Q: What does A-Level Physics: 10) Wave Motion & Polarisation Guide cover? A: From basic wave vocabulary to Malus' law, this post unpacks Section III Topic 10 of the 2026 H2 Physics syllabus for IP students and parents.
TL;DR Wave Motion is not “pure theory” - it is the marks engine behind interference, optics and even Modern Physics. This guide converts the SEAB bullet-points into lesson check-lists, graph-reading drills and WA timing hacks.
Concrete example: how to read the chapter
If a question gives frequency in MHz and wavelength in nm, convert units before using v=fλ. If a question gives distance from a point source, look for the inverse-square rule. This split keeps wave-speed questions and intensity questions from blending together.
Decision map - choose the wave route first
The same symbols can appear in several wave contexts. Identify the physical idea before reaching for a formula.
Question clue
Route to use
First move
Common trap
Frequency, wavelength, period, or wave speed
wave-speed relation
convert units, then use v=fλ
Reviewed by
Chee Wei Jie·Academic Advisor (Physics)
or
f=1/T
mixing MHz, nm, cm, and SI units
Displacement-time or displacement-position graph
graph reading
decide whether the horizontal axis gives T or λ
treating particle speed as wave speed
Amplitude changes
intensity-amplitude link
square the amplitude ratio
halving amplitude and halving intensity
Distance from a point source changes
inverse-square spreading
compare I1r12 with I2r22
using inverse-square law for non-point geometry
Polariser angle is changed
Malus' law
check whether the light is already polarised
forgetting the first polariser halves unpolarised light
Misconception check: wave speed is the speed of the disturbance pattern, not the back-and-forth speed of one particle in the medium.
Track how this topic feeds into interference, diffraction, and Modern Physics via the H2 Physics notes hub; it bundles the full Section III refresh plus printable drills.
1 Mechanical vs electromagnetic waves (LO a)
Mechanical waves need a medium; think slinky coils (longitudinal) or water ripples (transverse). Energy travels; the individual coils or water molecules only oscillate about equilibrium.
Electromagnetic (EM) waves are self-propagating oscillations of electric and magnetic fields in free space-no particles required.
Parent insight
A neat dinner-table demo is to compare sound (mechanical) with laser pointer light (EM). Block the speaker with a vacuum jar and the sound dies; block the laser and light still gets through.
2 Core wave vocabulary (LO b)
Symbol
Term
Quick definition
x
Displacement
How far a point is from equilibrium at an instant
A
Amplitude
Maximum displacement ±A
T
Period
Time for one complete oscillation
f
Frequency
Oscillations per second, f=T1
ϕ
Phase
Fraction of a complete cycle, in rad or °
Δϕ
Phase difference
Phase gap between two points or waves
λ
Wavelength
Distance between consecutive points in phase
v
Speed
Distance a given phase travels per second
3 The golden relationship v=fλ(LO c,d)
Start from definitions:
v=timedistance=Tλ=fλ.
Exam drill: Convert MHz to Hz and nm to m before substitution-missed prefixes cost marks.
Four worked examples with different units feature in this explainer video [link coming soon].
4 Reading space- and time-base graphs (LO e)
Displacement-time graph (at one point): gradient ↔ particle velocity; peak-to-peak time = T.
Savemyexams ' diagrams are perfect for self-quiz-cover the labels and annotate crests, troughs and compressions.
Graph axis checkpoint
Before measuring anything from a wave graph, use the horizontal-axis label to decide whether the graph is showing one point over time or the whole wave at one instant.
Horizontal axis
What one full cycle gives
Gradient meaning
Common trap
Time, t, at a fixed position
Period, T
Particle velocity at that point
Reading peak-to-peak time as wavelength.
Position, x, at one instant
Wavelength, λ
Shape slope, not wave speed
Reading peak-to-peak distance as period.
Two points shown on the same snapshot
Phase difference from Δx/λ
Not usually needed for speed
Comparing points from different times.
One point followed over time
Phase difference from Δt/T
Particle motion timing
Treating the particle as travelling along the wave.
Worked check: if adjacent crests are 0.80m apart on a displacement-position graph and the period from a separate displacement-time graph is 0.20s, then λ=0.80m, T=0.20s, and v=λ/T=4.0m⋅s−1. Do not call the 0.80m spacing a period just because it is one full cycle.
Misconception check: the drawn curve is not the path of a particle. A particle oscillates about its own equilibrium position while the wave pattern travels through the medium.
Phase-difference checkpoint
When two points or two instants are compared, first decide whether the separation is measured in space or in time. The same fraction of a cycle gives the phase difference.
