HookIn 1800, an astronomer found light that nobody can see
In 1800 the astronomer William Herschel — already famous for discovering Uranus — was measuring how much heat each colour of sunlight carries. He split a beam with a prism, laid thermometers with blackened bulbs in each band of the spectrum, and kept spare thermometers outside the light as controls. The readings climbed steadily from violet towards red. Then came the accident that made the experiment immortal: a thermometer sitting beyond the red end, where there was nothing visible at all, read hotter than any colour. Something invisible was arriving from the Sun and heating the glass. Herschel called the discovery 'calorific rays'; we call it infrared, and it was the first evidence that the spectrum of light continues far past what eyes can detect.
Two centuries on, you spend your whole life inside that invisible spectrum: radio waves carrying 5 Live into a car, microwaves linking your phone to a mast and your laptop to the router, infrared pouring off every warm object in the room, ultraviolet quietly ageing skin on a bright day, X-rays and gamma rays waiting in hospitals. P6 is the rulebook this entire family obeys. Every wave — water ripple, sound, seismic shudder or gamma ray — is described by the same few quantities and one equation, \(v = f\lambda\), and each electromagnetic family member gets both its job and its danger from where it sits in the spectrum.
ModelTwo ways to wiggle — transverse and longitudinal
All waves are oscillations that carry energy and information from one place to another without transferring matter. The proof is worth two marks on its own: a fishing float on rippled water bobs up and down on the spot — it does not surf to the shore — and when someone speaks to you across a room, the air itself does not travel from their mouth to your ear. What travels is the disturbance.
The two families differ in the direction of the wiggle. In a transverse wave the oscillations are perpendicular to the direction the wave travels — ripples on water are the standard example, and every electromagnetic wave is transverse too. In a longitudinal wave the oscillations are parallel to the direction of travel, so the medium bunches and spreads as the wave passes, forming compressions (particles squeezed together) and rarefactions (particles spread apart). Sound in air is the standard example: a loudspeaker cone pushes and pulls the air in front of it, and the pattern of squashed and stretched air marches outward at 330 m/s.
A slinky spring shows both in one piece of kit: flick it side-to-side and the pulse is transverse; push-pull it along its own length and you can watch compressions travel — the exam's favourite way of asking you to tell the two apart.
ModelAmplitude, wavelength, frequency — and the one wave equation
Four definitions carry this whole topic, and the mark scheme wants them exact. Amplitude is the maximum displacement of a point on the wave from its undisturbed (rest) position — from the middle to the crest, not from crest to trough. Wavelength \(\lambda\) is the distance from a point on one wave to the same point on the next — crest to crest is the easy version. Frequency \(f\) is the number of complete waves passing a point each second, in hertz (Hz). Period \(T\) is the time for one complete wave, and the two are reciprocals: \(T = \dfrac{1}{f}\).
Join them and you get the wave equation, which applies to every wave in the universe: \[v = f\lambda\] — wave speed (m/s) = frequency (Hz) × wavelength (m). It is a rate-times-size argument: if \(f\) waves leave per second and each is \(\lambda\) metres long, the front of the train advances \(f\lambda\) metres every second.
The practical skill is unit hygiene. Frequencies arrive dressed as kHz (×1,000) and MHz (×1,000,000); wavelengths arrive in centimetres. Undress everything to Hz and metres before substituting, or the powers of ten will bury you.
BBC Radio 4 long wave is broadcast from the Droitwich transmitter at 198 kHz. Radio waves travel at \(3.0 \times 10^8\) m/s, so each wave is \[\lambda = \frac{v}{f} = \frac{3.0 \times 10^8}{198{,}000} \approx 1{,}500\ \text{m}\] — every wavelength is nearly a mile of Worcestershire countryside. Now the same equation at human scale: concert-pitch A from a violin has \(f = 440\) Hz and travels through air at 330 m/s, giving \(\lambda = 330 \div 440 = 0.75\) m. One equation, spanning wavelengths from a school ruler's world to a kilometre and a half — that universality is the point.
DataRequired practical 20 — measuring waves in a ripple tank and on a string
Part one uses a ripple tank: a shallow tray of water, a lamp above, and a motor-driven dipper making continuous plane waves. The wavefronts cast moving shadow stripes on a screen below. The trick is that the pattern never sits still, so you freeze it — photograph the screen with a ruler lying in shot, or use a stroboscope. Then measure across ten gaps between wavefronts and divide by ten: a ten-wave measurement carries roughly a tenth of the percentage uncertainty of a single-wave one. Frequency comes from the dipper's power-supply setting, or by counting waves passing a mark in ten seconds and dividing. Multiply for speed. One honest limitation to quote: the shadows are slightly magnified compared with the real waves, a small systematic error.
