IB Physics HLTopic 3 — Oscillations & WavesPaper 1 & 2Transverse vs Longitudinal~11 min read
Transverse & Longitudinal Waves
Shake a rope up and down and the wiggle races away from your hand. Push a slinky in and out and the squeeze races away instead. Both are waves, both carry energy — but the particles are doing completely different jobs. That one difference sorts every wave in the universe into two families, and this page shows you how to spot which is which in seconds.
📘 What you need to know
In a mechanical wave, particles oscillate about fixed points — they never travel with the wave
A transverse wave has oscillations perpendicular to the direction of energy transfer
A longitudinal wave has oscillations parallel to the direction of energy transfer
Transverse waves show crests and troughs; longitudinal waves show compressions and rarefactions
All electromagnetic waves are transverse, so they can cross a vacuum
Sound is longitudinal and needs a medium — no particles, no sound
Particles wobble, the wave travels
Start with the idea from the last page: a wave carries energy, not matter. In a mechanical wave, each particle of the medium just oscillates about a fixed point. It jiggles, it returns, it jiggles again. It never packs its bags and follows the wave down the rope.
So if the particles all stay put, what makes one wave different from another? The direction in which they jiggle. Compare the jiggle direction with the direction the energy is travelling, and you get two — and only two — possibilities:
The particles move across the direction of travel → transverse wave
The particles move along the direction of travel → longitudinal wave
Here’s the trick I give every student: point your finger in the direction the wave is going, then watch one particle. If the particle moves at right angles to your finger, it’s transverse. If it slides back and forth along your finger, it’s longitudinal. That’s the whole test.
Transverse waves
Definition — transverse wave
A wave in which the oscillations are perpendicular to the direction of motion and energy transfer
Perpendicular means at 90°. If the wave travels left to right across the page, the particles bob straight up and down. Each one rises to a maximum, drops to a minimum, and comes back — while the shape of the wave marches steadily rightwards.
The particles move straight up and down (blue), while the energy travels left to right (teal). The two directions are at 90° — that is what makes the wave transverse.
Because the oscillation is sideways, a transverse wave gives you the familiar wavy shape with crests (the high points) and troughs (the low points).
Examples of transverse waves
All electromagnetic waves — radio, microwaves, visible light, UV, X-rays
Vibrations on a guitar string — the string moves across the direction the wave runs
Water surface waves — the ripples on a pond
Seismic S-waves from an earthquake
Vacuum note: a transverse wave transfers energy even when there is no net displacement of the medium — and electromagnetic waves need no medium at all. That’s why sunlight and UV reach us straight through the empty vacuum of space.
Longitudinal waves
Definition — longitudinal wave
A wave in which the oscillations are parallel to the direction of motion and energy transfer
Here the particles vibrate left and right, along the same line the wave is travelling. Think of pushing the end of a slinky: a squeeze runs down the coils while each coil only shuffles forwards and backwards a little.
Because the particles bunch up in some places and spread out in others, a longitudinal wave doesn’t look wavy at all. Instead you see two features repeating:
Compression — an area of high pressure, where the particles are squashed close together
Rarefaction — an area of low pressure, where the particles are spread further apart
Bunched lines are compressions (high pressure); spread-out lines are rarefactions (low pressure). The oscillation (blue) lies along the same line as the travel direction (teal).
Examples of longitudinal waves
Sound waves in air, water or steel
Ultrasound waves used in medical scans
Seismic P-waves from an earthquake
Longitudinal waves are mechanical waves: they need particles to pass the vibration along, so they cannot travel through a vacuum. That’s the physics behind the film-poster line — in space, nobody can hear you shout.
Energy still moves, though. A particle is given energy and vibrates; as it crowds into its neighbour it hands some of that energy on, creating a compression a little further along. Repeat, and the compression travels while every particle stays home.
Notice that a longitudinal wave still has a wavelength, even though it doesn’t look wavy. One full wave is the distance from one compression to the next compression — exactly the same idea as crest to crest. And v = fλ works on it just fine.
How to tell them apart
🔍 The two-arrow test
Draw arrow 1 — the direction the wave (and its energy) is travelling.