Question wording
Fraction of a cycle
Phase difference
Common trap
Two points on the same displacement-position snapshot
λΔx
Δϕ=2πλΔx
Using period when the graph axis is position.
One point observed at two different times
TΔt
Δϕ=2πTΔt
Points separated by one wavelength
1 cycle
2π rad, so they are in phase
Saying one wavelength apart means opposite phase.
Points separated by half a wavelength
21 cycle
π rad, so they are in antiphase
Calling any non-zero separation out of phase without quantifying it.
Worked check: if two points on the same snapshot are 0.30m apart and the wavelength is 1.20m, then
Δϕ=2π×1.200.30=2π.
Misconception check: phase difference compares positions within a cycle. It does not mean the particle has travelled from one point to the other.
5 Energy, intensity & the inverse-square law (LO f-h)
5.1 Progressive waves transfer energy, not matter
Particles only vibrate about equilibrium; net mass flow is zero.
5.2 Intensity-amplitude square law
For a progressive wave,
I∝A2.(1)
That means halving the amplitude quarters the intensity-key to sound-proofing calculations.
5.3 Inverse-square from a point source
Assuming no energy loss,
I∝r21.(2)
Origin: energy spreads over the surface area 4πr2.
Mini-drill: A torch gives 4.0W⋅m−2 at 2m. Estimate intensity at 5m.Answer:I2=I1(r2r1)2=4.0(52)2=0.64W⋅m−2.
Intensity-ratio checkpoint
Before using a square law, identify what physically changed. Amplitude changes and distance spreading are different reasons for intensity to change.
Wording clue
Ratio to use first
What it means
Common trap
Same wave at the same place, amplitude changes
I2/I1=(A2/A1)2
Intensity follows amplitude squared.
Saying half the amplitude gives half the intensity.
Same point source, distance changes and no energy is lost
I2/I1=(r1/r2)2
Amplitude and distance both change
Multiply the separate intensity factors only if the question explicitly says both changed.
Each factor describes a different physical cause.
Applying both square laws when the question only gives one change.
Source is not point-like, or the medium absorbs energy
State why inverse square may not apply directly.
The spreading model has changed.
Using I∝1/r2 for every intensity question.
Worked check: if the amplitude is halved and the distance from the same point source is doubled, the amplitude factor is (1/2)2=1/4, and the distance factor is (1/2)2=1/4. If both changes are truly part of the same comparison, the final intensity is 1/16 of the original.
Misconception check: "half amplitude" and "twice the distance" are not the same instruction. Read which quantity changed before choosing the ratio.
6 Polarisation-proof that EM waves are transverse (LO i)
Definition: restriction of oscillations to one plane perpendicular to propagation.
Why only transverse? Longitudinal oscillations are parallel to propagation, so there is no “plane” to filter.
6.1 Malus' law (LO j)
For light with intensity I0 after the first polarising filter, the analyser at angle θ transmits:
I=I0cos2θ.(3)
Here I0 is the intensity after the first polarising filter. If the incident light is unpolarised with intensity Iunpol, the first polariser transmits 21Iunpol. The next polariser then transmits I=I0cos2θ.
If θ=30∘, intensity drops to 0.75I0.
Student hack: Remember “cos squared controls colour of sunglasses” to recall Eq. (3).
6.2 Polariser intensity checkpoint
Before using Malus' law, decide what the given intensity describes. This prevents the common extra-half or missing-half error.
Starting description
First operation
Intensity after the analyser
Unpolarised light of intensity Iincident enters the first polariser
First polariser halves it: I0=21Iincident
I=21Iincidentcos2θ
Already polarised light of intensity I0 enters the analyser
No extra half factor
I=I0cos2θ
Two crossed polarisers
θ=90∘
I=0 for ideal polarisers
Misconception check: the cos2θ factor belongs to the angle between the polarisation direction and the analyser axis. The half factor appears only when unpolarised light first passes through a polariser.
7 Three WA timing rules
Use syllabus pacing as a guide: Paper 2/3 average ~1.6 min/mark - bank time on 1-mark definitions so you can draw graphs and optics geometry neatly.
Always copy unitsbefore numbers; it prevents prefix slips.
Quote final answers to the same sig-figs as raw data-paper 4 loves this.
8 Bridge to Practical Paper 4
Plot intensity vs distance on a log-log graph to verify gradient ≈ -2 (inverse-square).
Use phone lux meters for quick classroom demos-then verify with Eq. (2).
Need structured practice on Wave Motion and Polarisation? Our H2 Physics tuition programme covers this topic with weekly problem sets and Paper 4 practical drills.
