This question has been bothering me for a very long time.
Imagine a wire carrying electric current. It carries two alternating current (AC) signals of different frequencies (say $50$ Hz and $60$ Hz). Now, since both the signals are on the same medium (wire), if I see the resultant signal on an oscilloscope or other device, I would actually see a new resultant signal that is an algebraic sum of individual waves at every point, but not the original signals anymore.
How can the individual signals (waves) be separated from the wire after they combined to form a new wave? I know the telephone lines and TV cables carry multiple frequency signals on the same medium, and we successfully separate them at the receiver, but was thinking how is it possible to separate out individual signals when they combine and result in a different wave altogether? How can receiver figure out the original two waves or hundreds of waves that resulted in the combined wave?
I read about Fourier series analysis and signal filters but it just does not make sense fundamentally to me.
It is like adding two numbers 2 and 3 which results in 5 and being able to separate them again in to 2 and 3 and not 1 and 4 or some other combination. The medium (wire) has only the combined superimposed wave. How does the receiver know that 5 should be separated as 2 + 3 but not 1 + 4 or 2.5 + 2.5 I hope I'm making sense. I tried googling this but I think I'm not framing the right search terms.