The figures for skin depth you mentioned are for a specific wire gauge. The “mechanics” of skin effect is as follows:
There is an electrostatic force between electrons, and that force is making them “move away from each other”. You put a bunch of electrons in a conductor (such as a wire), and they want to keep separate from each other, while remaining inside the conductor, so they still will “even out” in terms of the spacing between them.
When you run DC down a wire, the same holds true. The cross section of the wire is “evenly distributed” in terms of electron spacing, so the whole copper gets used to conduct current.
But when you run AC, the electrons start moving back and forth, and the acceleration (and deceleration) of each electron produces a new force. This force is magnetic. The faster the acceleration (deceleration) the stronger the force. The combined force due to all the electrons makes the repulsion force at the center of the conductor be the strongest, and it gets weaker as you get away from center.
If it were only up to the magnetic force, all the electrons would end up right at the conductor surface. But the other force, the electrostatic one, does not let them be so near each other. The result is a balance between electrostatic and electromagnetic behavior. The electrostatic is a fixed force, the electromagnetic varies with frequency. The dependency on frequency is not linear – the skin effect goes up with the square root of the frequency (often expressed in MHz).
The dimensions of the wire (such as wire gauge, which relates to cross sectional area) do count. One way to relate to skin effect is as a multiplier of the DC resistance. The AC resistance will be the DC resistance multiplied by the square root of the frequency and also multiplied by a K factor. The K constant is different value for different wire gauges.
Say you have an 100 feet of an 18 gauge wire. The DC resistance is about 0.65 Ohms. The K factor for 18AWG wire is about 11. So the AC resistance is:
At DC .65 Ohms, at 20KHz it will become 1 Ohm, at 100KHz, 2.25 Ohm, at 1MHz we have 7 Ohms, 22 Ohms at 10MHz…
So yes, you may not want to use 100 feet of 18AWG for the speakers, but 10 feet is (0.1Ohm) probably fine, from skin effect standpoint. A 10AWG at 10feet yields DC resistance of 1 milliohm and with skin effect it comes to 4 milliohms, so even 100 feet of 10AWG is only 40 milliohms at 20 KHz (it is really 50 feet each direction).
Skin effect is “non capacitive” and “non inductive”. It is resistive only. No phase issues what so ever.
I guess one way to look at skin effect is through the “glasses of” “skin depth”. Skin depth is a bit of a simplification, an “average” because the wire is not really divided into 2 distinct zones (“electron flow zone” and “no electron zone”). A few electrons do run near the center, and the distribution is more gradual then a brick wall. But skin depth is a reasonable way to view skin effect.
Having said all of that, skin efect really does not matter for audio signals!
Regards
Dan Lavry