Given we have two Guassian wave pulses in the same medium (string) but in opposite directions. The principle of superposition states that they should pass through each other without being disturbed, and that the net displacement is the vector sum of the individual displacements.
My question is, how does the string have 'memory' of the information on the shape and velocity of both pulses separately? For instance, consider if the interference were destructive. Then when the string is perfectly flat, it cannot have memory of what brought it to this state; similar to how a particle does not continue to accelerate after a force has stopped acting: it has no memory. I understand that although the displacement is zero, the velocity is non zero and at this point the string has kinetic energy. How can the string know from the velocities of various points which waves will emerge?
How do both the waves emerge unchanged?
I think my confusion stems from a lack of conceptual clarity on the principle of superposition, I may not completely understand it. Any help is appreciated.
Note to moderators: I request that this question not be treated as a duplicate. While there are similar questions here and here, none of the answers are able to justify how this happens in terms that make sense to me.