Educerie · IB Diploma · Physics
Theme C Wave behaviour · C.2 Wave model
What you must be able to do
| You must be able to | Level | What it looks like in the exam |
|---|---|---|
| Describe transverse and longitudinal travelling waves, with examples | SL, HL | "Distinguish between transverse and longitudinal waves" (2–3 marks) |
| Explain that a travelling wave transfers energy without transferring the medium | SL, HL | "Outline what is meant by a travelling wave" (2 marks) |
| Define wavelength λ, frequency f, period T and wave speed v | SL, HL | Paper 1A definitions; read λ from a displacement–distance graph and T from a displacement–time graph |
| Use v = fλ = λ/T | SL, HL | Every wave calculation, 1–2 marks |
| Describe how particles move, from displacement–position and displacement–time graphs | SL, HL | "State the direction of motion of particle P" (1–2 marks); locate compressions |
| Explain what changes, and what does not, when frequency or medium changes | SL, HL | "Explain what happens to the wavelength when the sound enters water" (2–3 marks) |
| Describe the nature of sound waves | SL, HL | "Explain why sound cannot travel through a vacuum" (2 marks) |
| Describe the nature of electromagnetic waves and the orders of magnitude of their wavelengths | SL, HL | Paper 1A: order the regions of the spectrum; convert λ to f |
| Compare mechanical and electromagnetic waves | SL, HL | "State two differences between…" (2 marks) |
Before you start
You need C.1: every particle of a medium carrying a sine wave performs simple harmonic motion, so period, frequency, amplitude and displacement mean exactly what they meant there. You also need speed = distance ÷ time from A.1, and powers of ten for the electromagnetic spectrum.
1The idea in one paragraph
Flick one end of a rope and a bump runs along it to the other end. The bump arrives; the rope does not. That hand-on-hand disturbance is a travelling wave: energy moves along while every particle of the medium only oscillates about its own equilibrium position. If the particles move at right angles to the direction the wave travels, the wave is transverse; if they move along it, the wave is longitudinal. A repeating wave has a wavelength λ and a frequency f, and it travels one wavelength every period, which gives v = fλ. Sound is a longitudinal wave in a material medium. Light is a transverse wave of electric and magnetic fields that needs no medium at all.
2What a travelling wave is
A travelling wave is a disturbance that moves through a medium, transferring energy from one place to another without any overall movement of the medium itself. The medium is whatever the wave travels through: the rope, the water, the air.
Figure 1 is the definition drawn out. A single pulse runs along a rope. One point on the rope is marked.
At t₁ the pulse has not yet arrived and the marked point is at rest. At t₂ the pulse is passing and the point has been lifted to the top of the bump. At t₃ the pulse has gone by and the point is back exactly where it started. The pulse moved several metres. The marked point moved up and down and ended with zero resultant displacement. Yet energy has clearly travelled: whatever the pulse reaches is shaken.
The energy gets along because each piece of rope is joined to the next by tension: a lifted piece pulls its neighbour up a moment later, taking energy from behind and handing it on.
If the end of the rope is moved up and down continuously in SHM, a continuous wave travels along it rather than a single pulse, and every point on the rope performs the same SHM as the source, each a little later than the one before. That is the link to C.1: a sine wave is a row of simple harmonic oscillators, each slightly behind its neighbour.
A gull floating on ocean swell rises and falls as each wave passes, but the swell does not carry it to the beach.
3Transverse and longitudinal waves
Waves are classified by one question: which way do the particles of the medium oscillate, compared with the direction in which the wave, and its energy, travels? Figure 2 draws the two answers with a row of particles.
In a transverse wave the particles oscillate at right angles (perpendicular) to the direction of energy transfer. The high points are crests and the low points troughs. Examples: waves on a stretched string or rope, the S-waves of an earthquake, and all electromagnetic waves, where the things that oscillate are fields rather than particles.
In a longitudinal wave the particles oscillate parallel to the direction of energy transfer, backwards and forwards along the line the wave travels. This crowds them together in some places and spreads them apart in others. A region where the particles are closer together than normal is a compression, a region of higher pressure and density. A region where they are further apart than normal is a rarefaction, a region of lower pressure and density. Examples: sound in air and in water, the P-waves of an earthquake, and pulses sent along a stretched spring by pushing its end back and forth.
