Key Idea: Topic 3.2 is the wave model — a single picture for sound, light and ripples. A wave carries energy from place to place while the particles of the medium just vibrate on the spot. Four numbers describe any wave — its wavelength λ, frequency f, amplitude A and speed v — and one equation ties them together: the wave equation v = fλ = λ/T. It is examined on Paper 1A (quick MCQs — find one of v, f or λ from the other two, name an EM region from its wavelength, tell transverse from longitudinal) and on Paper 2 (read λ off a distance graph and T off a time graph then find the speed, deduce a particle's direction of motion, work with c = fλ for EM waves).
📐 Key formulas (both are given)
Both equations in this topic are given in the data booklet — so you do not memorise them, but you must know which form to reach for and how to rearrange it.
- wave speed (m s⁻¹)
- frequency — waves per second (Hz)
- wavelength — length of one full wave (m)
- period — time for one full wave (s)
- period — time for one full wave (s)
- frequency — waves per second (Hz)
- speed of an EM wave in vacuum = 3.00 × 10⁸ m s⁻¹ (a given constant)
- frequency (Hz)
- wavelength (m)
🌊 The four quantities — and which graph gives them
The most-tested skill in this topic is reading a wave off a graph. There are two graphs that look identical (both sine curves) — the axis label tells you which is which.
| Quantity | What it is | Where you read it |
|---|---|---|
| Wavelength λ | length of one full wave (e.g. crest to crest) | off a displacement–distance graph (x-axis in metres) |
| Amplitude A | maximum displacement from the middle (not crest to trough) | the height of a crest on either graph |
| Period T | time for one full wave to pass a point | off a displacement–time graph (x-axis in seconds) |
| Frequency f | number of waves per second (Hz) | found from f = 1/T |
↕️ Transverse vs longitudinal
Ask one question: which way does a particle move compared with the wave's direction of travel?
| Feature | Transverse | Longitudinal |
|---|---|---|
| Particle motion | perpendicular (across) the wave's travel | parallel (along) the wave's travel |
| What the wave shows | crests and troughs | compressions (bunched) & rarefactions (spread) |
| Everyday example | light (and all EM waves), a rope wave | sound, a push–pull on a spring |
📡 The EM spectrum — one speed, c
All EM waves are transverse and all travel at c = 3.00 × 10⁸ m s⁻¹ in a vacuum. Going up the spectrum, wavelength gets shorter and frequency gets higher (energy rises too).
| Order (long λ → short λ) | Region | Everyday use |
|---|---|---|
| longest λ, lowest f | Radio | TV, radio, phone signals |
| ↓ | Microwave | ovens, wifi, radar |
| ↓ | Infrared | heat, remote controls |
| ≈ 400–700 nm | Visible | the light your eyes see |
| ↓ | Ultraviolet | suntan, sterilising |
| ↓ | X-ray | seeing bones |
| shortest λ, highest f | Gamma | from nuclei, cancer treatment |
A wavefront is a line joining points all in phase (e.g. all the crests); neighbouring wavefronts are exactly one wavelength λ apart. A ray is an arrow showing the direction of travel, drawn perpendicular (at 90°) to the wavefronts.
✍️ IB-style worked examples
A loudspeaker plays a note of frequency 425 Hz into air, where the speed of sound is 340 m s⁻¹. Calculate the wavelength of the sound wave.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A wave is drawn on two graphs. Its displacement–distance graph shows one full wave spanning 1.5 m; its displacement–time graph shows one full cycle taking 5.0 ms. Find the speed of the wave.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A radio mast transmits electromagnetic waves of wavelength 2.5 m. Taking the speed of an EM wave in air as c = 3.00 × 10⁸ m s⁻¹, find the frequency, and name the region of the EM spectrum.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
On a snapshot of ripples, straight wavefronts sit at 0.30 m, 0.75 m and 1.20 m from one edge. The dipper that makes them vibrates at 8.0 Hz. Find the wavelength and the speed of the ripples.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
✅ Quick self-check
Tap each card to reveal the answer.
What does a wave actually transport? Energy — the particles of the medium just vibrate on the spot; they do not travel along with the wave.
Which graph gives λ, and which gives T? Wavelength λ off a displacement–distance graph (axis in metres); period T off a displacement–time graph (axis in seconds). Always check the axis label.
Write the wave equation, both ways. v = fλ (with a frequency) = λ/T (with a period). Speed = frequency × wavelength.
Transverse vs longitudinal — the one test? Particle motion perpendicular to travel → transverse (crests/troughs). Parallel → longitudinal (compressions/rarefactions).
How fast do EM waves travel, and what equation applies? All EM waves travel at c = 3.00 × 10⁸ m s⁻¹ in a vacuum (every region, same speed), so c = fλ.
How far apart are neighbouring wavefronts, and how is a ray drawn? Exactly one wavelength λ apart. A ray points along the direction of travel, drawn perpendicular to the wavefronts.
🎯 Highest-yield exam reminders
Exam Tips
- A wave moves energy, not matter — the medium's particles vibrate on the spot. State this clearly when asked what a wave transfers.
- Wavelength comes from a distance graph; period from a time graph — both look like the same sine curve, so always read the axis label first.
- The wave equation v = fλ = λ/T is given. Pick v = fλ when you have a frequency and v = λ/T when you have a period; rearrange to λ = v/f or f = v/λ as needed.
- Convert units before substituting: ms → s, kHz/MHz → Hz, and nm → m. A missed power of ten is the most common lost mark.
- Transverse = particles move across the travel direction (crests/troughs, e.g. light); longitudinal = along it (compressions/rarefactions, e.g. sound). Decide by comparing particle motion to wave direction.
- All EM waves are transverse and travel at c = 3.00 × 10⁸ m s⁻¹ in a vacuum — every colour and region at the same speed. Use c = fλ, and remember the order radio → micro → infrared → visible → UV → X-ray → gamma (λ shrinks, f and energy rise).
- On a wavefront diagram, neighbouring wavefronts are one wavelength apart and rays are perpendicular to them — measure the spacing to get λ, then use v = fλ.