I have looked everywhere for an answer but no one can provide an obvious account that explains all scenarios. Specifically, I want to know how the two interfering (constructive or destructive) waves can pass through each other, and end up on the other side unchanged in amplitude and "shape".
Is it possible to think of this as a one-dimensional wave instead of a real electromagnetic of mechanical wave, without losing any of the important parts of the process? I feel like this simplifies it for me and gives me a way to understand how physical waves can pass through another wave of the same nature and remain unchanged on the other side.
So let's consider two waves on a string. Say "Wave1" of an "amplitude" of +5, at its peak, is on the left, moving to the right. A second wave, "Wave2", of an "amplitude" of -2 is on the right, moving to the left. In other words, Wave1 is at a peak while Wave2 is at a trough. When the two waves, traveling towards each other, meet at the same location, a superposition is formed and their individual displacements add to form a net displacement. In this case, the combined wave will have an "amplitude" of +3 (... +5 + -2). After the waves go through each other, it is not clear to me how (after having passed through each other) the sum, "+3", can reform Wave1 on the right as +5 and Wave2 on the left as -2. Why don't they reform as something like +6 and -1 or +3 and -4, or as a function of an average of the two waves?
I hope I didn't provide an example that was too simplified. Also, I used to think I understood superposition but perhaps my confusion exists only because I simply don't understand it. Thanks!