Surface water waves are usually treated as transverse, although the water actually moves in rough circles, a mix of the two.
Notice in Figure 2(b) that the compressions are not where the particles have moved furthest. They are where neighbouring particles have moved towards each other. That idea is worth a mark in section 5.
4Wavelength, frequency, period and speed
Five quantities describe any repeating travelling wave.
- The wavelength, λ, is the distance between two adjacent points on the wave that are in step with each other: crest to next crest, or compression to next compression. Unit: metre.
- The amplitude is the maximum displacement of a particle from its equilibrium position. It is measured from the undisturbed position, not from crest to trough.
- The period, T, is the time taken for one particle to complete one full oscillation. Unit: second.
- The frequency, f, is the number of oscillations each particle makes per second, which is also the number of wavelengths that pass a point per second. Unit: hertz. f = 1/T.
- The wave speed, v, is the speed at which the wave, and its energy, travels through the medium.
The equation linking them comes from one observation. In one period T, the source makes one complete oscillation and sends out one complete wavelength. So the wave travels a distance λ in a time T:
v = fλ = λ/T
Two graphs carry this information, and Paper 2 relies on your telling them apart. Figure 3 draws them side by side.
A graph of displacement against distance is a snapshot of the whole medium at one instant, like a photograph of the rope. The repeat length along its horizontal axis is the wavelength.
A graph of displacement against time follows one single particle as the wave passes it, like filming one point on the rope. The repeat length along its horizontal axis is the period.
Read the axis label before you read anything else. The two curves in Figure 3 look identical; one gives λ = 0.80 m and the other T = 0.80 s. If they describe the same wave:
Distinguish the wave speed from the speed of the particles. The wave speed is constant in a given medium. A particle's speed changes all the time as it performs SHM: greatest as it passes through its equilibrium position and zero at its extremes. They are different quantities and usually have very different values.
5Reading particle motion from the graphs
Two skills cover how particles move as a wave passes.
Transverse: which way is a particle moving right now? Take the snapshot and imagine it a moment later. Because the wave travels, the whole shape slides a little in the direction of travel. Each particle stays at its own position along the rope and moves up or down to meet the new curve. Figure 4 does this for a wave travelling to the right.
- P sits at a crest. It is at the top of its oscillation, momentarily at rest, and about to move down.
- Q sits at a point where the curve crosses the axis going down. The dashed curve a moment later is above it, so Q is moving up, and at its greatest speed.
- R sits at a point where the curve crosses the axis going up. The dashed curve is below it, so R is moving down.
If the wave travelled to the left, every answer would reverse. So the first thing to write in an answer is the direction of travel you are assuming.
Longitudinal: where are the compressions? A longitudinal wave is often drawn as a graph that looks transverse. Its vertical axis is the displacement s of each particle along the direction of travel: positive means displaced forwards (to the right, say), negative means displaced backwards. It is not a picture of the particles moving up and down. Figure 5 lines the graph up with the particles it describes.
Look at the point where the curve crosses the axis going down, at x = 0.5 on the figure. Just to its left the displacement is positive, so those particles have moved right, towards the point. Just to its right the displacement is negative, so those particles have moved left, towards the point. Particles are crowding in from both sides: that point is the centre of a compression. Where the curve crosses the axis going up, the particles on either side have moved away: that is a rarefaction.
Two consequences examiners like. The centre of a compression is a particle with zero displacement, not maximum displacement. And the distance from one compression to the next is one wavelength.
6What changes when the frequency or the medium changes
Change one thing about a wave and you have to know which of f, v and λ responds. The rule is short:
- the frequency is set by the source. Nothing downstream can change how many oscillations per second are arriving.
- the speed is set by the medium: its tension, stiffness, density or temperature. For a given medium and a given type of wave, v is fixed.
- the wavelength is whatever is left over: λ = v/f.
Figure 6 shows both cases.
Same medium, higher frequency. Double the frequency of a loudspeaker. The air is the same, so the speed is the same, so the wavelength halves. Panel (a).
