Physics 9702 · syllabus 8
Cambridge A Level Physics 9702 — Superposition topical past papers
What happens when waves meet: stationary waves on strings and in air columns, diffraction, two-source interference and the diffraction grating.
- Questions
- 473
- Years
- 2009–2026
- With mark scheme
- 100%
- Questions 2022–2026
- 136
Anyone can browse these pages. Opening the questions and their mark schemes takes a free Momentum account.
What Superposition covers
When two waves meet, the resultant displacement at any point is the sum of their separate displacements: the principle of superposition. Two waves of the same frequency travelling in opposite directions form a stationary wave, with nodes that never move and antinodes of maximum amplitude between them. Adjacent nodes are half a wavelength apart, which is how a stationary wave on a string, in an air column or between a microwave source and a reflector gives you the wavelength.
Diffraction is the spreading of a wave as it passes through a gap or around an edge, most marked when the gap is comparable to the wavelength. Interference between two coherent sources, with a constant phase difference, produces a pattern of maxima and minima, and for light through a double slit the fringe separation x obeys λ = ax/D.
A diffraction grating uses many slits to give sharp, widely spaced maxima at angles given by d sin θ = nλ, which makes it the precise way to measure the wavelength of light. Superposition is AS content, examined on Papers 1 and 2. It depends on the wave vocabulary of the previous topic, and electron diffraction in quantum physics uses the same ideas.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- 8 Superposition
- 8.1 Stationary waves
- 8.2 Diffraction
- 8.3 Interference
- 8.4 The diffraction grating
What you should be able to do
- Explain how a stationary wave forms from two progressive waves, and identify nodes and antinodes
- Find the wavelength from node or antinode positions on strings, in air columns and with microwaves
- State the conditions needed to observe a two-source interference pattern
- Use λ = ax/D for a double slit, and path difference to decide between constructive and destructive interference
- Use d sin θ = nλ, including finding the highest order that can be seen
- Describe how the width of a gap relative to the wavelength affects diffraction
Key ideas
- Adjacent nodes, or adjacent antinodes, are λ/2 apart; a node and the next antinode are λ/4 apart
- For sources in phase: constructive interference where the path difference is nλ, destructive where it is (n + ½)λ
- Double slit: λ = ax/D, with a the slit separation, x the fringe separation and D the slit-to-screen distance
- Diffraction grating: d sin θ = nλ, with d = 1 ÷ (number of lines per metre)
How Superposition has been examined
From 2022 to 2026, Superposition was on Paper 2 · AS Level Structured Questions in 9 of 11 exam series, worth about 10% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Multiple Choice | 115 | 9% | 11 of 11 |
| Paper 2 · AS Level Structured Questions | 21 | 10% | 9 of 11 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 1.
Filed in Momentum under: Superposition.
A worked example
Light of wavelength 589 nm falls normally on a diffraction grating with 500 lines per millimetre. Find the angle of the second-order maximum and the highest order that can be seen.
- Line spacing: d = 1 / (500 × 10³ m⁻¹) = 2.00 × 10⁻⁶ m
- Second order: sin θ = nλ/d = 2 × 589 × 10⁻⁹ / 2.00 × 10⁻⁶ = 0.589
- θ = sin⁻¹ 0.589 = 36.1°
- Highest order: n ≤ d/λ = 2.00 × 10⁻⁶ / 589 × 10⁻⁹ = 3.40, and n must be a whole number, since sin θ cannot exceed 1
Answer: Second-order maximum at 36.1°; the highest order seen is the third
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Taking the distance between adjacent nodes as a whole wavelength — it is half a wavelength, so the answer comes out twice too large
- Using lines per millimetre directly as d — a grating with 500 lines per mm has d = 1/500 mm = 2.00 × 10⁻⁶ m
- Rounding d/λ up to find the highest order — if d/λ = 3.4, the third order is the highest, because sin θ cannot exceed 1
- Describing coherent sources as having the same frequency and amplitude — coherence needs a constant phase difference; equal amplitudes only make the minima darker
- Saying energy is destroyed at a minimum — it is redistributed to the maxima
Exam technique
- When explaining a stationary wave, mention reflection, two waves of the same speed and frequency travelling in opposite directions, and superposition
- Measure across several fringes and divide to find x, and say why: it reduces the percentage uncertainty
- For grating questions, convert lines per mm into d in metres first, and check that your calculator is in degree mode
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.