The Principle of Superposition
The Principle of Superposition
- Two waves can be in the same place at the same time. They do not hit each other, and they do not bounce. They just cross and keep going — like two sets of ripples passing on a pond.
- Where they meet, the point does both things at once: it adds the two waves. Both waves go up, so it moves up more. One goes up and one goes down by the same size, so they cancel and it does not move.
Adding the two waves
- At each point, add the two heights. The total is the — the new wave.
- Both up gives a taller wave here. One up and one down of the same size cancel to zero. In between, they add to something in the middle.
- Do this at every point along the wave. You get the resultant — the gold line below. It is just the blue wave plus the green wave.
Because waves add, they can also cancel. Two waves can meet at a point and the point stays completely still: zero. Every quiet point, dark band and standing wave in this chapter comes from this cancelling.
The exact statement
- Here is the line to learn for the exam, word for word: when two or more waves meet at a point, the resultant displacement is the algebraic sum of the displacements of the individual waves.
- It means: where waves meet, add them up with + and −. That plus-and-minus adding is , and the “+ and −” is exactly what lets them cancel. ( = how far the wave has pushed the point from rest, up or down.)
- It works for any number of waves, and for every kind — water, sound, light, microwaves.
- One rule only: the waves must be the same kind. You can't add a sound wave to a light wave.
Your turn— tap to reveal the worked answer (9702/13/M/J/24 Q27)
Two waves meet and add up at a point. What one thing must be true about them for superposition to work?
Answer: they must be the same kind of wave. They do not need the same size, the same frequency, or the same direction — superposition only needs two waves of the same kind. (9702/13/M/J/24 Q27)