Origins of the Sine Wave

Sinusoids are among the fundamental building blocks of any analog or digital audio signal. A single sine wave is said to be the purest tone you can audibly achieve, and because of this, they are used extensively as control signals for testing equipment and applications and plugins. But why? Why are sinusoids fundamental? And how are they formed? What even are they in the natural world? We’ll address all of this and more in the course.

The course starts from humbling beginnings where it looks at the geometry of right angled triangles, and explore a beautiful relation between static shapes and periodic functions. It takes a look at unit circles and deconstruct them to find that at the heart of all circles are periodic functions which we call sinusoids. It looks at all the attributes and properties of sinusoids and what real world effects they have when these properties are changed, and in that process derive an equation for a generic sine wave. And finally the course explores why they are fundamental in nature by observing how sinusoidal behavior is baked into every day objects that we might take for granted.

You don’t need to have any prior knowledge for this course. Any mathematics that appears in the course is accompanied by many illustrations and animations to visually paint a picture of these concepts. If you are getting started with digital signal processing, audio programming or if you’re just enthusiastic about understanding audio at a deeper level, this is a course for you.