Physics · Ch 11 — Waves
Superposition Principle
Superposition Principle
When two persons hold opposite ends of a stretched string and each gives a simultaneous jerk, the two resulting wave pulses travel toward each other, meet, and pass through one another, each pulse afterward continuing onward with its own original shape completely intact -- as though the other pulse had never been present. Only near the moment and location where the two pulses actually cross does their combined behaviour differ noticeably from either pulse considered alone, and exactly what that combined behaviour looks like depends on whether the two pulses share the same shape or are shaped oppositely. This observed behaviour is captured mathematically by the principle of superposition: when two or more waves overlap in a medium, the net (resultant) displacement at any point and instant is simply the algebraic sum of the individual displacements each wave would have produced there on its own, . This single principle, extended to any number of overlapping waves, is the foundation for three related and important …
What this figure shows. Two separate wave pulses are shown approaching each other from opposite ends of a stretched string, then shown at the moment they overlap in the middle, and finally shown after having passed fully through one another and separated again, continuing onward each with its own original shape unchanged. The figure visually introduces the principle of superposition before it is stated mathematically: it demonstrates that even though the two pulses' displacements combine (add together) at the instant they overlap, each pulse afterward emerges completely intact, exactly as if the other pulse had never been there at all -- a property unique to waves, …