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.
↕️ Transverse vs longitudinal
Ask one question: which way does a particle move compared with the wave's direction of travel?
📡 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).
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
IB-style question — wavelength of a sound wave (v = fλ)
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.
Solution:
Start with the given wave equation:
Rearrange to make λ the subject:
Substitute v = 340, f = 425:
Work it out — keep the unit:
wavelength λ = 0.80 m. At a fixed speed, a higher-pitched (higher-f) note has a shorter wavelength.
IB-style question — speed from two graphs (v = λ/T)
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.
Solution:
Read the wavelength off the distance graph:
Read the period off the time graph (5.0 ms = 5.0 × 10⁻³ s):
Use the given wave equation written with the period:
Substitute and work it out — keep the unit:
speed v = 300 m s⁻¹. Wavelength comes from the distance graph, period from the time graph — never swap them.
IB-style question — frequency of an EM wave (c = fλ)
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.
Solution:
Use the given wave equation with the speed fixed at c:
Rearrange to make f the subject:
Substitute c = 3.00 × 10⁸, λ = 2.5:
Work it out — keep the unit:
f = 1.2 × 10⁸ Hz (120 MHz). A metre-scale wavelength and this frequency put it in the radio region.
IB-style question — wavelength from wavefronts, then speed
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.
Solution:
Neighbouring wavefronts are one wavelength apart:
The vibration rate is the frequency (f = 8.0 Hz). Use the given wave equation:
Substitute f = 8.0, λ = 0.45:
Work it out — keep the unit:
λ = 0.45 m and v = 3.6 m s⁻¹. The gap 1.20 − 0.75 = 0.45 m confirms the wavelength.
✅ Quick self-check
Tap each card to reveal the answer.
🎯 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.