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 - Dax=λ, asinθ=nλ
and
bsinθ=λ
- 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 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 \(\lambda\) and hence \(c\)
Turns kitchen fun into physics; reinforces node-spacing = \(\dfrac{\lambda}{2}\)
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: Dax=λ.
Use it to find λ of red laser light quickly in the lab.
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≈bλ.
Smaller θ means sharper detail; astronomers fight atmospheric seeing to get below 1 arc-second.
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)
1 mark ≈ 1.5 min - budget graph sketches accordingly.
Label nodes/antinodes first - avoids losing easy pictorial marks.
Quote λ to 3 sf unless data dictate otherwise - SEAB penalises over-precision.
Comprehensive revision pack
9478 Section III, Topic 11 Syllabus outcomes at a glance
Outcome (a) - state and apply the superposition principle.
Outcome (b) - describe formation of standing waves in strings and air columns.
Outcome (c) - analyse interference patterns from two coherent sources (Young's slits).
Outcome (d) - apply diffraction grating and single-slit conditions.
Outcome (e) - use the Rayleigh criterion to discuss resolving power.
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
\( y = 2A \cos!\Bigl( \dfrac{\phi}{2} \Bigr) \sin!\Bigl( \omega t + \dfrac{\phi}{2} \Bigr) \)
Standing wave nodes
\( \Delta x = \dfrac{\lambda}{2} \)
Young's double slit
\( \dfrac{a x}{D} = n \lambda \)
Diffraction grating
\( a \sin \theta = n \lambda \)
Single-slit diffraction
\( b \sin \theta = m \lambda \) (first minimum \( m = 1 \))
Rayleigh criterion
\( \theta = \dfrac{\lambda}{b} \)
Pipe harmonics (open/closed)
\( L = n \dfrac{\lambda}{2} \) (open), \( L = (2n - 1) \dfrac{\lambda}{4} \) (closed)
Term guide
Symbol / term
Meaning
\( \phi \)
Phase difference between the interfering waves
\( A \)
Amplitude of each interfering wave
\( \omega, t \)
Angular frequency and time
\( \Delta x \)
Separation between successive displacement nodes
\( \lambda \)
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)
\( \theta \)
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 Dax=λ.
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.
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.
