In simple terms
A friendly intro before the formal notes — no formulas yet.
A Wave Is a Travelling Disturbance, Not Travelling Stuff
A wave carries energy from one place to another without carrying the material along with it. The particles of the medium just wobble on the spot; it is the pattern of that wobble — the disturbance — that moves. Give a wave its speed, its wavelength and its frequency and the single equation links all three.
Picture a 'Mexican wave' running around a stadium. The wave sweeps right around the ground, but no single person leaves their seat — each just stands up and sits down in turn. The people are the medium; their up-and-down motion is the oscillation; the sweeping pattern is the wave. Sound, water ripples and light all work the same way: something oscillates, and the pattern of oscillation travels while the medium stays put.
- 1
Decide the type: if the oscillation is at right angles to the direction the wave travels it is transverse (light, waves on a string); if it is along the direction of travel it is longitudinal (sound).
- 2
Read the size of the wobble: the amplitude is the maximum displacement from the rest position — it sets how much energy the wave carries.
- 3
Read the repeat in space and time: the wavelength () is the length of one full cycle; the period () is the time for one full cycle; the frequency () is how many cycles pass per second.
- 4
Link them with : the wave speed equals frequency times wavelength, so knowing any two gives the third.
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Step 1
Decide the type: if the oscillation is at right angles to the direction the wave travels it is transverse (light, waves on a string); if it is along the direction of travel it is longitudinal (sound).
38 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
38 simulations · 5 to start with
Start herein this order — each one shows a different piece of the topic
- oPhysicsStart here · 19702 7.1 · 9702 7.2 · IB C.2
Longitudinal and Transverse Wave Basics
Side-by-side longitudinal and transverse waves; adjust amplitude and frequency and read off wavelength
Why this one: Compare the two wave types side by side and read a wavelength off each.
Try this
- Increase the frequency and read the wavelength.
- Increase the amplitude and read the wavelength again.
- Compare the particle motion in the two waves.
Look for Wavelength shortens as frequency rises and is unaffected by amplitude; particles move across the wave in one and along it in the other.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- PhETStart here · 29702 7.1 · IB C.2
Wave on a String
Shake a string by hand, pulse or oscillator; set tension, damping and frequency.
Why this one: Set the oscillator frequency, measure the wavelength with the ruler and check v = f-lambda.
Try this
- Choose “Oscillate”, damping none, and measure λ with the ruler at 1.5 Hz.
- Raise the frequency to 3 Hz — λ halves while the wave speed stays the same.
- Increase tension — the wave moves faster and λ grows at fixed f.
Look for v = fλ with v set by the medium (tension), not by the source.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- PhETStart here · 39702 7.2 · IB C.2
Sound Waves
Watch pressure fronts leave a speaker; move a listener and show the pressure graph.
Why this one: Watch compressions leave the speaker and read the pressure graph at the listener: a longitudinal wave.
Try this
- Show “Graph” — the compressions in the picture line up with the peaks on the trace.
- Change the frequency and watch the spacing of the fronts (λ) change.
- On “Two Sources”, move the listener through loud and quiet spots.
Look for Longitudinal: particles move along the direction of travel; compressions ↔ pressure peaks.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- SimuPhysicsStart here · 49702 7.1 · IB C.2
Displacement vs. Distance and Time
Displacement against distance and displacement against time are drawn together for the same wave
Why this one: Read wavelength from the distance graph and period from the time graph of the same wave; never confuse them.
Try this
- Read the wavelength from the distance graph.
- Read the period from the time graph.
- Change the wave and compare both graphs.
Look for The distance graph shows the wavelength and the time graph shows the period.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- The Physics ClassroomStart here · 59702 7.4 · IB C.2
Electromagnetic Spectrum Infographic
Explore an interactive version of the classic 1944 electromagnetic spectrum infographic
Why this one: Walk the spectrum from radio to gamma and note every part travels at c in a vacuum.
Try this
- Find the visible band.
- Compare the wavelengths of radio waves and gamma rays.
- Read the frequency scale across the spectrum.
Look for Frequency rises as wavelength falls across the spectrum.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
More simulations33 more on this topic — core ones first
- PhETCoreJava · best on a laptop9702 7.4 · IB C.2
Radio Waves & Electromagnetic Fields
Oscillate the electron in a transmitting antenna, by hand or sinusoidally, and watch the radiated electric field reach the receiver.
Try this
- Drag the transmitter electron up and down by hand — watch the field ripple outward.
- Switch to sinusoidal oscillation and raise the frequency — the wavelength shortens.
- Watch the receiver electron — it copies the transmitter with a delay.
