What does the principle of superposition in wave mechanics state?

The principle of superposition in wave mechanics asserts that when two or more waves intersect or overlap in space, the resultant wave displacement at any point is equal to the algebraic sum of the displacements of the individual waves at that same point. This means that if one wave is cresting while another is troughing, the contributions of both waves can be added together to find the overall effect on displacement, leading to phenomena such as constructive and destructive interference.

This principle is foundational to various applications in physics, including sound waves, light waves, and water waves. It allows for the prediction of how waves will combine in various situations, providing a vital tool for understanding complex wave interactions in different mediums.