Part two puts waves on a stretched string: a vibration generator driven by a signal generator shakes a string held taut over a pulley by hanging masses. Adjust the frequency until the string settles into a clear, stable pattern of loops. Each loop is half a wavelength — the classic slip is calling one loop a full wave — so measure the length of several loops with a metre rule, work out \(\lambda\), read \(f\) from the signal generator, and use \(v = f\lambda\). Measuring across many loops, again, shrinks the reading error; so does repeating at several frequencies and checking the speed comes out consistent.
Variables, for either part: the independent variable is frequency, the dependent variable is wavelength, and you control the medium — the water depth in the tank, or the string's tension and type — because changing the medium changes the wave speed itself.
A ripple-tank photograph shows ten wavefront gaps spanning 24 cm, so \[\lambda = \frac{0.24}{10} = 0.024\ \text{m}.\] The dipper runs at 12 Hz. Wave speed: \[v = f\lambda = 12 \times 0.024 = 0.29\ \text{m/s (2 s.f.)}.\] Had you measured a single gap as '2 cm' with a ruler good to ±2 mm, that is a 10% uncertainty; across ten gaps the same ±2 mm is under 1%. Quoting that comparison — not just 'it is more accurate' — is what an AO3 evaluation mark looks like.
ModelThe electromagnetic spectrum — one family, seven names
Electromagnetic waves are transverse, need no medium, and all travel at the same speed through a vacuum (and effectively through air): \(3.0 \times 10^8\) m/s. They form a continuous spectrum, classified into seven regions by wavelength and frequency. From longest wavelength (lowest frequency) to shortest: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. Radio wavelengths stretch from metres to kilometres — Droitwich's 1,500 m again — while gamma wavelengths are smaller than an atom. Because \(v\) is fixed, wavelength and frequency see-saw: as one falls the other rises, and learning the order in both directions is a cheap AO1 mark. Human eyes detect only the sliver called visible light, a reminder that Herschel's thermometer knew more than his retina.
Waves change speed when they cross into a different substance, and that is the root of refraction. Hit the boundary at an angle and the direction of travel changes; hit it head-on (along the normal) and the wave slows or speeds up without bending. All students draw ray diagrams for this — the ray bends towards the normal entering a slower material, away leaving it.
Higher tier explains the bend with wave fronts. Think of a rank of marchers striding from tarmac into mud at an angle: the end that reaches the mud first slows first, the rank pivots, and the whole line swings towards the normal. Wavelength shortens in the slower medium while frequency — set by the source and unchangeable in transit — stays exactly the same.
DataRequired practical 21 — which surfaces emit and absorb infrared best
Every object emits infrared, and hotter objects emit more — but the surface decides how much, and this practical measures that. The emission rig is a Leslie cube: a hollow metal cube whose four vertical faces have different finishes — typically matt black, shiny black, white and polished silver. Fill it with just-boiled water, which is the crucial control: all four faces are now at the same temperature, so any difference in what you detect is caused by the surface alone. Hold an infrared detector at a fixed distance from each face in turn — same distance every time, or you have changed two variables at once. The pattern is unambiguous: the matt black face emits the most infrared, the polished silver face the least.
Absorption is the mirror-image experiment: place surfaces of different finish at equal distances from a radiant heater and track their temperature rise. Matt black warms fastest — the best emitters are also the best absorbers, which is why cooling fins are painted black and marathon foil blankets are shiny.
The systematic error to name: the cube cools throughout the experiment, so faces measured last emit less simply because the water is cooler. Work fast, re-check the water temperature between readings, or repeat the sequence in a different order and average. And keep hands off the cube — it is a scald hazard by design.
A typical emission run, detector 10 cm from each face of a Leslie cube filled at 90°C: matt black 34 units, shiny black 24, white 16, polished silver 8 — the matt black face radiating roughly four times the polished metal at the same temperature. If the silver face had been measured five minutes after the black one, part of that gap would be cube cooling, not surface physics: that is why 'measure all faces quickly, at the same distance, and repeat in reverse order' is the improvement examiners pay for.
