Fourier analysis is
exactly the answer to your curiosity.
Please allow me to make a comment. You seem to be a person who has anxiety in regards to science. You're waffling, with doubts in your mind. On one hand, you seem to respect scientific principles, but on the other hand, you seem to retain residual ties to the Subjectivist ways of thinking.
You can't have it both ways. There is no middle ground. You don't pick and choose which one you wish to believe for one issue and which to believe for another issue. It doesn't work that way.
You trust science for medicine, for cell phones, for cars, for weather radar ........ relax and trust it for audio, too.
Jim