The big idea: Drop two stones into a still pond and watch the ripples cross — where two crests meet the water heaves higher, where a crest meets a trough it flattens out. When two waves arrive at the same point, you add their displacements at every instant: that is superposition.
If they arrive in step (crest on crest) the result is bigger — constructive interference.
If they arrive half a cycle out of step (crest on trough) and are equal, they cancel — destructive interference.
Two words to know: Amplitude = the height of a crest above the middle (how 'big' the wave is).
In phase = exactly in step (crests line up). Antiphase = half a cycle out of step (a crest lines up with a trough).
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Just add the displacements: Crest + crest → a taller crest (constructive).
Equal crest + trough → zero (destructive).
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Often two waves start in step from a source but travel different distances to reach a point. The extra distance one wave travels is the path difference. That single number decides whether they end up in step (constructive) or out of step (destructive).
New term — path difference: Path difference = how much further one wave travels than the other to reach the point, measured in metres.
What matters is how this compares with the wavelength λ.
- extra distance one wave travels to reach the point (m)
- a whole number: 0, 1, 2, 3, …
- wavelength of the waves (m)
Constructive (in step)
- Path difference = 0, λ, 2λ, 3λ, … (nλ)
- Waves arrive in phase
- Amplitudes add → bright / loud
Destructive (out of step)
- Path difference = ½λ, 1½λ, 2½λ, … ((n+½)λ)
- Waves arrive antiphase
- Equal amplitudes cancel → dark / quiet
Two loudspeakers play the same note (wavelength 0.80 m), in step. At a point P the sound from one speaker has travelled 1.6 m further than from the other. Is the sound at P loud (constructive) or quiet (destructive)?
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How this is tested — interference comes up with sound, light and microwaves:
Paper 1A
- Add the amplitudes of two waves at a point.
- Or pick constructive vs destructive from a path difference.
Paper 2
- Explain why two sources must be coherent.
- Or outline why a point is quiet (destructive) using path difference.
The classic trap: For destructive cancellation to be complete the two amplitudes must be equal — otherwise only part cancels.
New word — coherent: Two sources are coherent if they keep a constant phase difference — the same wavelength and a fixed, unchanging step between them.
Only coherent sources give a steady interference pattern; if the phase difference kept changing, the bright and dark points would jump around and average out to nothing.
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Two small loudspeakers are driven by the same signal (so they are coherent) and emit sound of wavelength 0.50 m. (a) At a detector the sound from one speaker has travelled 0.25 m further than from the other — outline why the detector picks up almost no sound. (b) The demonstration only gives a steady pattern of loud and quiet points if the speakers are coherent. Explain what coherent means and why it is needed.
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See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.