Superposition links every wave idea you meet from sound to quantum.
Key points
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 - \\( x\_n = \dfrac\{n \lambda D\}\{a\} \\) (fringe spacing \\( \Delta x = \dfrac\{\lambda D\}\{a\} \\)), \\( a \sin \theta = n \lambda \\) and \\( b \sin \theta = \lambda \\) - plus the Rayleigh test for “too blurry to separate”.
These show up often in structured questions, so practising them pays off.
Planning a revision session? Use our study places near me map to find libraries, community study rooms, and late-night spots.
Read in layers
1 second
Read the summary above.
10 seconds
Scan the first few sections below.
100 seconds
Jump into the section that matches your decision.
Quick study map
Concrete example: how to use this page
1 Where this sits in the syllabus
2 Principle of superposition
Q: What does A-Level Physics: 11) Superposition Guide cover? A: Standing waves, double-slit fringes and the Rayleigh criterion sound abstract-until you melt chocolate in a microwave or tune a guitar string.
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 - xn=anλD (fringe spacing Δx=aλD
),
asinθ=nλ
and
bsinθ=λ
- plus the
Rayleigh test
for “too blurry to separate”. These show up often in structured questions, so practising them pays off.
Quick study map
If you only have...
Focus on...
1 second
Overlapping waves add their displacements
10 seconds
Superposition, nodes, antinodes, and fringe spacing
100 seconds
The principle statement and first standing-wave example
10 minutes
Diffraction, double-slit formulae, and Rayleigh criterion
Concrete example: how to use this page
If two waves arrive together, add their displacements, not their speeds. Bright and dark fringe questions usually become easier after you translate path difference into phase difference.
Keep the wave toolkit coherent by revisiting our free H2 Physics notes; it chains this topic with Wave Motion, Diffraction, and Quantum follow-ups so your superposition drills stay contextual.
1 Where this sits in the syllabus
The SEAB 2026 H2 Physics document parks Superposition under Section III “Waves” and lists 13 learning outcomes, from the principle itself to the Rayleigh criterion for resolution. Parents: this topic is commonly examined in both conceptual MCQs and multi-mark structured questions, making it a high-leverage chapter to revise.
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 ϕ:
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 ϕ=0,π/2,π. 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.
Medium
Demo
Why parents should care
Microwave oven
Take out the turntable, melt chocolate, measure node spacing to estimate λ and hence c
Turns kitchen fun into physics; reinforces node-spacing = 2λ
Stretched string
Vibrator + pulley illustrates harmonics; count antinodes to read n
Many WA questions hide “find mode number” marks here
Closed air column
Slide a piston to find loud spots (pressure antinodes)
Links sound labs to displacement vs pressure phase diagrams
3.1 Graphical formation
Plot incident and reflected waves every 4T. Nodes stay put at multiples of 2λ; antinodes halfway between.
3.2 Measuring sound wavelength
For a pipe closed at one end, first resonance occurs at L=4λ. Measure L with a metre rule and compute v=fλ 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≫a and small angles: xn=anλD,Δx=aλD.
Use it to find λ of red laser light quickly in the lab; Δx is the spacing between adjacent bright fringes.
5 Diffraction grating
Large arrays of slits sharpen the interference:
asinθ=nλ
For a typical 600mm−1 grating, a=1.67×10−6m. First-order green (λ=550nm) appears at θ≈19∘.
Exam tip: higher orders may “walk off the screen”. Check ∣sinθ∣≤1.
6 Single-slit diffraction
The first minima satisfy\
bsinθ=λ.
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:\
θ≈1.22bλ.
Smaller θ means sharper detail; astronomers fight atmospheric seeing to get below 1 arc-second. (The 1.22 factor comes from the first minimum of the circular Airy disk.)
8 Three common exam traps
Mixing displacement and pressure nodes - in sound pipes, they are half a loop out of phase.
Using v=fλ for standing waves - remember the wave still travels even though the pattern is stationary.
Using degrees in calculator set to radians - spot when your sinθ looks off.
9 WA timing rules (tested in our tuition drills)
Use syllabus pacing as a guide: Paper 2/3 average ~1.6 min/mark; Paper 4 ~3 min/mark.
Label nodes/antinodes first - avoids losing easy pictorial marks.
Match sig-figs to the data - avoid over-precision.
Need structured practice on Superposition? Our H2 Physics tuition programme covers this topic with weekly problem sets and Paper 4 practical drills.
Comprehensive revision pack
9478 Section III, Topic 11 Syllabus outcomes
Candidates should be able to:
(a) explain and use the principle of superposition in simple applications.