Look for An accelerating charge radiates; the wave travels at c, so λ = c/f.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- oPhysicsCore9702 7.1 · 9702 7.2 · IB C.2
Waves Basics & Types of Waves
Tutorial page (GIF animations, no applet): definitions of wave, medium, transverse vs longitudinal
Try this
- Read the definitions of wave and medium.
- Compare the transverse and longitudinal animations.
Look for A wave transfers energy without transferring the medium; particles oscillate across or along the direction of travel.
Open on oPhysicsRuns on their siteSimulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 7.1 · IB C.2
Wave Characteristics & Terminology
Tutorial with applet: period, frequency, amplitude, wavelength and v = f lambda on a travelling wave
Try this
- Change the frequency and read the wavelength.
- Change the amplitude and read the period.
- Check v = fλ with the values shown.
Look for Frequency and wavelength are inversely related at fixed speed; amplitude leaves the period unchanged.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 7.2 · 9702 8.1 · IB C.2
Longitudinal Waves
Longitudinal travelling or standing wave; adjust speed and amplitude; see compressions and rarefactions
Try this
- Run the travelling wave and follow one compression.
- Increase the amplitude and look at the compressions.
- Switch to the standing wave and find the particles that never move.
Look for Particles oscillate along the direction of travel; compressions move at the wave speed while each particle stays near its rest position.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 7.4 · IB C.2
Electromagnetic Waves
Animated EM wave with oscillating E (green) and B (red) field vectors perpendicular to propagation
Try this
- Watch the E and B vectors at one point over a cycle.
- Compare the directions of E, B and propagation.
Look for E and B oscillate in phase, perpendicular to each other and to the direction of travel.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 17.1 · 9702 7.1 · IB C.1
Simple Harmonic Motion, Circular Motion, and Transverse Waves
Link SHM, uniform circular motion and a transverse wave side by side with sliders and checkboxes
Try this
- Use the checkboxes to show SHM and circular motion together.
- Change the frequency slider and watch all three panels.
- Show the transverse wave and compare one particle with the SHM.
Look for The SHM is the projection of circular motion, and each wave particle performs the same SHM with a phase lag.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Full topic notes
Formal explanation with the rigour you need for the exam.
Two kinds of wave: transverse and longitudinal
Every wave carries energy through a repeating oscillation, but waves split into two families according to the direction of that oscillation. In a transverse wave the particles oscillate at right angles to the direction the wave travels — a wave sent along a rope, ripples on water, and every electromagnetic wave including light. In a longitudinal wave the particles oscillate back and forth along the direction of travel, squeezing the medium into regions of high density (compressions) and low density (rarefactions). Sound in air is the standard longitudinal wave. In both families the medium itself does not travel with the wave: each particle simply oscillates about its own fixed rest position while the disturbance moves on.
Transverse: oscillation perpendicular to energy transfer; shows crests and troughs. Examples: light and all EM waves, waves on a string, water ripples.
Longitudinal: oscillation parallel to energy transfer; shows compressions and rarefactions. Example: sound.
Both transfer energy, not matter: particles oscillate about a fixed point; only the disturbance advances.
A longitudinal wave can still be drawn as a sine curve by plotting displacement (or pressure) against position — the sine shape does not make it transverse.
The language of waves
To describe a wave quantitatively we need five terms. The amplitude () is the maximum displacement of a particle from its rest position, and it sets how much energy the wave carries. The wavelength () is the shortest distance between two points oscillating in phase — crest to crest, or compression to compression — measured in metres. The period () is the time for one complete oscillation, measured in seconds. The frequency () is the number of complete oscillations per second, measured in hertz (Hz). Finally the wave speed () is the distance the disturbance travels each second, in m s⁻¹.
Amplitude (): maximum displacement from equilibrium — NOT crest-to-trough distance, which is .
Wavelength (): length of one full cycle in space, in metres.
Period (): time for one full cycle, in seconds.
Frequency (): cycles per second, in hertz — set by the SOURCE.
Wave speed (): distance advanced per second, in m s⁻¹ — set by the MEDIUM.
The two equations that tie it together
Frequency and period describe the same repetition — one in cycles-per-second, the other in seconds-per-cycle — so they are reciprocals of each other. This gives the first relationship. The second, the wave equation, follows from a simple idea: in one period the wave advances exactly one wavelength, so its speed is one wavelength divided by one period, which rearranges to speed = frequency × wavelength.
T = \dfrac{1}{f} \qquad\qquad v = f\lambda
Here is the wave speed in m s⁻¹, is the frequency in Hz, is the wavelength in m, and is the period in s. Because links three quantities, knowing any two immediately gives the third. Keep firmly in mind which quantity is controlled by what: the frequency is fixed by the source, while the speed is fixed by the medium — so when a wave crosses into a new medium it is the wavelength that must change.
