IB Physics HL topic guide

Wave Behaviour

Wave Behaviour is a core part of IB Physics HL. This guide connects the syllabus ideas behind SHM Equations and Systems, Energy and Damping in SHM, Wave Properties, Superposition and Interference, Refraction and Total Internal Reflection and 6 more units, shows how they appear in worked problems, and points you to the formulas and full lessons needed for exam revision.

What you will learn

Wave Behaviour syllabus outline

The units below follow the structure used in the full Study to Learn course. Use the outline to identify exactly which idea needs attention, then work through the public example before continuing to the complete lesson path.

C.1

SHM Equations and Systems

SHM Definitions and Equations · Simple Pendulum and Mass-Spring System · Phase and Graphical Analysis of SHM

C.2

Energy and Damping in SHM

Energy in SHM · Damping and Resonance

C.3

Wave Properties

Properties of Waves · Polarisation and Electromagnetic Waves

C.4

Superposition and Interference

Superposition and Interference Principles · Young's Double Slit Experiment

C.5

Refraction and Total Internal Reflection

Refraction and Snell's Law · Total Internal Reflection and Applications

C.6

Single-Slit Diffraction

Diffraction and Huygens' Principle · Single-Slit Diffraction Pattern

C.7

Two-Source Interference

Two-Source Interference and Path Difference · Diffraction Gratings

C.8

Formation of Standing Waves

Formation of Standing Waves · Open and Closed Pipes

C.9

Standing Waves vs Travelling Waves

Standing Waves vs Travelling Waves · The Resonance Tube Experiment

C.10

Doppler Effect for Sound

The Doppler Effect · Doppler Effect Applications

C.11

Doppler Effect for Light and Cosmological Redshift

Doppler Effect for Light · Hubble's Law and Cosmological Redshift

Free worked preview

SHM Definitions and Equations

This complete preview comes from the SHM Equations and Systems unit. It introduces the core language, shows the method in context, and gives you a real example of the lesson quality before you create an account.

Simple Harmonic Motion

Oscillations are everywhere — from the quartz crystal in your watch to the suspension of a car — and the simplest, purest form is SHM, defined by a restoring force proportional to displacement and always directed toward equilibrium. This lesson supplies the mathematical description you will reuse for mechanical waves, alternating current, and quantum harmonic oscillators. By the end you will be able to identify SHM by its defining equation

a = -\omega^2 x

, calculate period and angular frequency, and write the displacement function in either sine or cosine form depending on the initial conditions.

An oscillation is simple harmonic if the restoring force (and hence acceleration) is:

Directed towards the equilibrium position
Proportional to the displacement from equilibrium

a = -\omega^2 x

where

a

acceleration at displacement x (m s⁻²) — always negative when x is positive, meaning it always points back toward equilibrium

\omega

angular frequency (rad s⁻¹) = 2πf — determined by the system's restoring force, not how far you displace it

x

displacement from the equilibrium position (m) — positive in one direction, negative in the other

The minus sign is crucial — it shows the restoring force always opposes displacement. Solutions: $x = A\cos(\omega t + \phi_0)$ or $x = A\sin(\omega t)$

Use cosine if the oscillator starts at maximum displacement (x = A at t = 0); use sine if it starts at equilibrium (x = 0 at t = 0).

Quantity	Symbol	Expression	Unit
Angular frequency	ω	$\omega = 2\pi f = 2\pi/T$	rad s⁻¹
Period	T	$T = 1/f = 2\pi/\omega$	s
Amplitude	A	Maximum displacement	m

Velocity and Acceleration in SHM

v = -A\omega\sin(\omega t) \qquad a = -A\omega^2\cos(\omega t)

where

v

velocity at time t (m s⁻¹) — maximum at equilibrium, zero at extremes

a

acceleration at time t (m s⁻²) — maximum at extremes, zero at equilibrium

A

amplitude — maximum displacement (m)

\omega

angular frequency (rad s⁻¹)

Maximum values: $v_{max} = A\omega$ at equilibrium (x = 0); $a_{max} = A\omega^2$ at the extremes (x = ±A).

Speed at any displacement x (without needing time): $v = \omega\sqrt{A^2 - x^2}$

Worked Example — SHM Quantities A particle oscillates in SHM with amplitude A = 0.12 m and frequency f = 4.0 Hz. Find its maximum speed, maximum acceleration, and its speed when x = 0.06 m.

ω = 2πf = 2π × 4.0 = 25.1 rad s⁻¹
v_max = Aω = 0.12 × 25.1 = 3.02 m s⁻¹
a_max = Aω² = 0.12 × 25.1² = 75.8 m s⁻²
At x = 0.06 m: v = ω√(A²−x²) = 25.1 × √(0.0144 − 0.0036) = 25.1 × 0.104 = 2.61 m s⁻¹

Reviewed by the Study to Learn editorial team · Updated 2026-07-24