Same source, new medium. A loudspeaker under a swimming pool sends a 500 Hz note from the air above into the water. The frequency is still 500 Hz on both sides: every compression arriving at the surface starts one compression in the water. But sound travels faster in water.
The wave speeds up and stretches out. Going the other way, into a slower medium, the wavelength shortens. That change of speed at a boundary is the cause of refraction, which is where C.3 begins.
7Sound waves
Sound is a longitudinal mechanical wave. A vibrating source, such as the cone of a loudspeaker, pushes forward into the air and makes a compression, then moves back and leaves a rarefaction. Each layer of air pushes on the next, so a train of compressions and rarefactions travels outwards. The air molecules themselves just oscillate back and forth about their average positions. In air and in liquids, sound is purely longitudinal.
Because it is a pressure wave passed from particle to particle, sound needs a medium. It cannot travel through a vacuum. The classic demonstration is an electric bell inside a sealed jar: as a pump removes the air, the sound fades away while the hammer can still be seen striking the bell.
Sound travels at different speeds in different media. Roughly, and for orientation only:
| Medium | Approximate speed of sound |
|---|---|
| air at room temperature | 340 m s⁻¹ |
| water | 1500 m s⁻¹ |
| steel | 5000 m s⁻¹ or more |
The pattern: sound is generally fastest in solids and slowest in gases, because the forces between neighbouring particles in a solid pass a disturbance on much more quickly.
The frequency of a sound is heard as its pitch, and its amplitude as its loudness. Healthy young human ears detect roughly 20 Hz to 20 kHz. Sound above that range is ultrasound, which is still sound, just too high-pitched to hear.
A quick estimate that uses all of this. You see lightning, and hear the thunder 3.0 s later. The light takes a few microseconds to reach you, so treat its arrival as instant; the distance is about 340 × 3.0 ≈ 1000 m, roughly a kilometre.
8Electromagnetic waves
An electromagnetic (EM) wave is a transverse wave made of an oscillating electric field and an oscillating magnetic field, at right angles to each other and both at right angles to the direction of travel. Figure 7 draws one.
EM waves are produced whenever charged particles accelerate, for example electrons oscillating up and down a radio aerial. Three facts define them.
They need no medium. A changing electric field creates a magnetic field, and a changing magnetic field creates an electric field. Each keeps the other going, so the wave carries itself across empty space. That is how sunlight reaches Earth through the vacuum between them.
All of them travel at the same speed in a vacuum: c = 3.00 × 10⁸ m s⁻¹, from the data booklet. In glass, water or air they travel more slowly; in air, only very slightly more slowly. In the 1860s James Clerk Maxwell calculated the speed of his predicted electromagnetic waves from purely electrical and magnetic measurements and found it matched the measured speed of light, which is how light was identified as an electromagnetic wave.
They are always transverse, since the fields oscillate at right angles to the direction of travel.
Because they share one speed, v = fλ becomes c = fλ, and the whole family can be laid out along one scale of wavelength, the electromagnetic spectrum. Figure 8 shows the orders of magnitude the data booklet gives.
From longest wavelength to shortest: radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays. Since c is fixed, the order of frequencies is the reverse. Visible light is a very narrow slice, roughly 400 nm (violet) to 700 nm (red).
Convert the prefixes first: nm is 10⁻⁹ m, MHz is 10⁶ Hz, GHz is 10⁹ Hz.
How part of the spectrum was found: in 1895 Wilhelm Röntgen, working with a cathode-ray tube wrapped in black card, noticed a nearby fluorescent screen glowing. Something invisible was passing through the card; not knowing what, he called it X. That X-rays are short-wavelength EM waves was settled later. An unexpected observation came first and the model after.
