AP® Physics 2: Algebra-Based · Unit 14 · Topic 14.6
Superposition and Interference
Superposition says overlapping waves simply add their displacements at every point in space. Where the adds line up you get constructive interference; where they cancel you get destructive interference, with the total energy always conserved.
Superposition is the rule that overlapping waves do not fight or block each other. At every point where waves meet, you just add the displacements together, moment by moment. If two crests arrive together, you get a bigger crest. If a crest meets a trough of equal size, they cancel to flat. This is why two speakers playing the same tone can create a dead spot in a room: at that exact location, one speaker's compression arrives at the same instant as the other's rarefaction, and the air barely moves even though both speakers are blasting.
Picture two stones dropped in a pond, each sending out circular ripples. Where two crests overlap, you see an extra-tall ripple: constructive interference. Trace outward and you find curved lines where a crest from one source permanently meets a trough from the other no matter how the pattern expands; along those lines the water stays nearly still. Those are nodal lines of destructive interference. The pattern is fixed in space because the two sources keep the same timing relationship, called coherence, so the same points cancel or reinforce every cycle.
None of this destroys energy. A dark spot just means the energy that would have gone there got redirected to the bright spots nearby, so the total energy spread across the whole pattern matches what the two sources put out. This connects directly to double-slit light patterns, where the same addition rule produces bright and dark fringes, and it sets up the idea that flipping one source's timing by half a cycle swaps every bright spot for a dark one, since the addition rule is still the same, only the inputs changed sign.
Key terms
- Superposition
- The principle that overlapping waves add their displacements point by point at every instant.
- Constructive interference
- Overlap where waves add to produce a larger displacement than either wave alone.
- Destructive interference
- Overlap where waves add to produce a smaller displacement, including cancellation to zero.
- Coherence
- A fixed, unchanging phase relationship between two sources that keeps their interference pattern stable over time.
- Nodal line
- A curve in space where destructive interference occurs continuously as two circular waves overlap.
Watch it explained
- How it worksHow do two overlapping waves simply add displacement by displacement at every point?
- How it worksWatch two circular ripple patterns overlap and trace the lines where they cancel.
- Common mistakeWhy doesn't destructive interference destroy the energy the two waves were carrying?
- Going furtherWhat changes about the pattern when one source is flipped to be exactly out of phase?
Check yourself
End of topic.