C Wave behaviour

Theme C: oscillations and waves, from simple harmonic motion to interference, standing waves, resonance and the Doppler effect, and how SL and HL differ.

IB Physics
SL and HL

5 subtopics in Wave behaviour

Each one has its own page once something is published for it.

C.1Simple harmonic motion83 questions · notes · 60 quick fire
C.2Wave model113 questions · notes · 55 quick fire
C.3Wave phenomena81 questions · notes · 80 quick fire
C.4Standing waves and resonance69 questions · notes · 61 quick fire
C.5Doppler effect52 questions · notes · 50 quick fire

An overview of C Wave behaviour

4 min readLast reviewed 14 Oct 2026

Theme C deals with oscillations and with the waves that carry them from place to place. It begins with a single body vibrating about a fixed position and ends with the light from distant galaxies, using one model throughout: a disturbance that carries energy from place to place without carrying matter with it.

How the subtopics fit together

Flow diagram of theme C. C.1 Simple harmonic motion leads to C.2 Wave model (oscillating sources) and to C.4 Standing waves and resonance (natural frequency, damping). — How the subtopics of wave behaviour build on each other: the two models (blue) and the phenomena explained with them (green). Oscillations (C.1) are the source of every wave; the wave model (C.2) then underpins the behaviour of waves at boundaries and when they meet (C.3, C.4) and when the source or observer moves (C.5).

C.1 Simple harmonic motion. The oscillation of a body pulled back towards equilibrium by a force proportional to its displacement, $a = -\omega^2 x$ . The mass on a spring and the simple pendulum are the standard examples, and the graphs of displacement, velocity, acceleration and energy against time describe every oscillation that follows.
C.2 Wave model. Transverse and longitudinal travelling waves, the quantities that describe them (wavelength, frequency, period, amplitude, speed) and the wave equation $v = f\lambda$ . Sound is the main example of a mechanical wave; light and the rest of the electromagnetic spectrum are the main examples of waves that need no medium.
C.3 Wave phenomena. What happens when waves meet a boundary or an obstacle (reflection, refraction and total internal reflection, diffraction) and when two waves meet each other (superposition and interference, including Young's double-slit experiment).
C.4 Standing waves and resonance. Two identical waves travelling in opposite directions form a standing wave with fixed nodes and antinodes, which sets the notes produced by strings and pipes. A system driven at its natural frequency oscillates with a large amplitude, an effect called resonance, whose size is limited by damping.
C.5 Doppler effect. The change in observed frequency and wavelength when a source and an observer move relative to each other, for sound and for light, with applications from radar speed traps to measuring how fast stars and galaxies move.

Big ideas across the theme

Oscillations are the source of waves. Every wave starts with something oscillating: a loudspeaker cone, an electron in an aerial, the bar of a ripple tank. As a wave passes, each particle of the medium oscillates too, often in simple harmonic motion, so the SHM graphs of C.1 reappear as the displacement–time graphs of C.2.

Energy moves; matter does not. A travelling wave transfers energy without any net movement of the medium. In an oscillator, energy is passed back and forth between kinetic and potential forms; this is the same conservation of energy used in A.3, and its gradual loss through damping is the key to resonance in C.4.

One model for very different waves. The same wave model describes waves on strings, sound, water waves, seismic waves and electromagnetic waves, although they differ in what oscillates and whether a medium is needed. Superposition explains interference (C.3) and standing waves (C.4) for all of them.

The wave model and its limits. The interference of light in Young's experiment is strong evidence that light is a wave. In theme E, the photoelectric effect shows behaviour the wave model cannot explain, and electron diffraction shows that matter can behave as a wave (E.2). Spectral lines, produced by atoms (E.1) and separated by diffraction gratings, are shifted by the Doppler effect when stars move, and stellar spectra are used again in E.5. Electromagnetic waves themselves are oscillating electric and magnetic fields, and those fields are the subject of theme D.

Standard level and higher level

No subtopic in theme C is HL only: every student studies all five. Three of them, however, contain additional HL sections, which appear only in the HL view of the notes.

