A wave is nature’s way of moving energy around without moving stuff around. Before we can do anything clever with waves, we need a shared vocabulary — wavelength, amplitude, period, frequency and speed — and one equation that ties them together.
📘 What you need to know
A travelling wave carries energy from one place to another without transferring matter
Waves are made by an oscillating source, and the oscillation spreads outwards
Displacementx is how far a point is from equilibrium; amplitudeA is the biggest displacement it reaches (both in metres)
Wavelengthλ is the length of one complete wave — crest to crest (metres)
PeriodT is the time for one full oscillation (s); frequencyf is how many pass per second (Hz), with f = 1/T
The wave equation links them: v = fλ
What a Travelling Wave Actually Does
Here’s the big idea, and it trips a lot of people up: a wave transfers energy, not matter. Drop a stone in a pond and ripples race outwards, but a floating leaf just bobs up and down on the spot — it doesn’t get carried to the edge. The water stays put; only the energy travels.
Every wave starts with an oscillating source — something vibrating — and that oscillation spreads away from it. Depending on the type of wave, it can travel through a medium like air or water, or (for some waves) straight through a vacuum with no particles at all.
Displacement, Wavelength and Amplitude
Freeze a wave in place and look at it along its direction of travel. The displacementx tells you how far any point sits above or below the middle equilibrium line. The wavelengthλ is the length of one full wave — easiest to measure from one crest to the next (or one trough to the next). The amplitudeA is the maximum displacement, from the equilibrium line up to a crest.
Displacement against distance: the wavelength λ runs crest-to-crest, and the amplitude A is the height from the equilibrium line to a crest (or depth to a trough).
Period and Frequency
Now stop watching the whole wave and stare at a single point instead, timing how it moves. The periodT is the time for that point to complete one full oscillation. The frequencyf is how many complete oscillations happen each second, measured in hertz (Hz). They’re two sides of the same coin:
Frequency and periodf = 1 / T
This is where a graph can catch you out. A displacement graph can have distance along the bottom (giving you the wavelength) or time along the bottom (giving you the period). They look almost identical — always check the axis label first.
Displacement against time: the period T is the time for one complete oscillation. Same-shaped curve, but the axis is now time — so it gives T, not λ.
The Wave Equation
Finally, how fast does the wave travel? The wave speedv is the distance a wave moves each second. Since a wave advances exactly one wavelength in one period, speed = wavelength ÷ period — which rearranges into the equation you’ll use constantly:
The wave equationv = fλ = λ / T
For a wave travelling at a fixed speed, f and λ trade off against each other: squeeze the wavelength shorter and the frequency shoots up; stretch the wavelength longer and the frequency drops. Their product always stays equal to the speed.
🧭 Reading and using wave properties
Check the x-axis of any graph — distance gives you λ, time gives you T
Measure over one whole wave (crest-to-crest) to avoid halving or doubling your answer
Need frequency? Use f = 1/T — but make sure T is in seconds first
For speed, wavelength or frequency, reach for v = fλ and rearrange
Convert units early: cm → m, ms/μs → s, before substituting anything
Quick recap: waves move energy not matter; λ is crest-to-crest, A is max displacement, f = 1/T, and the wave equation v = fλ ties speed, frequency and wavelength together.
WE 1
A displacement–time graph of a wave shows an amplitude of 10 cm and one complete oscillation lasting 1.0 ms.
(a) State the amplitude in metres. (b) Calculate the frequency of the wave.
Part (a)
Convert cm to m: A = 10 cm ÷ 100
A = 0.10 mPart (b)
The period is one full oscillation: T = 1.0 ms = 1.0 × 10⁻³ s
f = 1/T = 1 ÷ (1.0 × 10⁻³)f = 1000 HzIf you’d left T in milliseconds you’d have got 1 Hz — a thousand times too small. Always go to seconds first.
WE 2
A sound wave travels at 340 m s⁻¹ and has a period of 0.28 ms.
Determine the wavelength of the wave.
Set up
The wave moves one wavelength each period, so λ = vT
Convert & substitute
T = 0.28 ms = 0.28 × 10⁻³ s
λ = vT = 340 × (0.28 × 10⁻³)λ ≈ 0.095 mSame answer as going the long way: f = 1/T ≈ 3571 Hz, then λ = v/f ≈ 0.095 m.
💡 Top tips
Waves carry energy, not matter — the classic exam line, and worth a mark on its own
A distance-axis graph gives λ; a time-axis graph gives T — they look the same, so read the label
Measure a whole wave crest-to-crest, never half of one
For a hertz answer the period must be in seconds — not ms or μs
At fixed speed, longer wavelength means lower frequency, and vice versa
⚠ Common mistakes
Saying a wave “moves the water along” — the medium only oscillates on the spot
Confusing period (time axis) with wavelength (distance axis) on a graph
Forgetting to convert cm, ms or μs before using f = 1/T or v = fλ
Reading amplitude as the full crest-to-trough height instead of just crest-to-equilibrium
Mixing up frequency and wavelength in the wave equation
Up next: we look at the two ways a wave can wiggle — Transverse & Longitudinal Waves — and see why some waves need a medium while others can cross empty space.
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