Cecil Moore wrote:

W. Watson wrote:

Thanks for your reply. I have a few questions. When you say "standing
waves", I take it that one can have more than one on the line?


Standing waves are created by two coherent traveling waves moving
in opposite directions in a transmission line. In a conventional
....

How does one know they want to improve their impedance match?

....
antenna tuners to tune for maximum received signal on our S-meters.
At the Z0-match point, maximum available energy is transferred.

If you know the input impedance to a receiver, you can match your
antenna system to it to achieve maximum available energy transfer
from the antenna.
Thanks.
A standing wave is the sum of an incident added to the reflective wave.
Isn't it possible to send two incident waves down an xline with different
frequences, and produce two different standing waves by having some
multiplicative relationship between the two incident waves and the xline length?

Not a bad explanation from Wikipedia:

SWR has a number of implications that are directly applicable to radio use.

1. SWR is an indicator of reflected waves bouncing back and forth within
the transmission line, and as such, an increase in SWR corresponds to an
increase in power in the line beyond the actual transmitted power. This
increased power will increase RF losses, as increased voltage increases
dielectric losses, and increased current increases resistive losses.
2. Matched impedances give ideal power transfer; mismatched impedances
give high SWR and reduced power transfer.
3. Higher power in the transmission line also leaks back into the radio,
which causes it to heat up.
4. The higher voltages associated with a sufficiently high SWR could
damage the transmitter. Solid state radios which have a lower tolerance for
high voltages may automatically reduce output power to prevent damage. Tube
radios may arc. The high voltages may also cause transmission line
dielectric to break down and/or burn. Abnormally high voltages in the
antenna system increase the chance of accidental radiation burn if someone
touches the antenna during transmission.