Representing waves: wavefronts and rays
There are two complementary ways to draw a wave as it spreads out. A wavefront is a line (or surface) joining points that are all in phase — for instance the line running along the top of one crest. Successive wavefronts are therefore spaced exactly one wavelength apart. A ray is an arrow drawn at right angles to the wavefronts, pointing in the direction the wave travels — that is, the direction of energy transfer. A wave spreading out from a point source has circular wavefronts; a wave far from its source, or a beam, has straight (plane) wavefronts. Rays and wavefronts always cross at 90°, so a diagram with either one implies the other.
Wavefront: joins points in phase; consecutive wavefronts are one wavelength apart.
Ray: an arrow perpendicular to the wavefronts, showing direction of travel / energy transfer.
Point source: circular (or spherical) wavefronts. Distant source / beam: plane (straight) wavefronts.
Rays and wavefronts are always mutually perpendicular.
Reading waves off graphs: distance vs time
The single most tested — and most confused — skill in this topic is reading a wave off a graph, because a displacement–distance graph and a displacement–time graph look identical yet mean different things. A displacement–DISTANCE graph is a snapshot: it freezes the whole wave at one instant and plots the displacement of every particle along the wave. The horizontal length of one full cycle is therefore the WAVELENGTH. A displacement–TIME graph is a movie of a single particle: it plots how that one particle's displacement changes as time passes. The horizontal length of one full cycle is therefore the PERIOD. Both graphs are sine curves and both show the amplitude on the vertical axis — so always read the horizontal axis label first to know whether you are getting a wavelength or a period.
Displacement–distance (horizontal axis = distance): snapshot of the whole wave → one cycle gives the wavelength .
Displacement–time (horizontal axis = time): history of one particle → one cycle gives the period .
Amplitude is the peak height of EITHER graph, read off the vertical axis.
Get from a displacement–time graph via , then combine with from a displacement–distance graph to find .
The electromagnetic spectrum
Visible light is one small band of a much larger family of transverse waves called the electromagnetic (EM) spectrum. In order of increasing frequency (and therefore decreasing wavelength) the regions are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Although they interact with matter in wildly different ways — radio waves pass through walls while gamma rays are ionising — they share one defining property: in a vacuum every one of them travels at the same speed, m s⁻¹. Because is fixed in a vacuum, the higher-frequency regions automatically have the shorter wavelengths.
Order (long , low → short , high ): radio → microwave → infrared → visible → ultraviolet → X-ray → gamma.
All EM waves are transverse and require no medium.
All travel at m s⁻¹ in a vacuum, so links their frequency and wavelength.
Visible light runs from red (longest ) to violet (shortest ) within the spectrum.
Mechanical waves need a medium
A mechanical wave is a disturbance passed from particle to particle through a material, so it cannot exist without that material. Sound, water waves, waves on a string and seismic waves are all mechanical — remove the medium and the wave disappears, which is why a bell ringing inside a jar goes silent as the air is pumped out and why space is soundless. Electromagnetic waves are the exception: they are oscillations of electric and magnetic fields that carry themselves along, needing no particles at all, so light from the Sun crosses the vacuum of space to reach us. This is the fundamental practical divide between the two categories of wave.
Common mistakes examiners penalise
Misusing — dividing when you should multiply, or forgetting to convert nm, cm, kHz or MHz to base SI units before substituting. Rearrange symbolically first, then put numbers in.
Thinking the medium sets the frequency — frequency is fixed by the source. When a wave changes medium the speed and wavelength change together but stays constant, so use with held fixed.
Confusing transverse and longitudinal — the test is the direction of oscillation relative to travel: perpendicular = transverse, parallel = longitudinal. Sound is longitudinal even though it is often drawn as a sine curve.
Reading wavelength off a displacement–time graph (or period off a displacement–distance graph) — check the horizontal axis: distance gives wavelength, time gives period. They are not interchangeable.
Calling the crest-to-trough height the amplitude — the amplitude is measured from the rest position to a crest; crest-to-trough is twice the amplitude.
Claiming some EM waves are faster than others in a vacuum — every part of the EM spectrum travels at exactly in a vacuum; they differ only in frequency and wavelength.
Saying sound can travel through space — sound is mechanical and needs a medium; only electromagnetic waves cross a vacuum.
Model answer — marked the way our engine marks it
In Paper 2 the marks are analytic: each is tied to a specific line of working — a method mark (M) or an answer mark (A) — and error-carried-forward (ECF) means a wrong number early on does not have to cost you the marks that follow. But that protection only exists if your method is written down. The question below deliberately mixes a calculation with a 'state and explain' part, because the explaining marks are earned by distinct physics statements, not by the number.
