I'm afraid you are incorrect on a few details.
The damping factor is defined as "the ratio of the speaker's input impedance to the impedance of the source that is driving it".
When the electrical model is drawn properly, the "output impedance of the source" is everything up to the input terminals of the speaker.
In the model, you end up with a "perfect amplifier", with zero output impedance, in series with a single resistor - which is the SUM of the amplifier's output impedance and all the wiring in between.
(In that model, the speaker is "the load", and everything before it is "the source".)
In most modern amplifiers, there is lots of negative feedback, and the feedback loop is closed at the output terminals.
Because of this, WHEN MEASURED AT THE OUTPUT TERMINALS, the output impedance of an amplifier can be extremely low, and the damping factor extremely high.
These are the values that are given in the amplifier specs.
However, when modelling the entire system, the output impedance of the amplifier, AS EXPERIENCED BY THE SPEAKER, is in series with the impedance of the speaker wire.
You are also incorrect in treating the entire system as a single purely open loop.
A dynamic loudspeaker, like a cone woofer with a voice coil, acts as both a motor and a generator.
The amplifier "pushes" current through the voice coil, which generates a magnetic field, which causes the cone to move (as in a motor).
That part of the system can be considered to operate as a sort of open loop.
HOWEVER, the moving mass of the speaker cone is attached to a coil in a magnetic field, which causes it to act as a generator.
If you simply push on the speaker cone, the voice coil acts as a generator, and produces a voltage that causes current to flow if a path is present.
The same thing happens when the speaker continues to move due to momentum after the amplifier stops driving it actively.
If there is a path for current to flow, that current flows through the voice coil, and generates a mechanical force that opposed the original motion.
(This is the way "dynamic braking" works in electric cars. Each motor acts as a generator, and, by "shorting out the generator", braking force is created.)
In a speaker, this dynamic braking force causes the cone to stop moving, rather than continue to vibrate, and continue to produce sound, after the amplifier stops driving it.
In this part of the process, the speaker is generating a signal, that signal is acted upon by the amplifier's damping, and that action affects the speaker - as an entirely separate feedback loop.
The higher the damping factor, the more current is caused to flow by the back EMF generated by the speaker, and the more powerful the "dynamic braking force" is.
By preventing the speaker from continuing to make sound after the drive from the amplifier stops, this process results in the speaker sounding "tighter" and "more well controlled".
And, if you look at excess cone movement due to momentum as "mechanical overshoot", then the amplifier's damping does indeed "control overshoot".
(And, yes, this effect may not be present on types of speakers that don't generate back EMF - like electrostatics and even some planars.)
This is easily demonstrated simply by disconnecting the speaker from the amplifier.
With nothing connected, tap on the woofer cone, and listen to the sound.
With most speakers you will hear a somewhat hollow thump and output that dies down somewhat gradually.
If you try this again, with a short piece of wire connected directly across the speaker's terminals, you will hear a much tighter and more well controlled thump,
You are hearing the effect of damping on the speaker.
(That piece of wire is electrically equivalent to an amplifier, with a high damping factor, and a zero volt output signal.
Electrically, those two signal paths are "superimposed".......
Which means that the amplifier both drives the speaker and provides a path for current generated by the back EMF to flow.
(And the output impedance of the amplifier, expressed as a damping factor, affects both of them, but its effect on the back EMF is more significant than the Ohmic losses.)
And, yes, the OPTIMUM speaker wire would be infinitely thick, with infinitely low resistance, capacitance, or inductance.
Likewise, the optimum amplifier, according to most modern audio engineers, would have a zero ohm output impedance.
However, what we're talking about here are diminishing returns.
(Also remember that the resistance of the wires in the speaker's voice coil must also be counted as part of the overall series resistance.)
And, yes, it would be an interesting idea to run sense wires to the speaker terminals, and close the feedback loop to there.
This topology is, in fact, relatively common for DC power supplies, but there are numerous reasons that make it impractical for audio (or other AC signals).
It is only practical to do this inside certain subwoofers - because the distances are very short and the frequencies involved are relatively low.
If you want to hear what an amplifier with a very LOW damping factor would sound like with your speakers...
Simply purchase a pair of 2 Ohm power resistors (10 or 20 watts) and put them in series with your speakers.
If your speakers are 8 Ohms, and you have a solid state amplifier with a relatively high damping factor, with the resistors in place, you will have an effective damping factor of about 4.0
(This is similar to the damping factor provided by most tube amplifiers).
You will probably notice that the bass sounds "softer", "less well controlled", and perhaps slightly louder (the results will vary wildly with different speakers).
I should also note that measuring the output impedance of an amplifier isn't complicated - but it gets tricky when extreme values are involved.
For example, you can calculate that value by measuring the output voltage across a 4 Ohm resistor, and then across an 8 Ohm resistor, with the same exact source signal, and performing a few calculations.
The tricky part is that it requires VERY precise measurements of VERY small differences to achieve accurate results.... especially when high damping factor values are involved.
Most manufacturers simply don't bother to measure or specify damping factor values above a few hundred....
Because they're tricky to measure accurately and any value above 500 or so simply doesn't make a practical difference.
(But some few vendors will take the effort to measure ridiculously high numbers - mostly for bragging rights.)
Hi
Because it is an open loop, the only way to get the speaker obey to the audio signal is by brute force. If there would be a feedback (not a bad idea for a new startup) the feedback would take care of that.
DF is not a: "It is a ratio of speaker impedance to amplifier + speaker wire impedance". The speaker wire impedance is your idea. By definition, the DF is given (By SDT) at 8 ohms and 1KHz, regardless to the speaker actual impedance, nominal or at that specific frequency.
Your way of looking at the issue, as overshoot / undershoot to DF performance is not the right way to do. By listening, the differences between a good DF amplifier and a poor one are far beyond "overshoot / undershoot". There is a different quality of bass and mid and that may even get to the highs (bad bass and mid may mask it).
There are amplified speakers (Meridian and Cabase had some) but so far none solved the problem properly (heard them both). With subs' it's easier, because they have the built in amplification. Adding a sensor and closing the loop is obvious.
The conventional system (at most of us) include an amplifier connected to a pair of coil based speakers at some distance, with speaker cables. None of the sides (amplifier or speaker manufacturer) do not tackle the speaker's wires. Most advices are general, without being too specific, for a reason.
After this subject was left out there unguarded, many jumped on the opportunity to offer cables that came with astronomic price tags, a pile of crap (skin effect, burn in, bi-wire, cryogenic treatment, silver) But no technical statement!
Since SS amplification (since the last 45 years or more) no one never put their finger and said: The optimal cable for A and B at L length, is X AWG.
I also do not accept the say that it is a waist spending on speaker cables more than 1$/feet. Even in India it costs more. Who buys his system at K-mart, to save that much on speaker cables?
? I'll give you a pass on the whole star wars thing. Horrible movies.
