1. Introduction

Oscillating and wave behaviour are some of the most common ways in which energy is transferred in nature, whether it is the light waves that our eyes have evolved to see or the water waves that batter our coastlines, these all have one fundamental, universal concept at their foundation, waves and wave-like phenomena.

To start off we need to look at oscillations and how to characterise this mathematically, which really starts off as a discussion of ordinary differential equations (ODEs)

We will look at both longitundinal and transverse waves, outlining how we can derive a wave equation to model their behaviour and finding that, through anonalogy, they follow the same wave equation, which is a simple example of a partial differential equation (PDE) - you will find many more emerge in Physics!

Waves are one way to trasmit energy, however the amount of energy that a wave can carry is something that we can carefully work out, along with the power of this energy transmission.