how can a line cord affect frequency response ?

Some time when I have a few grand to get rid of I will try out some different power cords. Til then I will stick to my belief that a properly designed power supply will produce DC without artifacts of the input AC power. There are many instances where physical characteristics are completely lost in a transitional state.
A simple analogy might be a river going over a waterfall. The smoothly flowing water below the falls shows no evidence of ripples above the falls. The river has been reconstituted from millions of droplets falling through the air, and has "lost its memory" of what happened above the falls.

For decades I have experimented and listened for changes in my system. Sometimes I hear something, sometimes I don't. When I hear something I am open minded. When I don't I am a naysayer. C'est la vie.

Albertporter...I don't wish to argue the merits of exotic power cords, isolation devices, and similar audiophile paraphinalia, but some manufacturers doing demos at shows will admit that they have to incorporate these things in their setup or else their potential customers will not take the demo seriously. Like chicken soup...can't hurt.

Twl...Most of the parameters which are spec'd for audio equipment are good for verifying that the circuit is working properly, but relate only imperfectly to sonic quality. However, there are tests that one can perform which I think would satisfy your objection. One such test is to observe (by oscilloscope or by listening to it) the difference between a signal waveform going into the device and what comes out, adjusted for gain of course. This signal can be any waveform, music if you like, although other waveforms like a square wave may present more of a challenge. Note that I did not say to measure the difference, because quite disparate waveforms may have similar measurements.

For another example, if you drive two identical power amps with the same signal you should (ideally) see nothing when you measure across the two hot output terminals. Note that this can be done with real music and driving real speakers. Now put an aftermarket PC on one of the amps. If the measurement is still zero (or the same tiny number) it is safe to say that the PC did nothing. If there is a difference you could make a recording of it and play it back so you could listen to it, and form some opinion of the sonic effect of the PC.

Twl...Have you ever determined the noise level and output impedance of your battery? It ain't zero! However, if the 12vdc feeds a capacitor, as with a normal power supply, you won't have a problem.

In accordance with Shadorne's observations about coal-fired power plants, have you noticed any difference in your sound depending on whether the solar panels were exposed to bright sunlight or only a dingy overcast?