# Wave behaviour

> IB Physics SL · IB SL Physics 2025 Syllabus
> Source: https://www.owlsprep.com/study/ib-physics-sl-u3-overview/
> Weight: 18-20% of overall IB Physics SL exam

This unit covers oscillatory motion, core wave properties, and superposition phenomena. It is foundational for optics, sound, and quantum concepts, and is heavily tested on IB SL exams.

**Prerequisites:** Basic kinematics and energy conservation; Fundamental force and motion concepts

## Learning objectives

- Describe the properties of simple harmonic motion and solve related kinematic and energy problems
- Distinguish between different wave types and core wave characteristics
- Explain wave interference phenomena using the principle of superposition
- Analyze standing wave patterns for strings and open/closed air columns

## Unit at a Glance

We start with simple harmonic motion (SHM), the simplest form of repeating oscillatory motion, before expanding to generalized travelling wave properties. The unit progresses from describing individual waves to exploring how multiple waves interact with each other via superposition.

This sequence builds from foundational definitions to complex applied problems that commonly appear on IB exams. All sub-topics build on concepts introduced earlier in the unit.

The core sub-topics in this unit are:
- [Simple harmonic motion](https://www.owlsprep.com/study/ib-physics-sl-u3-simple-harmonic-motion/) — Learn the definition, kinematics, and energy of SHM systems including mass-springs and pendulums.
- [Wave characteristics](https://www.owlsprep.com/study/ib-physics-sl-u3-wave-characteristics/) — Distinguish between transverse and longitudinal waves and learn core wave parameters.
- [Wave interference](https://www.owlsprep.com/study/ib-physics-sl-u3-wave-interference/) — Apply superposition to explain constructive and destructive interference in common experimental setups.
- [Standing waves](https://www.owlsprep.com/study/ib-physics-sl-u3-standing-waves/) — Analyze standing wave patterns on strings and air columns and solve harmonic frequency problems.

## Common pitfalls

- **Wrong:** Confusing SHM acceleration direction, assuming acceleration always follows motion.
  - Why it fails: SHM acceleration is always directed toward equilibrium, opposite displacement.
  - Correct: Remember $a = -\omega^2 x$: the negative sign confirms acceleration opposes displacement from equilibrium.
- **Wrong:** Mixing up boundary conditions and harmonics for open vs closed air columns.
  - Why it fails: Closed ends form nodes and open ends form antinodes, which changes the allowed harmonic sequence.
  - Correct: Start by identifying boundary conditions, then derive allowed wavelengths/frequencies from there.

## Cheatsheet

| Concept / Formula | Key Description |
| --- | --- |
| $a = -\omega^2 x$ | Defining relationship for simple harmonic motion |
| $v = f \lambda$ | Universal wave speed relation for all travelling waves |
| Constructive interference path difference: $n\lambda$, $n=0,1,2...$ | Condition for constructive superposition of two coherent waves |
| Destructive interference path difference: $(n+\frac{1}{2})\lambda$, $n=0,1,2...$ | Condition for destructive superposition of two coherent waves |
| Fixed string (both ends): $f_n = \frac{nv}{2L}$, $n=1,2,3...$ | Harmonic frequencies for standing waves on a fixed string |
| Closed tube (one open end): $f_n = \frac{nv}{4L}$, $n=1,3,5...$ | Harmonic frequencies for standing sound waves in a closed tube |

## What's next

Begin your study of this unit with the first sub-topic on simple harmonic motion, which builds the foundational oscillatory concepts you will need for all later wave topics. Work through the sub-topics in order, as each one depends on knowledge from the previous. Once you complete all topics in this unit, you will move on to the next unit on thermal physics.

- [Simple harmonic motion](https://www.owlsprep.com/study/ib-physics-sl-u3-simple-harmonic-motion/)
- [Wave characteristics](https://www.owlsprep.com/study/ib-physics-sl-u3-wave-characteristics/)
- [Wave interference](https://www.owlsprep.com/study/ib-physics-sl-u3-wave-interference/)

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From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/ib-physics-sl-u3-overview/