AQA A-Level Physics: Waves — Complete Revision Guide

Waves is the topic that ties physics together. The mathematics you learn here — v = fλ, superposition, path difference, harmonic series — reappears in nuclear physics (electron diffraction), in fields (electromagnetic radiation), in optional units (medical imaging, turning points), and in any future university course you might take in physical sciences. Section 3.3 of the AQA A-Level Physics specification (7408) is examined on Paper 1, and the practical-skills content carries through to Paper 3. Two of the twelve required practicals — RP3 (stationary waves on a string) and RP4 (Young's double-slit interference) — sit inside this topic.

This guide walks through the full content of AQA Section 3.3: progressive versus stationary waves; transverse versus longitudinal waves; the electromagnetic spectrum and its applications; superposition and interference (single-slit, double-slit, and diffraction-grating); refraction and total internal reflection; stationary waves and the harmonic series; polarisation and Malus's law. It also unpacks the two required practicals at the level of detail the Practical Endorsement and Paper 3 Section A demand.

Where Waves Sits in the Specification

Section 3.3 is examined on Paper 1, where it accounts for a substantial fraction of the 85 marks. It links forward to almost every other topic on the course — questions on quantum behaviour assume fluency with photon energies; questions on electromagnetic induction draw on EM-wave concepts; questions on simple harmonic motion (AQA A-Level Physics: Further Mechanics) extend the wave equation to oscillating systems. Our AQA A-Level Physics: Waves course covers the topic in ten lessons.

Wave Basics: Properties and Types

A wave is a disturbance that transfers energy through a medium (or, for electromagnetic waves, through space) without net transfer of matter. Every wave is described by the same handful of quantities.

Quantity	Symbol	Definition
Wavelength	λ	Distance between adjacent points in phase
Frequency	f	Number of complete oscillations per second (Hz)
Period	T	Time for one complete oscillation (T = 1/f)
Amplitude	A	Maximum displacement from the equilibrium position
Wave speed	v	v = fλ
Phase difference	Δφ	Fraction of a cycle separating two points, in radians or degrees

The relationship v = fλ is the most-used equation in this topic. Internalise it: if you double the frequency at constant speed, the wavelength halves; if you halve the wavelength at constant speed, the frequency doubles.

Transverse Versus Longitudinal

Waves split into two families based on the direction of oscillation relative to the direction of energy propagation.

• Transverse waves oscillate perpendicular to the direction of energy transfer. Examples: waves on a stretched string, waves on the surface of water, every electromagnetic wave.
• Longitudinal waves oscillate parallel to the direction of energy transfer. Examples: sound waves in air, primary seismic waves, compression waves on a slinky.

Only transverse waves can be polarised — a critical distinction examined repeatedly.

Progressive Versus Stationary

A progressive wave transports energy from one point to another. A travelling pulse on a string, a sound wave from a loudspeaker, an EM wave from a star — all progressive. Every point oscillates in turn as the wave passes, and the disturbance moves through space.

A stationary (standing) wave is formed by the superposition of two progressive waves of equal frequency and amplitude travelling in opposite directions — usually a wave and its reflection. The result is a pattern fixed in space: nodes (points of zero amplitude) alternating with antinodes (points of maximum amplitude). No net energy is transferred along a stationary wave.

Feature	Progressive	Stationary
Energy transfer	Yes	No
Phase along wave	Increases continuously	Each loop in phase; adjacent loops antiphase
Amplitude along wave	Same at every point	Varies from zero at nodes to maximum at antinodes
Wavelength	One wavelength = one cycle	One wavelength = two loops (node-antinode-node-antinode-node)

The Electromagnetic Spectrum

All electromagnetic waves are transverse, travel at c = 3.00 × 10⁸ m s⁻¹ in vacuum, and consist of perpendicular oscillating electric and magnetic fields. The spectrum spans roughly 18 orders of magnitude in frequency.

