Piratelord, you cannot prove a negative. Everyone knows that.
If you contend that a power cord makes a difference, the burden of proof is on you.
Also, you're offering the unknown as "proof" that something might work. That makes no sense whatsoever.
You're acting like cables exist in a vacuum where anything is possible. The problem with that position is that there are - literally - hundreds of millions of electrical products out there. Similarly, there have been hundreds of millions of tests, going back a good 120 years. If there was a mysterious force governing power cables, then you must assume that these anomalies would turn up in all sorts of electrical goods. But they don't. Everything behaves according to understood physics and science. So if your power cord actually produces a different result, all sorts of strange results should be turning up in - again, literally - millions of different electrical products. If what you're proposing is true, then you should be finding anomalous results with light bulbs and electric motors, just to name two.
Further, if the electrical signal is changed enough to be heard, then that ought to show up on a DMM, oscilloscope, spectrum analyzer, etc., as well. That they don't strongly suggests that there is no difference.
Again, the burden of proof is on the person making the claim. If you assert something, then back it up. You can't expect someone to prove a negative.
If you think your personal experience is enough to justify a claim, then you must demonstrate that you are free of bias and not susceptible to placebo or expectation. That's tough, since the human mind is a complete sucker for those things. If you can demonstrate that you aren't biased and placebo doesn't work on you, I imagine you could make quite a bit of money as a test subject.