9Mechanical and electromagnetic waves compared
A mechanical wave is a wave that travels through a material medium by the oscillation of its particles: sound, water waves, waves on strings, seismic waves. The comparison below is a common two-mark question, and it pays to learn it as a table.
| Mechanical waves | Electromagnetic waves | |
|---|---|---|
| What oscillates | particles of the medium | electric and magnetic fields |
| Medium needed? | yes; cannot cross a vacuum | no; travels through a vacuum |
| Type | transverse or longitudinal | always transverse |
| Speed | set by the medium; for sound, hundreds to thousands of m s⁻¹ | 3.00 × 10⁸ m s⁻¹ in a vacuum, less in materials |
| Examples | sound, ultrasound, water waves, waves on a string, seismic waves | radio, microwave, infrared, visible, ultraviolet, X-ray, gamma |
What they share is the wave model itself: both transfer energy, both have a wavelength, frequency and speed linked by v = fλ, and both show the behaviours of C.3.
10Where marks are lost
Saying the wave carries the medium along. The wave transfers energy. The particles oscillate about fixed positions and have no overall displacement once the wave has passed.
Reading a wavelength off a time axis. The repeat distance on a displacement–time graph is the period, not the wavelength. Check the axis label every time.
Measuring amplitude crest to trough. Amplitude is from the equilibrium position to a crest. Crest to trough is twice the amplitude.
Confusing particle speed with wave speed. The wave moves at constant speed v; a particle's speed varies from zero to a maximum during each oscillation.
Thinking the frequency changes at a boundary. The source sets the frequency. When a wave enters a new medium its speed and wavelength change and its frequency does not.
Putting the compression at the peak of a longitudinal displacement graph. Compressions sit where the displacement is zero and the graph is falling, with particles on either side displaced towards that point.
Saying sound travels fastest in air or through a vacuum. Sound needs a medium, and it is generally faster in liquids and fastest in solids.
11Draw it right
- Label the axes of any wave graph with quantity and unit, and decide first whether the horizontal axis is distance or time.
- Mark λ between two matching points (crest to crest, or two equivalent zero crossings) on a displacement–distance graph; mark T the same way on a displacement–time graph.
- Mark amplitude from the equilibrium line to a crest.
- Show direction of travel with an arrow whenever you draw a snapshot, since particle directions depend on it.
- For a longitudinal wave drawn as particles, crowd them at compressions and spread them at rarefactions, and keep the number of particles the same; nothing is created or lost.
- For an EM wave, draw E and B at right angles to each other and to the direction of travel, in step with each other.
12Try it
Marks in brackets. Answers and marker's notes are at the end.
Q1. Adjacent crests of a water wave are 0.40 m apart. A float on the water bobs up and down 5 times in 2.0 s. What is the speed of the wave? 1 mark
A. 0.16 m s⁻¹ B. 1.0 m s⁻¹ C. 2.0 m s⁻¹ D. 6.3 m s⁻¹
Q2. Distinguish between transverse and longitudinal waves, giving one example of each. 3 marks
Q3. A travelling wave on a stretched string has a speed of 12 m s⁻¹. A particle of the string completes 30 oscillations in 5.0 s, travelling a total path of 0.12 m during each oscillation.
(a) Calculate the frequency of the wave. 1 mark
(b) Calculate the wavelength. 1 mark
(c) Determine the amplitude. 2 marks
(d) State how far the wave travels while the particle completes one oscillation. 1 mark
Q4. A student measures the speed of sound with two microphones a distance d apart, in line with a loudspeaker that emits a sharp click. A timer records the delay Δt between the click reaching the two microphones. Her results (invented) are:
| d / m | 0.50 | 1.00 | 1.50 | 2.00 | 2.50 |
|---|---|---|---|---|---|
| Δt / ms | 1.5 | 2.9 | 4.4 | 5.9 | 7.4 |
(a) Determine the speed of sound from these data. 3 marks
(b) The timer adds the same small delay to every reading. Explain why a graph of Δt against d still gives a correct value for the speed. 2 marks
Q5. (a) State two differences between sound waves and light waves. 2 marks
(b) A radio station broadcasts at 97.5 MHz. Calculate the wavelength of its waves. 2 marks
Q6. A loudspeaker above a swimming pool emits a note that passes from the air into the water. Explain what happens to the frequency, speed and wavelength of the sound as it enters the water. 3 marks
13In one breath
A travelling wave transfers energy through a medium while its particles only oscillate about fixed positions, each in SHM a little behind its neighbour: at right angles to the energy transfer in a transverse wave, along it in a longitudinal wave, which makes compressions and rarefactions. v = fλ = λ/T because the wave moves one wavelength each period. A displacement–distance graph is a snapshot and gives λ; a displacement–time graph follows one particle and gives T. The source sets the frequency and the medium sets the speed, so λ adjusts. Sound is a longitudinal mechanical pressure wave that needs a medium and is fastest in solids. EM waves are transverse oscillations of electric and magnetic fields that need no medium and all travel at 3.00 × 10⁸ m s⁻¹ in a vacuum, from radio at metres and more down to gamma at about 10⁻¹² m.