Where this leads
The wave model you have built here is the foundation for everything in wave behaviour that follows. The wave equation reappears whenever a wave changes medium — the physics of refraction is simply with the frequency held constant. Wavefronts and rays become the tools for describing reflection, refraction and diffraction, and the amplitude you learned to read off a graph is what determines intensity when waves superpose and interfere. Master the habit — identify the wave type, read the right graph for the right quantity, rearrange before you substitute, and keep frequency and medium in their proper roles — and the rest of the topic becomes variations on a model you already own.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A wave travels along a stretched string at 12 m s⁻¹ with a wavelength of 0.40 m. Calculate (a) its frequency and (b) its period. [3]
- 1
List what you know. m s⁻¹, m, ,
A single wave is described by two graphs. Its displacement–distance graph shows one complete cycle spanning 0.80 m, with a peak displacement of 3.0 cm. Its displacement–time graph shows one complete cycle spanning 0.20 s. Determine (a) the amplitude, (b) the wavelength, (c) the period and frequency, and (d) the wave speed. [4]
- 1
Read each graph for what it uniquely gives.
Green light has a wavelength of m in a vacuum. Taking m s⁻¹, calculate (a) its frequency and (b) its period. [3]
- 1
List what you know. m, m s⁻¹.
A sound wave has a frequency of 512 Hz and travels at 340 m s⁻¹ in air. Calculate its wavelength, then state and explain what happens to the wavelength if the wave passes into water, where it travels faster. [4]
- 1
Model answer — full working.
How it all connects
The big idea sits in the middle — tap a linked idea to explore the link.
Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Key terms for this topic — skim now; the Check step will test them.
- Transverse wave
A wave in which the oscillations are perpendicular (at right angles) to the direction of energy transfer. Examples: light and all electromagnetic waves, waves on a string, water surface ripples.
- Longitudinal wave
A wave in which the oscillations are parallel to the direction of energy transfer, forming compressions and rarefactions. The classic example is sound travelling through air.
- Wavelength ()
The shortest distance between two points oscillating in phase — e.g. crest to crest, or compression to compression. Measured in metres (m). Read it off a displacement–DISTANCE graph.
- Frequency ()
The number of complete oscillations passing a point per second, measured in hertz (Hz). It is set by the source of the wave, not by the medium.
- Period ()
The time for one complete oscillation, measured in seconds (s). Read it off a displacement–TIME graph. Related to frequency by .
- Amplitude ()
The maximum displacement of a particle from its equilibrium (rest) position. It sets the energy the wave carries; it is NOT the distance between a crest and a trough (that is twice the amplitude).
- The wave equation
Wave speed equals frequency multiplied by wavelength. Knowing any two of , , gives the third. Speed depends on the medium; frequency depends on the source.
- Period–frequency relationship
Period and frequency are reciprocals: and . A 50 Hz wave has a period of s.
- Wavefront
A line or surface joining points that are all in phase (e.g. all at a crest). Wavefronts are spaced one wavelength apart. They show the shape of the wave — plane or circular.
- Ray
An arrow drawn perpendicular to the wavefronts showing the direction the wave travels (the direction of energy transfer). Rays and wavefronts always meet at right angles.
- Displacement–distance vs displacement–time graph
A displacement–DISTANCE graph is a snapshot of the whole wave at one instant — read the WAVELENGTH from it. A displacement–TIME graph tracks ONE particle over time — read the PERIOD from it. Both show amplitude.
- The electromagnetic spectrum (order)
From longest wavelength / lowest frequency to shortest / highest: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. All are transverse and all travel at m s⁻¹ in a vacuum.
- Mechanical vs electromagnetic waves
Mechanical waves (sound, water, waves on a string) need a material medium to travel through and cannot cross a vacuum. Electromagnetic waves need no medium and travel through empty space.
Name it
Read the meaning, then pick which of this lesson’s terms it describes. Miss one and you see what your choice really means.
The maximum displacement of a particle from its equilibrium (rest) position. It sets the energy the wave carries; it is NOT the distance between a crest and a trough (that is twice the).
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
If you can explain it simply, you own it — gaps here are marks you’d lose.
Teach it back
Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.
Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
Transverse: oscillation perpendicular to energy transfer; shows crests and troughs. Examples: light and all EM waves, waves on a string, water ripples.
Longitudinal: oscillation parallel to energy transfer; shows compressions and rarefactions. Example: sound.
Both transfer energy, not matter: particles oscillate about a fixed point; only the disturbance advances.
A longitudinal wave can still be drawn as a sine curve by plotting displacement (or pressure) against position — the sine shape does not make it transverse.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Get a Paper 2 calculation marked: solve a wave-equation problem with full working
Get a Paper 2 calculation marked: solve a wave-equation problem with full working
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
One marked question is worth ten re-reads — close the loop before you move on.
Reading it isn’t knowing it — prove it.
Before you move on: do Get a Paper 2 calculation marked: solve a wave-equation problem with full working on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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