Has anyone tested using an RTA or a similar measuring device if cables really change the sound?
I don't know of such a test, as measurement error may be big enough to mask differences (unless we're talking long cable lengths) in uncontrolled environments (such as our homes).
Here's a graph of computed response based on the electrical performance of 6 different speaker cables (supposedly 14 awg or larger in cross section) with a 10 ft length, driven by the perfect amp (zero output impedance) and connected to a stable 4 ohm load:
The computation shows that some cables can lope off as much as half a db on the limits of our audible range, in this very typical cable length (or cut about a quarter of a dB relative to the lower octaves) due to cable inductance. This may be audible to some, and not to others. Perhaps you can test with an EQ if a change that small above 10 kHz is noticeable -- many tone control knobs nowadays center close to 20 kHz (and run a broad Q), so this should be quite easy to simulate.
With a 50 ft length (for those with big HTs), the same cable can lope off over 4 dB in the uppermost frequencies (or cut 3 dB relative to the lower freqs) and introduce 4 ms of delay due to phase shift.
What may be surprising to some is that this happened to a supposedly high tech audiophile cable, which the manufacturer claims to be a "truly wonderful performer" in the mids and highs. It probably sounds warmer and smoother subjectively (and a lot of people are after this sound), because the highs are curtailed.
Capacitive cables are also known to curtail the highs in a high impedance application (e.g. analogue interconnects). In this case, high capacitance cables can cut as much as half a dB in the top octave with something as short as 10 ft or so, and cause considerable phase shift. Longer lengths would have a more pronounced effect. As with the speaker cables, the result is of course largely dependent on the electrical properties of the components attached.
What's in common with both is that they largely affect high frequency reproduction only (as long as a reasonable girth is maintained). Generally, a lower capacitance IC cable will alter the resulting sound less, while a lower impedance speaker cable will have the same benefit -- both should result in a relatively bright and airy sound. The opposite direction will yield a warmer (and marginally more distorted) sound, which may work in taming excessive HF output (or suiting the listener's preference).
Of course there's also talk about the speaker cable's capacitance causing some amps (probably poorer-designed ones) to oscillate a bit. Ringing from an IC's signal reflections is supposedly also possible, depending on the source component's output circuit. Then there's Skin Effect (which many think is absurd at audio frequencies), Maxwell Effect, etc. These are quite a bit harder to substantiate.