Comprehensive revision pack
9478 Section III, Topic 10 Syllabus outcomes
Candidates should be able to:
(a) show an understanding that mechanical waves involve the oscillations of particles within a material medium, such as a string or a fluid, and electromagnetic waves involve the oscillations of electromagnetic fields in space and time.
(b) show an understanding of and use the terms displacement, amplitude, period, frequency, phase, phase difference, wavelength and speed.
(c) deduce, from the definitions of speed, frequency and wavelength, the equation v=fλ.
(d) recall and use the equation v=fλ.
(e) analyse and interpret graphical representations of transverse and longitudinal waves with respect to variations in time and position (space).
(f) show an understanding that energy is transferred due to a progressive wave without matter being transferred.
(g) recall and use the term intensity as the power transferred (radiated) by a wave per unit area, and the relationship intensity∝ (amplitude)2 for a progressive wave.
(h) show an understanding of and apply the concept that the intensity of a wave from a point source and travelling without loss of energy obeys an inverse square law to solve problems.
(i) show an understanding that polarisation is a phenomenon associated with transverse waves.
(j) recall and use Malus' law (intensity∝cos2θ) to calculate the amplitude and intensity of a plane-polarised electromagnetic wave after transmission through a polarising filter.
Concept map (in words)
Identify wave type → list properties → pick representation (t-graph or x-graph). Apply v=fλ to link frequency and wavelength. For intensity, square the amplitude and consider geometric spreading. Polarisation demonstrates transverse nature; combine with Malus' law for quantitative predictions.
Key relations
Concept
Expression / reminder
Wave speed
v=fλ
Angular frequency
ω=2πf
Particle velocity
vp=∂t∂y (from displacement-time graph)
Intensity-amplitude link
I∝A2
Inverse-square law
I∝r21
Malus' law
I=I0cos2θ
Phase difference
Δϕ=λ2πΔx (same t) or T2πΔt
Derivations & reasoning to master
Wave equation: show that displacement y(x,t)=Asin[2π(Tt−λx)] satisfies v=Tλ.
Intensity drop: derive the inverse-square law I∝r21 for a point source by spreading energy over a sphere area.
Malus' law: explain using projection of electric field component through successive polarisers.
Phase difference: convert between spatial and temporal separations using Δϕ=λ2πΔx=T2πΔt
Worked example 1 - graph interpretation
A displacement-distance graph shows adjacent crests 16cm apart at t = 0. A displacement-time graph at x = 0 indicates a period of 0.040s. Determine wave speed, frequency, and write the wave equation.
Unpolarised light of intensity 12W⋅m−2 passes through three polarisers. The first is aligned vertically, the second at 30∘ to the vertical, the third at 90∘ to the first. Find the transmitted intensity.
Method: after the first polariser, I=6W⋅m−2. After the second: I=6cos230∘=4.5W⋅m−2. After the third (60∘ to the second): multiply by cos260∘ ⇒ 1.1W⋅m−2.
Practical & data tasks
Use ripple tanks or simulations to visualise wavelength and frequency relationships.
Measure light intensity vs distance with a lux meter, plot log I vs log r to confirm slope ≈ -2.
Rotate polaroid filters in front of a phone camera sensor to observe Malus' law experimentally and record readings.
Common misconceptions & exam traps
Confusing particle speed with wave speed.
Forgetting that only transverse waves can be polarised.
Mixing degrees and radians when applying Malus' law.
Misreading graphs: wavelength comes from distance between crests at the same time, not just any two points.
Quick self-check quiz
If frequency doubles while speed remains constant, what happens to wavelength? - It halves.
What is the intensity transmitted through a polariser pair at 90°? - Zero.
How do you tell whether a graph is displacement-time or displacement-distance? - Look at axis labels; time axis indicates period, distance axis indicates wavelength.
Name one everyday application of polarisation. - Polarised sunglasses / LCD screens.
Why does sound not exhibit polarisation? - Sound is longitudinal in air; oscillations are parallel to propagation so no plane to filter.
Revision workflow
Recreate key definitions and equations on flashcards; test with spaced repetition.
Solve two waveform graph problems and one polarisation calculation each week.
Summarise mechanical vs EM wave characteristics in a single-page comparison chart.
Watch a resonance demo or ripple tank video and explain the physics verbally to reinforce understanding.
Practice Quiz
Test yourself on the key concepts from this guide.
Parents: book a 1-hr Wave Motion booster before WA 2; it saves future headaches in interference.
Students: memorise Eqs. (1)-(3) and test them in tomorrow's lab light-box worksheet.
Last updated 14 Jul 2025. Next review when SEAB issues the 2027 draft syllabus.
