Origins of the Sine Wave

A comprehensive lecture on understanding sinusoids and deriving the wave equation for audio
Properties of sinusoids
Trigonometry and unit circles
Understanding sine waves


  • None


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.

Who this course is for:

  • Audio programmers
  • Music producers
  • Digital audio processing

Course content

1 section7 lectures40m total length
  • Introduction
  • Trigonometric Functions
  • Unit Circles
  • Degree vs Radian
  • Sine Function Over Time
  • Properties of Sinusoids
  • Understanding Sinusoidal Motion


Audio Programmer
Akash Murthy
  • 4.8 Instructor Rating
  • 36 Reviews
  • 427 Students
  • 2 Courses

I have been an audiophile for about half my life. I get interested in any aspect of audio, especially when related to audio technology, and I tend to dig deep till I get a working knowledge of a concept. I have a Master's degree in Creative Music Technology from Maynooth University, Ireland, and I write audio applications and plugins. Besides that, I've spent a fair few years producing music commercially, and as a musician, have released 2 studio albums.

I decided to teach here at Udemy to impart the knowledge that I know, to learn more myself and to comprehensively and illustratively draw out complicated concepts in audio technology and give you a simple yet powerful understanding of these concepts.

Please feel free to reach out to me for suggestions, tips, criticism and whatever else.