# Theme C: Wave behaviour

> IB Physics HL · IB Physics HL 2025 Syllabus
> Source: https://www.owlsprep.com/study/ib-physics-hl-u3-overview/
> Weight: 15-17% of overall exam

This unit covers core and additional higher level (AHL) wave behaviour, from simple harmonic motion fundamentals to advanced interference and diffraction phenomena. Waves are central to nearly all fields of physics, from sound and light to quantum mechanics and communications.

**Prerequisites:** [IB Physics HL Unit 1: Mechanics fundamentals](https://www.owlsprep.com/study/ib-physics-hl-u1-overview/)

## Learning objectives

- Describe and calculate properties of oscillating motion and simple harmonic motion (SHM)
- Differentiate between travelling and standing waves and apply core wave properties to problem solving
- Analyze key wave phenomena including interference, diffraction, Doppler effect and resonance
- Solve IB-style problems for advanced AHL topics including thin film interference and optical resolution

## Unit at a Glance

We start with the foundational oscillatory motion of simple harmonic motion (SHM), the repeating motion that acts as the building block for all wave phenomena. From SHM, we move to the core properties of travelling waves, before exploring fundamental wave behaviours like reflection, refraction, dispersion and polarisation.

The unit progresses to standing wave formation and resonance, then covers AHL extensions building on core concepts: the Doppler effect, multi-source interference, diffraction, optical resolution, and thin film interference. Topics build progressively, so we recommend working through sub-topics in order.

This unit includes the following core and AHL sub-topics:
- [C.1 Simple harmonic motion](https://www.owlsprep.com/study/ib-physics-hl-u3-c-1-simple-harmonic-motion/) — Learn the defining characteristics, energy changes and mathematical description of SHM.
- [C.2 Travelling waves](https://www.owlsprep.com/study/ib-physics-hl-u3-c-2-travelling-waves/) — Explore wave types, properties, and the relationship between speed, frequency and wavelength.
- [C.3 Wave phenomena](https://www.owlsprep.com/study/ib-physics-hl-u3-c-3-wave-phenomena/) — Cover core wave behaviours including reflection, refraction, dispersion and polarisation.
- [C.4 Standing waves and resonance](https://www.owlsprep.com/study/ib-physics-hl-u3-c-4-standing-waves-and/) — Analyze standing wave formation via superposition and resonance conditions for different systems.
- [C.5 Doppler effect (AHL)](https://www.owlsprep.com/study/ib-physics-hl-u3-c-5-doppler-effect/) — Derive and apply Doppler effect formulas for moving sources and observers for sound and light.
- [C.6 Interference (AHL)](https://www.owlsprep.com/study/ib-physics-hl-u3-c-6-interference/) — Study conditions for constructive and destructive interference from multiple coherent sources.
- [C.7 Diffraction and resolution (AHL)](https://www.owlsprep.com/study/ib-physics-hl-u3-c-7-diffraction-and-resolution/) — Analyze single-slit diffraction and apply the Rayleigh criterion for optical resolution.
- [C.8 Thin film interference (AHL)](https://www.owlsprep.com/study/ib-physics-hl-u3-c-8-thin-film-interference/) — Calculate interference conditions for thin films, accounting for phase changes upon reflection.

## Common pitfalls

- **Wrong:** Forgetting to account for 180° phase changes when calculating thin film interference path differences.
  - Why it fails: A phase change adds an extra $\lambda/2$ effective path difference that reverses constructive/destructive conditions.
  - Correct: Always check each reflection to see if a phase change occurs from a higher refractive index medium.
- **Wrong:** Confusing Doppler effect equations for moving sources vs moving observers.
  - Why it fails: Frequency shift formulas differ depending on which object is moving relative to the wave medium.
  - Correct: Derive from first principles if unsure, remember $f'$ increases when source/observer move towards each other.
- **Wrong:** Mixing up wavelength values in thin film interference calculations.
  - Why it fails: Wavelength in a medium of refractive index $n$ is shorter than wavelength in vacuum.
  - Correct: Always use $\lambda_n = \frac{\lambda}{n}$ for the wavelength inside the thin film.

## Cheatsheet

| Concept | Key Formula/Rule |
| --- | --- |
| SHM defining equation | $a = -\omega^2 x$ |
| Universal wave speed relation | $v = f \lambda$ |
| Brewster's law for polarisation | $n = \tan \theta_p$ |
| First harmonic (fixed string) | $f_1 = \frac{v}{2L}$ |
| Doppler effect (moving source) | $f' = f \frac{v}{v \mp u_s}$ |
| Double-slit constructive interference | Path difference = $n\lambda$, $n = 0, 1, 2...$ |
| Rayleigh resolution criterion | $\theta = 1.22 \frac{\lambda}{b}$ |
| Thin film (1 phase change, constructive) | $2nt = (m + \frac{1}{2})\lambda$ |

## What's next

Start your exploration of this unit with the first sub-topic, C.1 Simple harmonic motion, the foundational oscillatory motion that underpins all wave behaviour. Work through each sub-topic in order, as concepts build progressively from core fundamentals to advanced AHL applications. Once you complete all sub-topics in this unit, move on to the next IB Physics HL unit covering circular motion and gravitation.

- [C.1 Simple harmonic motion](https://www.owlsprep.com/study/ib-physics-hl-u3-c-1-simple-harmonic-motion/)
- [Theme D: Circular motion and gravitation](https://www.owlsprep.com/study/ib-physics-hl-u4-overview/)
- [C.2 Travelling waves](https://www.owlsprep.com/study/ib-physics-hl-u3-c-2-travelling-waves/)

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