H2 Physics Wave Motion & Polarisation Notes | 9478

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 $v=f\lambda$. 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.

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)

3 The golden relationship $v = f \lambda$ (LO c,d)

Start from definitions:

$$v = \dfrac{\text{distance}}{\text{time}} = \dfrac{\lambda}{T} = f \lambda.$$

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 = $T$.
• Displacement-position graph (snapshot): peak-to-peak distance = $\lambda$.

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.

Worked check: if adjacent crests are $\pu{0.80 m}$ apart on a displacement-position graph and the period from a separate displacement-time graph is $\pu{0.20 s}$, then $\lambda=\pu{0.80 m}$, $T=\pu{0.20 s}$

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.

Worked check: if two points on the same snapshot are $\pu{0.30 m}$ apart and the wavelength is $\pu{1.20 m}$, then

$$\Delta \phi = 2\pi \times \frac{0.30}{1.20} = \frac{\pi}{2}.$$

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,

$$I \propto A^{2}. \tag{1}$$

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,

$$I \propto \dfrac{1}{r^{2}}. \tag{2}$$

Origin: energy spreads over the surface area $4 \pi r^{2}$.

Mini-drill: A torch gives $4.0 \pu{W.m-2}$ at $2 \pu{m}$. Estimate intensity at $5 \pu{m}$.Answer: $I_2 = I_1\left(\dfrac{r_1}{r_2}\right)^2 = 4.0\left(\dfrac{2}{5}\right)^2 = 0.64\,\pu{W.m-2}$

Intensity-ratio checkpoint

Before using a square law, identify what physically changed. Amplitude changes and distance spreading are different reasons for intensity to change.

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 $1/16$

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 $I_0$ after the first polarising filter, the analyser at angle $\theta$ transmits:

$$I = I_0 \cos^{2} \theta. \tag{3}$$

Here $I_0$ is the intensity after the first polarising filter. If the incident light is unpolarised with intensity $I_{\text{unpol}}$, the first polariser transmits $\tfrac{1}{2}I_{\text{unpol}}$

If $\theta = \pu{30 ^\circ}$, intensity drops to $0.75 I_0$.

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.

Misconception check: the $\cos^2\theta$ 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

1. 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.
2. Always copy units before numbers; it prevents prefix slips.
3. 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 $v = f\lambda$.
• (d) recall and use the equation $v = f\lambda$.
• (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 $\propto$

Concept map (in words)

Identify wave type → list properties → pick representation (t-graph or x-graph). Apply $v = f \lambda$ 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

Derivations & reasoning to master

1. Wave equation: show that displacement $y(x,t) = A \sin \biggl[2\pi \left(\dfrac{t}{T} - \dfrac{x}{\lambda}\right) \biggr]$

Worked example 1 - graph interpretation

A displacement-distance graph shows adjacent crests $16 \pu{cm}$ apart at t = 0. A displacement-time graph at x = 0 indicates a period of $0.040 \pu{s}$. Determine wave speed, frequency, and write the wave equation.

Solution outline: $\lambda = 0.16 \pu{m}$, $T = 0.040 \pu{s} \implies f = 25 \pu{Hz}$, $v = f \lambda = 4.0 \pu{m.s-1}$

Worked example 2 - polarisation application

Unpolarised light of intensity $12 \pu{W.m-2}$ passes through three polarisers. The first is aligned vertically, the second at $30^\circ$ to the vertical, the third at $90^\circ$

Method: after the first polariser, $I = 6 \pu{W.m-2}$. After the second: $I = 6 \cos^{2} 30^\circ = 4.5 \pu{W.m-2}$

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

1. If frequency doubles while speed remains constant, what happens to wavelength? - It halves.
2. What is the intensity transmitted through a polariser pair at 90°? - Zero.
3. 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.
4. Name one everyday application of polarisation. - Polarised sunglasses / LCD screens.
5. Why does sound not exhibit polarisation? - Sound is longitudinal in air; oscillations are parallel to propagation so no plane to filter.

Revision workflow

1. Recreate key definitions and equations on flashcards; test with spaced repetition.
2. Solve two waveform graph problems and one polarisation calculation each week.
3. Summarise mechanical vs EM wave characteristics in a single-page comparison chart.
4. 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.

9 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• MIT OCW - Physics III: Vibrations and Waves
• OpenStax University Physics - Polarisation

10 Call-to-action

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.