IB Physics SLTopic C.3 — How Waves BehavePaper 1 & 2path difference = nλ~8 min read
Interference
When two waves overlap, superposition adds their displacements — and the pattern we observe from that adding is interference. In some spots the waves reinforce into a big signal; in others they wipe each other out completely. Which happens where comes down to one thing: path difference.
📘 What you need to know
Interference is the observable effect of the superposition of two or more waves
Constructive interference: waves in phase (peak-to-peak) add to a bigger amplitude
Destructive interference: waves in antiphase (peak-to-trough) cancel to zero
A clear, steady pattern only forms when the sources are coherent: same frequency and a constant phase difference
Path difference is the difference in distance each wave travels from its source to the meeting point
Constructive when path difference = nλ; destructive when path difference = (n + ½)λ
Constructive and Destructive Interference
Superposition can play out in two extreme ways. When two waves meet in phase — crest lined up with crest — their displacements add and you get a wave of bigger amplitude: constructive interference. When they meet in antiphase — crest lined up with trough — they cancel out to leave nothing: destructive interference.
Left: two in-phase waves (dashed) build a resultant of double amplitude (purple). Right: two antiphase waves (dashed) cancel to a flat line (purple).
Coherence
You only get a stable, observable interference pattern if the two sources are coherent. That means they must have:
the same frequency, and
a constant phase difference between them
If the phase difference keeps jumping around, the bright and dark spots wander and smear out, so no steady pattern forms. This is why monochromatic laser light and two speakers driven at the same frequency are the classic coherent sources. At points that are neither fully in phase nor fully in antiphase, the resultant amplitude sits somewhere in between the two extremes.
Path Difference
What decides whether two waves arrive in phase or antiphase at a given point is the path difference — how much farther one wave has travelled than the other to reach that point.
Two coherent sources reach point P by different distances. The path difference (r₂ − r₁) sets whether they arrive in phase or antiphase.
Compare the path difference with the wavelength and you know instantly what you’ll see:
where n = 0, 1, 2, 3… A path difference of a whole number of wavelengths brings the waves back into step (constructive); an odd number of half-wavelengths puts them exactly out of step (destructive). On a wavefront diagram you can just count wavelengths from each source to the point and subtract.
🧭 Finding the interference at a point
Count the wavelengths (or measure the distance) from each source to the point
Subtract to get the path difference
A whole number of wavelengths (nλ) → constructive
A half-integer number of wavelengths ((n + ½)λ) → destructive
Check the sources are coherent first, or no steady pattern exists
Quick recap: constructive interference (in phase, bigger) happens at path difference nλ; destructive interference (antiphase, cancels) at (n + ½)λ — and only coherent sources give a steady pattern.
WE 1
Two coherent sources S₁ and S₂ emit waves of wavelength λ. At point P the waves travel 6λ and 6.5λ from the sources. At point Q they travel 7λ and 6λ.
On a wavefront diagram from two coherent sources, the distances to three points are: X → 5.5λ and 4.5λ; Y → 3.5λ and 3.5λ; Z → 4λ and 3.5λ.
Identify the interference at X, Y and Z.
Point X
5.5λ − 4.5λ = λ → constructivePoint Y
3.5λ − 3.5λ = 0 → constructivePoint Z
4λ − 3.5λ = 0.5λ → destructiveEqual distances (path difference 0) are constructive — it’s still a whole number of wavelengths, just n = 0.
💡 Top tips
Path difference nλ → constructive; (n + ½)λ → destructive — the two conditions in the data booklet
A path difference of zero is constructive (n = 0), not nothing
Coherent means same frequency and constant phase difference — both are needed
“Constructive builds, destructive destroys” is a handy memory hook
To find path difference on a wavefront diagram, count wavelengths from each source and subtract
⚠ Common mistakes
Treating zero path difference as destructive — it’s constructive (n = 0)
Confusing path difference (distance) with phase difference (angle)
Forgetting that only coherent sources give a stable interference pattern
Using nλ for destructive and (n + ½)λ for constructive — it’s the other way round
Mixing up interference (the effect) with superposition (the underlying adding)
Up next: we put all of this to work in the most famous interference experiment of all — Young’s Double-Slit Experiment — and derive the equation for the fringe spacing.
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