Bruce, this is not about you...you posted very pleasantly..thank you.
Allow me to disagree somewhat. You're applying standard transmission line theory to audio bandwidths. There is no possible transmission line theory that would support any type of reflection on a cable at audio frequencies in any length less than many kilometers. The characteristic impedance of a transmission line is only valid at high frequencies - audio doesn't qualify.
What Bruce states is roughly what is taught in an E/M course. However, these are strictly approximations which have been created artificially, guidelines for the engineer to use so that they do not bog down in details. The exponential skin effect approximation is another such "rule", allowing us to quickly get a reasonable good answer without working the bessels.
The characteristic impedance of a transmission line is invariant of length. It is precisely Z = sqr(L/C). Note that it also is frequency independent. In other words, the statement ""
The characteristic impedance of a transmission line is only valid at high frequencies "" has no merit.
This equation also clearly defines the relationship between the current and voltage within the line such that the energy that is stored within the cable is equally distributed between magnetic field and electric field.
If one were to attempt to perform the normal tricks one is used to at rf and microwave frequencies, such as quarter wave matching or stub tuning, the length of the cable with respect to wavelength comes heavily into play. For very short t-lines, movement on the smith chart is far too small to do anything useful That is why the wavelength relationship is "assumed". It has nothing to do with whether a t-line has characteristic impedance or reflections at any frequency or wavelength, it is all about practicality when pulling the ol' smith chart out.
So, as far as standing waves on a few meter piece of cable when we're dealing with a 10 kilometer wavelength, the cable appears as DC. No reflections possible, it won't happen.
Another error based on assumptions. First, we are not talking about standing waves. Standing waves require appropriate wavelengths. Reflections are not standing waves. Reflections are required for standing waves, but standing waves are not required for reflections. Causality.
Reflections do occur. If the slew rate of the impetus signal is slow in comparison to the system response, in this case the wire length, it will not be possible to see the reflections. Overall, the entire cable voltage and current will appear to be reflection free, but that is an artifact of the prop speed, the signal speed, and our ability to resolve the effect via measurements.
Look at the settling times we speak of. 6 uSec? How would one measure that for a 1Khz signal? Not easily. This concern is "approximated out" by microwave engineers, but yet humans can hear this level of change interaurally.
With regard to the L and C of a cable, it's important to consider the interface. In an audio amplifier interfacing to a low impedance load, such as a speaker, other than the simple DCR, the inductance is the most important, while the capacitance can essentially be ignored.
Actually, no.
It is well known that a high bw amp can oscillate if the cable is excessively high in capacitance. What is NOT generally known, is it is not the capacitance per se that is the problem. It is the cable to load end matching.
If you have an 8 ohm cable feeding a pure 8 ohm load, the amp will not oscillate. It will see NO capacitance, no matter how long the cable is. If the load decouples as frequency goes up (impedance rises) such that the load Z is far greater than the cable Z, then most of the energy stored within the cable will be electric field based. The amp has a problem with that if it still has gain at those frequencies.
If you wish to discuss, that would be excellent.
Cheers, John