Hi Chris,
The impedance presented by an inductance is directly proportional to frequency, and the inductance of a cable (and consequently the impedance it presents) is directly proportional to length. Assuming the goal is for the cable to behave in as neutral a manner as possible one would want the impedance presented by that inductance to be a very small fraction of the impedance of the speaker at all relevant frequencies. But as you alluded to, one would want to accomplish that without raising capacitance to excessively high levels, that might affect the performance or even the stability of the amplifier.
More often than not the impedance of dynamic/box type speakers rises at high frequencies, due to the inductance of the tweeter. At the other extreme are many electrostatic speakers, which have impedances that can descend to very low levels at high frequencies (e.g., some Martin Logan models have 20 kHz impedances in the area of 0.5 ohms). So cable inductance will tend to be most critical with electrostatics.
The impedance presented by an inductance is given by the formula:
XL = 2 x pi x f x L
where XL is the impedance (referred to as "inductive reactance") in ohms;
pi is approximately 3.14;
f is frequency in Hertz;
L is inductance in Henries;
A reasonable ballpark figure for the inductance of an audiophile-oriented low inductance cable might be something like 0.1 uH (microHenries) per foot. So the inductive reactance of a 10 foot length of that cable at 20 kHz can be calculated to be 0.13 ohms. But to provide a fully comfortable margin, that would assure that audible phase shifts do not occur in the upper treble region (phase shifts can be caused by the interaction between a series inductance and a load impedance), let’s use 50 kHz rather than 20 kHz, which for that cable calculates to an inductive reactance of 0.31 ohms.
0.31 ohms is an insignificant fraction of the impedance of nearly all speakers at high frequencies, aside mainly for some electrostatics as I mentioned. On the other hand, for cables having relatively high inductance the 0.1 uH/foot figure may increase by a factor of as much as 7x or so, resulting in an impedance in the vicinity of 2 ohms at 50 kHz for a 10 foot cable.
So hopefully that provides a useful quantitative perspective on the issue.
Regards,
-- Al
