A-Level Physics — 11) Superposition (IP-Friendly Guide)

TL;DR
Superposition links every wave idea you meet from sound to quantum. Master:
<1> the add-and-subtract rule for overlapping waves,
<2> node-antinode spotting to read standing-wave diagrams at speed,
<3> three exam-grade formulae — \(ax/D = \lambda\), \(a \sin \theta = n \lambda\) and \(b \sin \theta = \lambda\) — plus the Rayleigh test for “too blurry to separate”. Nail these and Paper 2 Section B usually gifts 8-10 marks.

1 Where this sits in the syllabus

The SEAB 2026 H2 Physics document parks Superposition under Section I “Waves” and lists 13 learning outcomes, from the principle itself to the Rayleigh criterion for resolution.
Parents: this is traditionally examined in both conceptual MCQs and 6-mark structured problems, making it high-ROI for tuition sessions.

2 Principle of superposition

Rule: If two or more disturbances overlap in a linear medium, the resultant displacement is the algebraic sum of the individual displacements.

2.1 Quick check

Add two sine waves of the same frequency but a phase difference \(\phi\):
\[ y = y_1 + y_2 = A\sin(\omega t) + A\sin(\omega t + \phi) = 2A\cos\Bigl(\tfrac{\phi}{2}\Bigr)\sin\Bigl(\omega t + \tfrac{\phi}{2}\Bigr). \]
Amplitude modulation pops straight out of the maths — the entire idea behind noise-cancelling headphones.

2.2 Mini-drill

Sketch the resultant at \(t = 0\) for \(\phi = 0, \space \pi/2, \space \pi\). Label points of constructive and destructive interference.

3 Standing waves

A standing (stationary) wave forms when two identical waves travel in opposite directions and superpose. Nodes (zero displacement) and antinodes (max displacement) appear at fixed positions.

3.1 Graphical formation

Plot incident and reflected waves every \(\tfrac{T}{4}\). Nodes stay put at multiples of \(\tfrac{\lambda}{2}\); antinodes halfway between.

3.2 Measuring sound wavelength

For a pipe closed at one end, first resonance occurs at \(L = \tfrac{\lambda}{4}\). Measure \(L\) with a metre rule and compute \(v = f\lambda\) to within 3 %.

4 Two-source interference

Ripple tank, twin loudspeakers or Young 's double-slit—same physics. Conditions:

• Coherence (constant phase difference),
• Similar amplitudes,
• Path-difference governed phase.

4.1 Double-slit formula

Derivation assumes \(D \gg a\) and small angles:
\[ \frac{ax}{D} = \lambda. \]
Use it to find \(\lambda\) of red laser light quickly in the lab.

5 Diffraction grating

Large arrays of slits sharpen the interference:
\[ a \sin \theta = n \lambda. \]
For a typical 600 lines mm⁻¹ grating, \(a = 1.67 \times 10^{-6} \space \text{m}\). First-order green \((\lambda = 550 \space \text{nm})\) appears at \(\theta \approx 19°\).

Exam tip: higher orders may “walk off the screen”. Check \(|\sin \theta| \le 1\).

6 Single-slit diffraction

The first minima satisfy
\[ b \sin \theta = \lambda. \]
Narrowing the slit widens the central peak—exactly the opposite of photographic aperture behaviour.

7 Rayleigh criterion — resolving power

Two point sources are just resolved when the principal maximum of one falls on the first minimum of the other:
\[ \theta \approx \frac{\lambda}{b}. \]
Smaller \(\theta\) means sharper detail; astronomers fight atmospheric seeing to get below 1 arc-second.

8 Three common exam traps

1. Mixing displacement and pressure nodes — in sound pipes, they are half a loop out of phase.
2. Using \(v = f\lambda\) for standing waves — remember the wave still travels even though the pattern is stationary.
3. Using degrees in calculator set to radians — spot when your \(\sin \theta\) looks off.

9 WA timing rules (tested in our tuition drills)

1. 1 mark ≈ 1.5 min — budget graph sketches accordingly.
2. Label nodes/antinodes first — avoids losing easy pictorial marks.
3. Quote \(\lambda\) to 3 sf unless data dictate otherwise — SEAB penalises over-precision.

10 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Isaac Physics — Superposition
• Wikipedia — Superposition principle
• Physics Classroom — Nodes & Antinodes
• HyperPhysics — Standing Waves on a String
• Save My Exams — Two-Source Interference
• LibreTexts — Diffraction Gratings
• Lumen Learning — Single-Slit Diffraction
• Lumen Learning — Rayleigh Criterion
• Science Buddies — Measure Speed of Light with a Microwave

11 Call-to-action

Parents: book a 60-min Superposition clinic two weeks before WA 1—it typically lifts wave-topic marks by 15 %.
Students: pin the three key formulae on your study wall and practise switching between degrees and radians on your calculator.

Last updated 14 Jul 2025. Next review when SEAB releases the 2027 draft syllabus.