How come a power cable changes the sound?

if you want to test an expensive power cable be SURE you can return it - and then use a double blind test

insulting people that DO hear a difference is less than helpful, but people that think they hear a difference are highly likely to be victims of confirmation bias and are insulting everyone else

writing about speculative notions as to why something could possibly sound different is of use only to engineers who want to test those hypotheses - not to consumers

cognitive psychologists have clearly established the effects of visual and other biases on sensory perception - either guard against that or waste your money

It's interesting that I have been seeing someone post on an older thread.  This particular thread is 16 years old, so I doubt the OP and original postings really care about this subject anymore.  lol

A Larger gauge power cord may help for high current components. A power cord without ground may change things compared to one with a ground - due to ground loops. Otherwise, unless there is a filter built into the cable then differences should be negligible if the power supply of your equipment is well designed.

If your equipment has a lousy power supply design then all bets are off - turning on the light or even your fridge may affect the sound and so might simply unplugging the power cord and plugging back in. Perhaps, in this case, you might even worry about the electrical transformer on your block or the kind of coal burned at the power station!

A well designed power supply should isolate the line level audio electronics from mains noise and provide clean power as required by the circuits - pretty simple really.

Back in the 80's I remember salesmen trying to convince audiophiles that the first generation CD players were the "ultimate" and totally superior to vinyl.  But to realise the benefits that "superior" CD offered - it required another investment.  A special very high cost isolation stand was required to remove the obvious harsh digital distortion that was caused by vibration.

This was of course all sales bunkum - but it extracted a lot of money from the gullible who did not realise the real issue was the CD player design and limitations of the medium.

From my perspective there is a hierarchy in audio systems - based on proven engineering principles:  The system foundations are the amps, loudspeakers and of course the quality of cd/anologue sources.  Room acoustics and personal hearing are also important factors.
Second comes the interconnects/speaker cables that we all agree can make or break the system.  

At the third level,  I believe good mains filtering produces audible improvements in a high-end system and I use one!
However, I personally have not detected any audible improvements in changing from good stock (Isotek) mains cables to very high cost esoteric alternatives. 

Instead of spending big money on mains cables I suggest a  "signal path component upgrade"  may be more rewarding.