IB Physics SLTopic C.3 — How Waves BehavePaper 1 & 2y = y₁ + y₂~6 min read
Superposition
What happens when two waves try to occupy the same spot at the same time? They don’t collide or bounce off — they simply add up. That single rule, the principle of superposition, is the foundation of everything that follows about interference.
📘 What you need to know
Superposition is what happens when two or more waves overlap at the same point
The principle of superposition: the resultant displacement is the sum of the individual displacements
Displacements are vectors — add them algebraically, keeping track of positive and negative
Crest meeting crest ⇒ a bigger displacement; crest meeting trough ⇒ they cancel
Two pulses combine while overlapping, then carry on unchanged afterwards
The observable effect of superposition is called interference
The Principle of Superposition
When waves meet, each one keeps doing its own thing — but at every point the medium feels the combined push of both. So the total displacement at any instant is just the two individual displacements added together:
Principle of superpositionyresultant = y1 + y2
Because displacement is a vector, a downward (negative) displacement counts as negative in the sum. Two crests together build a larger crest; a crest landing on an equal trough cancels to zero. The clearest way to see it is to draw both waves on the same displacement axis and add them point by point.
Two in-phase waves (dashed) add at every point to give the resultant (solid teal). At each crest the resultant displacement is y1 + y2.
Superposition of Pulses
The same rule works for single pulses. As two pulses pass through each other, the displacement where they overlap is the algebraic sum of the two — so two upward pulses briefly make one taller pulse. The neat part: once they’ve passed, each pulse carries on exactly as before, as if nothing had happened.
Two upward pulses approach, briefly overlap into one taller pulse (their displacements add), then move apart completely unchanged.
🧭 Adding waves by superposition
Line the waves up on the same displacement axis at the same instant
At each point, read off the displacement of each wave (with its sign)
Add them algebraically: up + up is bigger, up + down partly (or fully) cancels
Plot the sums to get the resultant wave
Remember pulses separate unchanged after overlapping
Quick recap: where waves overlap, add their displacements as vectors — the resultant is y1 + y2 at every point, and the effect we observe is interference.
WE 1
Two waves overlap at a point. At one instant, wave 1 has a displacement of +0.7 cm and wave 2 also has +0.7 cm. At a different point, wave 1 is +0.5 cm and wave 2 is −0.5 cm.
Find the resultant displacement at each point.
First point
Add the displacements: y = (+0.7) + (+0.7)
y = +1.4 cmSecond point
y = (+0.5) + (−0.5)
y = 0 cmSame rule both times — just keep the signs; equal-and-opposite displacements cancel.
WE 2
Two waves, each of amplitude 3.0 cm, arrive at a point.
State the resultant amplitude if they meet (a) in phase, (b) in antiphase.
Part (a) — in phase
Crests line up, so amplitudes add: 3.0 + 3.0
6.0 cmPart (b) — in antiphase
Crest meets trough, so they cancel: 3.0 + (−3.0)
0 cmThese two extremes are constructive and destructive interference — the subject of the next page.
💡 Top tips
Superposition is just adding displacements — nothing bounces or blocks
Keep the signs: displacements are vectors, so downward is negative
Add point by point along the axis, not amplitude-to-amplitude in one go
After overlapping, pulses and waves continue unchanged
Maximum sum = in phase; full cancellation = in antiphase
⚠ Common mistakes
Thinking waves collide or block each other — they pass straight through
Ignoring signs and adding magnitudes, so cancellation is missed
Adding only the amplitudes instead of the displacement at each individual point
Believing pulses are altered after they overlap — they emerge unchanged
Confusing superposition (the adding) with interference (its observed effect)
Up next: the observable result of all this adding — Interference of Waves, where we meet constructive and destructive interference, coherence and path difference.
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