Region	Wavelength range	Typical use
Radio	> 0.1 m	Broadcasting, communications
Microwave	1 mm – 0.1 m	Radar, cooking, satellite links
Infrared	700 nm – 1 mm	Thermal imaging, remote controls
Visible	400 – 700 nm	Vision, optical instruments
Ultraviolet	10 – 400 nm	Sterilisation, fluorescence
X-ray	0.01 – 10 nm	Medical imaging, crystallography
Gamma	< 0.01 nm	Radiotherapy, nuclear processes

For unit-conversion practice: a wavelength of 500 nm is 5 × 10⁻⁷ m, and its frequency is c/λ = 3 × 10⁸ / 5 × 10⁻⁷ = 6 × 10¹⁴ Hz — solidly in the visible region.

Superposition and Interference

When two waves meet at a point, the resulting displacement is the vector sum of the individual displacements. This is the principle of superposition.

If two waves of equal amplitude arrive in phase (path difference of 0, λ, 2λ, …), they reinforce — constructive interference. If they arrive in antiphase (path difference of λ/2, 3λ/2, …), they cancel — destructive interference. The condition for constructive interference is:

path difference = nλ (where n = 0, 1, 2, …)

The condition for destructive interference is:

path difference = (n + ½)λ

For interference to produce a stable, observable pattern, the two sources must be coherent — same frequency, constant phase relationship. Two separate light bulbs are not coherent; their phase relationship fluctuates randomly on timescales of nanoseconds. A laser is highly coherent, which is why double-slit experiments use one. Alternatively, you can produce coherent sources by splitting a single wave at two slits.

Young's Double-Slit Experiment

Two narrow slits, separated by a small distance s, are illuminated by coherent light. On a screen at distance D from the slits, you observe a pattern of alternating bright and dark fringes — direct evidence of wave interference.

The fringe spacing w (distance between adjacent bright fringes) is:

w = λD / s

This relationship lets you measure the wavelength of light from a measurement of w, D and s. A laser of wavelength 632.8 nm passing through slits 0.25 mm apart, observed on a screen 2.0 m away, produces fringes spaced w = (632.8 × 10⁻⁹ × 2.0) / (0.25 × 10⁻³) = 5.1 × 10⁻³ m ≈ 5 mm apart — comfortably measurable with a ruler.

The fringe pattern is the central piece of evidence that light is a wave. No purely particulate model can produce it.

Single-Slit Diffraction

When a wave passes through a single narrow slit, it spreads out — diffraction. The single-slit diffraction pattern consists of a wide, bright central maximum flanked by narrower subsidiary maxima of decreasing intensity. The width of the central maximum increases as the slit width b decreases:

Angular width of central max ≈ 2λ / b

For appreciable diffraction, the slit must be comparable in size to the wavelength. A 1 mm slit barely diffracts visible light; a 0.1 mm slit produces a clearly visible pattern.

The single-slit pattern is what you actually see in a Young's-slits experiment — the double-slit pattern is the interference fringes modulated by the single-slit diffraction envelope. The envelope is the reason the bright fringes get dimmer as you move away from the centre.

Diffraction Gratings

A diffraction grating is a large array of equally spaced slits (typically several hundred per millimetre). When monochromatic light passes through a grating, constructive interference occurs at angles satisfying:

d sin θ = nλ

where d is the slit spacing (1/N, where N is the lines per metre), n is the order of the maximum, and θ is the angle from the central maximum.

Diffraction gratings are used in spectrometers because they produce very sharp, well-separated maxima — far better resolution than a double slit. The maximum number of observable orders is bounded by sin θ ≤ 1, giving n(max) ≤ d/λ.

White light through a grating splits into a continuous spectrum at each non-zero order, because each colour deflects to a different angle. The central maximum (n = 0) is undeflected and remains white.

Refraction and Total Internal Reflection

When a wave crosses a boundary between two media, its speed changes. If it strikes the boundary at an angle to the normal, this change in speed produces a change in direction — refraction.

The refractive index n of a medium is the ratio of the wave speed in vacuum to the wave speed in the medium:

n = c / v

For air, n ≈ 1.00. For water, n ≈ 1.33. For crown glass, n ≈ 1.50. The denser the medium (optically), the higher n, and the slower light travels through it.

Snell's law relates the angles to the refractive indices:

n₁ sin θ₁ = n₂ sin θ₂

When light travels from a denser medium into a less dense one (e.g. glass into air), it bends away from the normal. Above a certain critical angle θ_c, the refracted ray would lie along the boundary; beyond that, no refraction occurs and the light is totally internally reflected. The critical angle is given by:

sin θ_c = n₂ / n₁ (with n₁ > n₂)

For a glass–air boundary with n(glass) = 1.5, sin θ_c = 1/1.5, giving θ_c ≈ 41.8°. Any ray inside the glass striking the surface at more than 42° from the normal is totally internally reflected. This is the principle behind optical fibres: the glass core carries light in a series of total internal reflections, losing almost no intensity over many kilometres.

Stationary Waves on a Stretched String

Pluck a stretched string fixed at both ends, and the resulting vibrations form a stationary wave pattern. The string is constrained to nodes at both fixed ends; only certain wavelengths fit.

The simplest pattern — the fundamental (first harmonic) — has a single antinode at the midpoint and two nodes at the ends. The string length L equals half a wavelength: λ₁ = 2L. The fundamental frequency is:

f₁ = v / (2L)

The wave speed on a stretched string depends on the tension T and the mass per unit length μ:

v = √(T / μ)

So the fundamental frequency is f₁ = (1/2L) × √(T/μ).

Higher harmonics fit n half-wavelengths into the string:

Harmonic	n	Wavelength	Frequency
Fundamental (1st)	1	2L	f₁ = v / 2L
2nd	2	L	2f₁
3rd	3	2L/3	3f₁
n-th	n	2L/n	nf₁

For a tube open at both ends, the boundary condition is the same as a string fixed at both ends (antinodes at the ends instead of nodes, but the same wavelength relationship), so the same series of harmonics is supported. For a tube closed at one end (closed–open), only odd harmonics are supported: f = (2n − 1) × v / (4L), with the fundamental wavelength 4L.

Polarisation

A transverse wave can oscillate in any plane perpendicular to its direction of propagation. Plane-polarised light oscillates in a single plane.

Unpolarised light contains oscillations in many planes; passing it through a polarising filter transmits only the component aligned with the filter's transmission axis. The transmitted intensity is half the incident intensity (you have removed all but one direction of the perpendicular plane).

If you pass already-polarised light through a second filter (an analyser) at angle θ to the first, the transmitted intensity follows Malus's law:

I = I₀ cos²θ

So at θ = 0° the analyser passes everything; at 45° it passes half; at 90° (crossed polarisers) it passes nothing.

Polarisation has practical uses: polarising sunglasses reduce glare from horizontal reflective surfaces (which polarise the reflected light horizontally — the sunglasses are oriented to block the horizontal component); LCD screens use polarisers to control which pixels are visible.

Sound waves cannot be polarised because they are longitudinal — there is no perpendicular plane to oscillate in. This is sometimes asked directly in exam questions as a one-mark differentiator between transverse and longitudinal.

Required Practical 3: Stationary Waves on a Stretched String

The setup: a string is attached at one end to a vibration generator driven by a signal generator, and at the other end runs over a pulley to a hanging mass that provides constant tension. The vibrating end acts as a node (close enough — the displacement amplitude there is negligible). The fixed-by-pulley end is also effectively a node.

The method:

1. Set a fixed tension by suspending a known mass. Calculate T = mg.
2. Slowly increase the frequency from zero. The string will pass through a series of resonances — frequencies at which the string adopts a stable stationary-wave pattern.
3. Record the resonance frequency for the fundamental (one antinode) and for several higher harmonics.
4. Use v = fλ and the relationship λ_n = 2L/n to extract the wave speed.
5. Repeat for several values of tension. Plot v² against T. The graph should be a straight line through the origin with gradient 1/μ.

Sources of uncertainty: the position of the effective nodes (the vibration generator is not perfectly at a displacement node — there is a small correction), tension fluctuations as the mass swings, and the difficulty of identifying the exact resonance frequency (the resonance peak has finite width).

This practical exercises the entire toolkit of AQA A-Level Physics: Measurements and Their Errors — uncertainties on L, f and T, propagated through v² = T/μ.

Required Practical 4: Young's Double-Slit Interference

The setup: a laser of known wavelength illuminates a double slit, and the interference pattern is observed on a screen.

The method:

1. Set up the laser, double slit and screen on a clean optical bench. Measure the slit-to-screen distance D with a ruler.
2. Observe the fringe pattern. Measure the distance across several fringes (e.g. across ten bright fringes), then divide by the number to get the fringe spacing w. Measuring across many fringes reduces the percentage uncertainty in w.
3. Calculate λ = ws/D, where s is the manufacturer-quoted slit spacing.
4. Compare with the laser's quoted wavelength. The discrepancy is the experimental error; the percentage uncertainty in your measurement should be at least as large as the percentage discrepancy.

Sources of uncertainty: the fringe spacing is small (millimetres) and contributes the dominant percentage uncertainty. The slit-to-screen distance is large (metres) but measured with a metre rule, so its percentage uncertainty is small. The slit spacing is quoted by the manufacturer and treated as exact.

Safety: laser light, even at low power, can damage retinas. Never look directly into the beam, never reflect it into the audience, and label the apparatus clearly.

How to Study This Topic

Three habits separate strong waves performances from weak ones.

1. Get fluent with v = fλ under unit conversion. Practice converting between Hz, kHz, MHz and GHz; between metres, millimetres, micrometres and nanometres. A surprising fraction of mistakes here come from misplaced powers of ten.
2. Learn the harmonic series for strings and tubes by drawing it. Sketch the fundamental and the next three harmonics for (a) a string fixed at both ends, (b) a tube open at both ends, (c) a tube closed at one end. Don't memorise the formulas — derive them from the boundary conditions every time, and the formulas will follow.
3. Practise the interference and diffraction maths under exam conditions. d sin θ = nλ for gratings; w = λD/s for double slits. The unit traps — converting "300 lines per millimetre" to d in metres — cost marks reliably.

Common pitfalls to inoculate against:

• Treating diffraction and interference as separate phenomena (single-slit diffraction and double-slit interference are both consequences of superposition).
• Forgetting that longitudinal waves cannot be polarised.
• Using the wrong harmonic-series formula for a closed–open tube (it's odd harmonics only).
• Forgetting that Malus's law applies to intensity (cos²θ), not to amplitude (cos θ).
• Quoting the angle of incidence instead of the angle measured from the normal in Snell's law.

Related LearningBro Courses

• AQA A-Level Physics: Waves — the ten-lesson home course for Section 3.3
• AQA A-Level Physics: Particles, Antiparticles and Quantum Phenomena — wave–particle duality and electron diffraction
• AQA A-Level Physics: Further Mechanics — simple harmonic motion as the time-domain wave equation
• AQA A-Level Physics: Measurements and Their Errors — uncertainty propagation in RP3 and RP4
• AQA A-Level Physics: Exam Strategy and Required Practicals — Paper 3 strategy on practical-skills questions

Quick FAQ

Can two coherent sources of different frequencies produce stable interference? No. Coherence requires a fixed frequency and a fixed phase relationship between the sources. If the frequencies differ, the phase difference drifts continuously, fringes shift around faster than the eye or detector can track, and the time-averaged pattern washes out to uniform illumination. The Young's double-slit arrangement guarantees coherence by deriving both slits from a single primary source.

Does the speed of a transverse wave on a stretched string depend on how hard the string is plucked? No. The wave speed v = sqrt(T / mu) depends only on tension T and mass per unit length mu, not on amplitude. Plucking harder simply makes the standing wave louder; the resonant frequencies and wave speed are unchanged.

Why is the central maximum in single-slit diffraction twice as wide as the side maxima? Because the first minima sit at sin(theta) = +/- lambda / a on either side of the central peak, while subsequent minima are separated by only lambda / a. The bright central fringe is therefore twice the angular width of those that follow on either side.

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Related Reading

• AQA A-Level Physics: Particles and Quantum Guide — the wave–particle duality follow-up
• AQA A-Level Physics: Exam Strategy Guide — how the two waves required practicals appear on Paper 3