MechanismWhere electromagnetic waves come from — and what they do to tissue
Electromagnetic waves are born in matter. Changes inside atoms and their nuclei can generate — or absorb — EM waves across a huge frequency range: electrons shuffling between energy levels handle light and its neighbours, while gamma rays originate in the nucleus itself, released as an unstable nucleus sheds energy. Higher tier adds the engineering end: radio waves can be produced by oscillations in electrical circuits — an alternating current sloshing charge up and down a transmitter aerial radiates waves at the same frequency — and when those waves are absorbed by a receiving aerial, they induce an alternating current at, again, exactly the same frequency. That frequency-matching is broadcasting in one sentence.
Danger scales with frequency. Radio, microwave, infrared and visible sit at the low-energy end. Ultraviolet, X-rays and gamma rays are ionising: energetic enough to strip electrons from atoms, damaging cells and DNA. Ultraviolet ages skin prematurely and raises the risk of skin cancer; X-rays and gamma rays can cause mutation and cancer at high doses.
Risk is quantified as radiation dose, in sieverts — a measure of the risk of harm from an exposure, not an amount of energy. Since 1 Sv is enormous, real doses come in millisieverts: 1,000 mSv = 1 Sv. The numbers keep the fear honest: a dental X-ray is about 0.005 mSv, a transatlantic flight about 0.07 mSv from cosmic rays, and average UK annual background radiation about 2.7 mSv. A dental X-ray is under a day of ordinary background — a risk worth taking to find an abscess, which is exactly the benefit-versus-dose reasoning AO3 questions ask for.
CaseMatching the wave to the job
The applications question is never 'list the uses' — it is 'explain why this wave suits this job', a two-clause answer linking a property to a purpose. Work along the spectrum. Radio waves carry television and radio broadcasts: they travel long distances and are cheap to generate and detect across whole regions. Microwaves do two jobs for two reasons — satellite communication, because they pass cleanly through the atmosphere to reach a satellite where longer radio wavelengths would be reflected or absorbed; and cooking, because water molecules in food absorb microwave energy and heat through the food. Infrared is heating made visible to the right camera: electric heaters and grills radiate it, food absorbs it, and infrared cameras turn the emission of warm bodies into images — the RP21 result earning its keep in search-and-rescue helicopters.
Visible light runs fibre-optic communication: flickering pulses down a glass thread carry phone and internet traffic with little loss. Ultraviolet makes energy-efficient fluorescent lamps work — UV generated inside the tube strikes a coating that re-emits it as visible light — and drives tanning, sunbeds included, with the skin-damage cost priced in. X-rays image bones because they pass through soft tissue but are absorbed by dense bone, printing a shadow on the detector. Gamma rays sterilise surgical instruments and, aimed carefully, kill cancer cells in radiotherapy — the same ionising violence that makes them dangerous, pointed at a tumour on purpose.
Notice the recurring exam logic: penetration, absorption or reflection by the right material is always the 'because' clause. Name the property, then the job; either half alone is worth little.
VocabularyKey terms the mark scheme pays for
TrapsMisconceptions that cost marks
ExamWhat examiners want
P6 sits on Physics Paper 2, and its calculations are nearly all one equation deep: v = fλ, plus T = 1/f. The equations sheet (permanent since the 2025 series) hands you both, so the marks hide in the conversions — kHz and MHz into Hz, centimetres into metres, and standard form handled cleanly at 3 × 10⁸ m/s. Show the substitution line before the answer; an arithmetic slip after a correct substitution usually keeps the method marks, but an answer alone keeps nothing.
Definitions are hard currency here because AO1 is 40% of the paper: amplitude measured from the rest position, wavelength point-to-same-point, frequency per second, the spectrum in order both by wavelength and by frequency, and the transverse/longitudinal distinction with sound as the stock longitudinal example. Draw and label rather than describe where the question allows — a wave front diagram with wavelengths visibly shortening in the slower medium is the whole Higher-tier refraction answer in one picture.
The two required practicals carry the AO3 weight. For RP20, the rewarded improvements are always the same trio: freeze the moving pattern (photo with ruler in shot, or strobe), measure across ten wavelengths and divide, and repeat for a mean — quote the percentage-uncertainty argument if you want the top of the level. For RP21, the control logic is the answer: same cube temperature (boiled water, work fast), same detector distance, only the surface changing. On uses-and-dangers questions, structure every point as property → consequence: 'microwaves pass through the atmosphere, so they can reach satellites'; 'ultraviolet is ionising, so it raises skin-cancer risk'. And when a question asks whether an X-ray or CT scan is 'safe', answer like a physicist: compare the dose in millisieverts to background, then weigh it against the diagnostic benefit — refusing to give a number is the mark you drop.