slinky" coil attached to the wall. Shake one end up and
down to create a transverse wave in which the slinky moves up and down.
Push and pull on the end to produce compression and dilution to cause
longitudinal waves in which the slinky does not move up and down but in
which the distance between turns moves back and forth. This slinky analogy
sort of illustrates the differences. Meanwhile in electromagnetic wave
phenomena you have as well as the most common TEM mode which is only
transverse vibrations, also there exists a plethora of TM and/or TE modes,
or even in the near field, where the fields may not be at right angles to
each other or to the direction of propagation, but the vibrations are still
talways transverse, i.e. not compressive-dilutive.

Back in the mid-1800's after Maxwell produced his celebrated equations and
Heaviside improved them by expressing them in vector form most scientists
of the time noted that Maxwell's formulation provided no explicit form for a
medium for the electromagnetic waves to propagate in, and they also noted
that there were only transverse and not longitudinal [compressive-dilutive]
vibrations supported by his equations. Several eminent scientists of the
day felt that this left openings for several more discoveries and so...
Then ensued for several decades a search for the "ether". The "ether" was
supposed to be the media which supported the electromagnetic waves. During
that period several of the eminent scientists of the time proposed that the
"ether" once it was found might actually be compressible and they proposed
that Maxwell and Heaviside had left out of their formulations the
possibility of compressive-dilutive or longitudinal vibrations. Several
scientists of the time actually formulated equations which supported
compressive-dilutive em waves and actually conconcted and, to no avail,
actually conducted experiments to try to find out if such
compressive-dilutive vibrations actually occured with electromagnetic
phenomena.

As we all know, eventually the existence of the "ether" was discredited,
mainly by the Michelson-Morley experiments, and today we all know that
electromagnetic waves do not have a media or "ether" to support their
propagation and vibrations.

Electromagnetic waves propagate just fine in a complete vacuum, and a vacuum
is incompressible, and so the search for compressive-dilutive vibrations of
electromagnetic waves became moot and a search for experimental evidence of
them was abandoned by all who were interested. One can add terms to the
Maxwell-Heaviside equations to support compressive waves, and this has been
done by several theoretical physicists, but there is no sense doing so since
none have ever been discovered!

The book, I referred to above, "Physics of Waves" gives all the details of
the wave equation for media that supports compressive waves. An important
such field is the field of seismology. Indeed the field of siesmology
studies waves that vibrate in all modes, transversally and longitudinally,
as well as surface waves. Seismic waves are processed regularly with beam
forming arrays of seismometers and processed by tomographic techniques to
image the earth in all wave modes.

Seismology is a facinating field and seismologists are generally the most
sophisticated of all wave mechaics!

A good modern book on the seismic wavefield is:

B. L. N. Kennett, "The Siesmic Wavefield", Cambridge University Press, New
York, NY, 2001. ISBN: 0-521-00663-5.

But be aware it is full of gratuitous partial differential equations and
tensor analysis. The stress-strain variables of compressible-dillutive
media are expressed as tensors and the partial differential equations are
cast in tensor form.

All this to say that electromagnetic wave phenomena are a particularly
simple form of wave phenomena when compared to the most complicated types.

--
Peter K1PO
Indialantic By-the-Sea, FL.