Let us take a look at the next video:
In this video, two pulses are traveling: one from left to right and the other from right to left. These two pulses are overlaid at the center and the resultant pulse becomes bigger (its maximum height becomes twice as high as the single pulse). After overlaying each other, they continue to travel as if nothing happened. Thus, waves travel independently, and when they are overlaid, the displacement of each dot becomes addition of their original displacements. This is called the principle of superposition.
What is going to happen, if the second pulse from left to right is inversed (not an upward pulse but a downward pulse)? Then, when the pulses are overlaid, the displacements of the dots become 0 at that moment.
The next video clip shows three cycles of two sinusoidal waves when traveling one from left to right and the other from right to left.
When the second sinusoidal wave is inversed, it looks like this: