Skin effect is a real electrical phenomenon, but it is often misunderstood in audio discussions. When alternating current flows through a wire, the current density is slightly higher near the outside surface of the conductor than it is at the center. The depth where the current density has fallen to about 36.8% of the surface value is called the skin depth. Mathematically, current density falls with depth like this:
J(d) = Js * e^(-d / δ)
where J(d) is the current density at depth d, Js is the surface current density, and δ is the skin depth. For copper, skin depth depends mostly on frequency. As frequency goes up, skin depth gets smaller. At low frequencies, the skin depth is large, so current flows through most or all of the wire. At very high radio frequencies, skin depth becomes small enough that most of the current is pushed toward the surface. This is why skin effect usually does not matter much for normal speaker wire. Audio is alternating current, so skin effect technically exists, but the frequency range is low: roughly 20 Hz to 20,000 Hz. Those are tiny frequencies compared with radio-frequency or microwave applications, where skin effect becomes a major design concern. In normal copper speaker wire, especially common sizes like 18 AWG, 16 AWG, 14 AWG, 12 AWG, and 10 AWG, the skin depth at audio frequencies is often comparable to or larger than the wire radius for much of the audio band. That does not mean wire does not matter. It means skin effect is usually not the main thing to worry about. For speaker wiring, the bigger practical issues are wire gauge, total wire length, resistance, connection quality, copper vs. copper-clad aluminum, and how much current the amplifier needs to deliver. Skin effect is real physics, but for normal audio wiring it is usually much smaller than the internet arguments make it sound. Check out this visualization tool so you can see for yourself the impact of frequency on skin effect.
Skin Effect in a Round Copper Wire
Wire Cross-Section
Density vs Depth
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