Answers
Q1. B. f = 5 ÷ 2.0 = 2.5 Hz, and v = fλ = 2.5 × 0.40 = 1.0 m s⁻¹. A divides λ by f. C uses 5 as the frequency. D divides f by λ.
Q2. In a transverse wave the particles of the medium oscillate perpendicular to the direction of energy transfer, for example a wave on a stretched string or any electromagnetic wave. In a longitudinal wave the particles oscillate parallel to the direction of energy transfer, forming compressions and rarefactions, for example sound in air. 1 for perpendicular, 1 for parallel, each relative to the direction of energy transfer, 1 for an example of each. "Up and down" with no reference to the direction of travel scores 0.
Q3. (a) f = 30 ÷ 5.0 = 6.0 Hz. (b) λ = v ÷ f = 12 ÷ 6.0 = 2.0 m. (c) In one oscillation a particle goes from equilibrium to one extreme, back, to the other extreme, and back: four amplitudes. So 4A = 0.12 m and A = 0.030 m. (d) 2.0 m, one wavelength. (a) A1; (b) A1, follow through from (a); (c) M1 for path = 4 × amplitude, A1 for 0.030 m — 0.12 m or 0.060 m scores 0; (d) A1 for one wavelength or 2.0 m.
Q4. (a) Using the first and last readings, v = Δd ÷ Δ(Δt) = (2.50 − 0.50) ÷ ((7.4 − 1.5) × 10⁻³) = 2.00 ÷ 5.9 × 10⁻³ = 339 m s⁻¹. A best-fit line through all five points has gradient 2.96 ms per metre, giving v = 1 ÷ (2.96 × 10⁻³) = 338 m s⁻¹. (b) A constant delay adds the same amount to every Δt, so it shifts the whole line up without changing its gradient. The speed comes from the gradient, so it is unaffected; the delay shows up only as the intercept. (a) M1 for a difference in d over a difference in Δt, or the gradient, M1 for ms to s, A1 for 335 to 345 m s⁻¹; (b) 1 for a constant shift or intercept, 1 for gradient and so speed unchanged. One d divided by one Δt earns M1 only, since it includes the delay.
Q5. (a) Any two: sound is longitudinal, light is transverse; sound needs a medium, light can travel through a vacuum; sound is an oscillation of particles, light of electric and magnetic fields; light is far faster, 3.00 × 10⁸ m s⁻¹ in a vacuum against about 340 m s⁻¹ for sound in air. (b) λ = c ÷ f = 3.00 × 10⁸ ÷ 97.5 × 10⁶ = 3.08 m. (a) 1 each for two genuine differences stated as a comparison; (b) M1 for c = fλ with 10⁶ for MHz, A1 for 3.08 m. An answer of 3.08 × 10⁶ m or 3.08 × 10⁻⁶ m shows the prefix mishandled and scores M1 only.
Q6. The frequency stays the same, because it is set by the source and each oscillation arriving at the surface produces one oscillation in the water. The speed increases, because sound travels faster in water than in air. Since λ = v ÷ f with f unchanged, the wavelength increases in proportion to the speed. 1 for frequency unchanged with the reason, 1 for speed increases, 1 for wavelength increases linked to v = fλ. "The wavelength increases because the frequency decreases" scores 0 for the last two marks.
Educerie · written from the published IB Diploma Programme Physics guide, first assessment 2025, section C.2 Wave model. Original text, examples and questions. Diagrams drawn by Educerie. Last reviewed 25 September 2026.