C.1 Simple harmonic motion: describing SHM with the phase angle $\phi$ (in radians) and phase differences between oscillators; solving problems with $x = x_0\sin(\omega t + \phi)$ , $v = \omega x_0\cos(\omega t + \phi)$ and $v = \pm\omega\sqrt{x_0^2 - x^2}$ , including the maximum speed $\omega x_0$ ; and the quantitative energy of an oscillator, $E_\mathrm{T} = \tfrac12 m\omega^2 x_0^2$ and $E_\mathrm{p} = \tfrac12 m\omega^2 x^2$ . At SL, energy changes are described qualitatively.
C.3 Wave phenomena: single-slit diffraction, including the intensity pattern and the angle of the first minimum $\theta = \lambda/b$ ; how the single-slit pattern modulates the double-slit interference pattern; and multiple slits and diffraction gratings, $n\lambda = d\sin\theta$ , including the spectra produced from white light. At SL, diffraction is treated qualitatively.
C.5 Doppler effect: the equations for the observed frequency of sound and other mechanical waves when the source moves, $f' = f\left(\dfrac{v}{v \pm u_\mathrm{s}}\right)$ , and when the observer moves, $f' = f\left(\dfrac{v \pm u_\mathrm{o}}{v}\right)$ . At SL, the Doppler effect for sound is explained qualitatively and calculations use the light equation $\Delta f/f = \Delta\lambda/\lambda \approx v/c$ .

C.2 Wave model and C.4 Standing waves and resonance are the same at SL and HL. HL students spend more time on the theme (29 hours compared with 17 at SL); 10 of the 12 extra hours go to the HL sections of C.1 and C.3.

Flashcards for C

The official decks for this part of the syllabus.

C.1 Simple harmonic motion163 cards
C.2 Wave model149 cards
C.3 Wave phenomena255 cards
C.4 Standing waves and resonance154 cards
C.5 Doppler effect110 cards

From the data booklet

The entries of the physics data booklet that C uses. Each opens in the explained booklet.

And 19 more in the data booklet.

Carry on with C in Augment

With a free account, Augment remembers where you stopped and what you have practiced.

Start free Open C in Augment

How the subtopics fit together

How the subtopics of wave behaviour build on each other: the two models (blue) and the phenomena explained with them (green). Oscillations (C.1) are the source of every wave; the wave model (C.2) then underpins the behaviour of waves at boundaries and when they meet (C.3, C.4) and when the source or observer moves (C.5).

C.1 Simple harmonic motion. The oscillation of a body pulled back towards equilibrium by a force proportional to its displacement, $a = -\omega^2 x$ . The mass on a spring and the simple pendulum are the standard examples, and the graphs of displacement, velocity, acceleration and energy against time describe every oscillation that follows.

C.2 Wave model. Transverse and longitudinal travelling waves, the quantities that describe them (wavelength, frequency, period, amplitude, speed) and the wave equation $v = f\lambda$ . Sound is the main example of a mechanical wave; light and the rest of the electromagnetic spectrum are the main examples of waves that need no medium.

C.3 Wave phenomena. What happens when waves meet a boundary or an obstacle (reflection, refraction and total internal reflection, diffraction) and when two waves meet each other (superposition and interference, including Young's double-slit experiment).

C.4 Standing waves and resonance. Two identical waves travelling in opposite directions form a standing wave with fixed nodes and antinodes, which sets the notes produced by strings and pipes. A system driven at its natural frequency oscillates with a large amplitude, an effect called resonance, whose size is limited by damping.

C.5 Doppler effect. The change in observed frequency and wavelength when a source and an observer move relative to each other, for sound and for light, with applications from radar speed traps to measuring how fast stars and galaxies move.

Big ideas across the theme

Standard level and higher level

No subtopic in theme C is HL only: every student studies all five. Three of them, however, contain additional HL sections, which appear only in the HL view of the notes.

C.1 Simple harmonic motion: describing SHM with the phase angle $\phi$ (in radians) and phase differences between oscillators; solving problems with $x = x_0\sin(\omega t + \phi)$ , $v = \omega x_0\cos(\omega t + \phi)$ and $v = \pm\omega\sqrt{x_0^2 - x^2}$ , including the maximum speed $\omega x_0$ ; and the quantitative energy of an oscillator, $E_\mathrm{T} = \tfrac12 m\omega^2 x_0^2$ and $E_\mathrm{p} = \tfrac12 m\omega^2 x^2$ . At SL, energy changes are described qualitatively.

C.3 Wave phenomena: single-slit diffraction, including the intensity pattern and the angle of the first minimum $\theta = \lambda/b$ ; how the single-slit pattern modulates the double-slit interference pattern; and multiple slits and diffraction gratings, $n\lambda = d\sin\theta$ , including the spectra produced from white light. At SL, diffraction is treated qualitatively.

C.5 Doppler effect: the equations for the observed frequency of sound and other mechanical waves when the source moves, $f' = f\left(\dfrac{v}{v \pm u_\mathrm{s}}\right)$ , and when the observer moves, $f' = f\left(\dfrac{v \pm u_\mathrm{o}}{v}\right)$ . At SL, the Doppler effect for sound is explained qualitatively and calculations use the light equation $\Delta f/f = \Delta\lambda/\lambda \approx v/c$ .