(b) show an understanding of experiments which demonstrate standing (stationary) waves using microwaves, stretched strings and air columns.
(c) explain the formation of a standing (stationary) wave using a graphical method, and identify nodes and antinodes, differentiating between pressure and displacement nodes and antinodes for sound waves.
(d) determine the wavelength of sound using standing (stationary) waves.
(e) show an understanding of the terms diffraction, interference, coherence, phase difference and path difference.
(f) show an understanding of phenomena which demonstrate two-source interference using water waves, sound waves, light and microwaves.
(g) show an understanding of the conditions required for two-source interference fringes to be observed.
(h) recall and use the equation Dax=λ to solve problems for double-slit interference, where a is the slit separation and x is the fringe separation.
(i) recall and use the equation asinθ=nλ to solve problems involving the principal maxima of a diffraction grating, where a is the slit separation.
(j) describe the use of a diffraction grating to determine the wavelength of light (knowledge of the structure and use of a spectrometer is not required).
(k) show an understanding of phenomena which demonstrate diffraction through a single slit or aperture, or across an edge, such as the diffraction of water waves in a ripple tank with both a wide gap and a narrow gap, or the diffraction of sound waves from loudspeakers or around corners.
(l) recall and use the equation bsinθ=λ to solve problems involving the positions of the first minima for diffraction through a single slit of width b.
(m) recall and use the Rayleigh criterion θ≈bλ for the resolving power of a single aperture, where b is the width of the aperture.
Concept map (in words)
Start with linear superposition: add displacements to obtain resultant wave. Standing waves arise from counter-propagating waves with equal amplitude. Two-source interference depends on coherence and path difference. Diffraction creates envelope patterns that govern resolution; Rayleigh criterion links aperture size to angular detail.
Key relations
Context
Expression
Resultant of equal waves
y=2Acos(2ϕ)sin(ωt+2ϕ)
Standing wave nodes
Δx=2λ
Young's double slit
Dax=nλ
Diffraction grating
asinθ=nλ
Single-slit diffraction
bsinθ=mλ (first minimum m=1)
Rayleigh criterion
θ=1.22bλ
Pipe harmonics (open/closed)
L=n2λ (open), L=(2n−1)4λ
Term guide
Symbol / term
Meaning
ϕ
Phase difference between the interfering waves
A
Amplitude of each interfering wave
ω,t
Angular frequency and time
Δx
Separation between successive displacement nodes
λ
Wavelength of the wave
a
Slit separation or grating spacing
x
Fringe spacing on the observation screen
D
Distance from the slits/grating to the screen
b
Slit width / aperture diameter (single slit or telescope)
n,m
Order numbers (n for maxima, m for minima)
θ
Diffraction / interference angle
L
Length of the air column or string segment
Derivations & reasoning to master
Standing wave equation: superpose sin(kx−ωt) and sin(kx+ωt) to obtain 2Asin(kx)cos(ωt).
Double-slit fringe spacing: use geometry for small angles (tanθ≈x/D) to derive xn=anλD
Grating orders: explain why maxima sharpen as number of slits increases (constructive interference, destructive elsewhere).
Resolution limit: interpret Rayleigh criterion with diagrams of overlapping Airy disks and the 1.22 factor.
Worked example 1 - string harmonics
A string fixed at both ends has length 0.90m and supports standing waves at frequencies 120Hz and 160Hz but not in between. Find the fundamental frequency and wave speed.
Solution: consecutive harmonics differ by f0⇒f0=40Hz. Use v=2Lf0=72m⋅s−1.
Worked example 2 - diffraction grating spectrum
Light of wavelengths 450nm and 650nm hits a grating with 500mm−1. Determine the highest observable order for each colour.
Method: grating spacing a is approximately 2.00⋅10−6m. Because sin(θ) must not exceed 1, n is limited by a/λ. For 450nm, take nmax=4; for 650nm, nmax=3.
Practical & data tasks
Capture node/antinode positions with a stroboscope and string vibrator; measure λ.
Use a laser and double slit to photograph the fringe pattern; calculate λ from fringe spacing.
Build a DIY spectrometer with CD grating; record angles versus colour for cross-checking grating equation.
Common misconceptions & exam traps
Confusing phase difference with path difference (missing λ2π factor).
Forgetting that intensity ∝A2 when combining waves.
Mixing displacement nodes with pressure nodes in wind instruments.
Ignoring missing orders in grating problems when nλ equals the slit spacing.
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.