Draw arrow 2 — the direction one single particle moves.
Compare them. At 90° → transverse. Along the same line → longitudinal.
Particle motion arrow 2
compare with energy direction
Perpendicular? transverse
or
Parallel? longitudinal
Side by side
Feature
Transverse
Longitudinal
Oscillation direction
Perpendicular to energy transfer
Parallel to energy transfer
Particle motion
Up and down
Left and right
Shape features
Crests and troughs
Compressions and rarefactions
One wavelength
Crest to crest
Compression to compression
Can cross a vacuum?
Yes, if electromagnetic
No — always needs a medium
Examples
Light, guitar string, water waves
Sound, ultrasound, P-waves
WE 1
The diagram shows a transverse wave at time t = 0, travelling to the right. State the direction in which point P moves immediately afterwards.
Point P sits on the equilibrium line, with a crest behind it and a trough ahead of it.
Step 1 — which directions are even possible?
The wave is transverse, so P can only move perpendicular to the travel direction: up or down.
Step 2 — ask what arrives at P next
The wave shifts to the right, so whatever is just to the left of P moves onto P. To P’s left is a crest.
Step 3 — read off the answer
The crest is chasing P, so P must rise to meet it.
P moves upwardsTempting wrong answer: “the trough is nearer the arrow, so P goes down.” No — the trough is running away from P, not towards it.
WE 2
In a sound wave travelling through air at 340 m s⁻¹, the distance from a compression to the very next rarefaction is 0.17 m. Calculate the frequency of the sound.
Step 1 — turn the clue into a wavelength
A compression to the next rarefaction is only half a wave.
λ = 2 × 0.17 = 0.34 mStep 2 — rearrange the wave equation
f = v / λ
Step 3 — substitute v = 340 m s⁻¹f = 340 / 0.34f = 1000 HzCompression → compression is a full λ. Compression → rarefaction is λ/2. Sketch it before you substitute.
WE 3
A transverse wave on a stretched string has a period of 2.0 ms. Four complete waves fit into a 1.2 m length of the string. Calculate the speed of the wave.
Step 1 — find the wavelengthλ = 1.2 / 4 = 0.30 mStep 2 — convert the period, then find f
T = 2.0 ms = 2.0 × 10⁻³ s
f = 1 / (2.0 × 10⁻³) = 500 HzStep 3 — use v = fλv = 500 × 0.30v = 150 m s⁻¹The wave being transverse doesn’t change the maths — v = fλ is the same for both families.
💡 Top tips
Two arrows, one comparison. Travel direction vs particle direction — that’s the whole classification.
Mechanical waves can be either type. Sound is longitudinal, but water and S-waves are transverse mechanical waves.
Electromagnetic waves are always transverse — and only they can cross a vacuum.
On a longitudinal diagram, count compression to compression for one wavelength.
Exam questions love asking about the motion of one particle, not the wave. Read carefully which one they want.
⚠ Common mistakes
Saying particles travel along the wave — they only oscillate about a fixed point
Assuming all mechanical waves are longitudinal — water waves and S-waves are transverse
Thinking a longitudinal wave has no wavelength because it isn’t wavy — it does: compression to compression
Mixing up compression (high pressure, particles close) and rarefaction (low pressure, particles spread)
Reading a particle’s next move from the trough ahead of it instead of what is arriving from behind
Quick recap: Particles in a mechanical wave oscillate about fixed points. If they oscillate perpendicular to the energy transfer, the wave is transverse (crests and troughs; light, water, guitar strings). If they oscillate parallel to it, the wave is longitudinal (compressions and rarefactions; sound, ultrasound). Only transverse electromagnetic waves can cross a vacuum — and v = fλ applies to both families.
You’ve now met the longitudinal family, and its most famous member deserves a page of its own. Next we look at sound waves — how compressions and rarefactions reach your ear, why frequency sets the pitch and amplitude sets the volume, and why sound races through steel but crawls through air.
Waves clicking into place? Let’s keep going.
Book a free meeting and we’ll practise particle-motion questions, wave diagrams and past-paper problems together.
