Fourier: Making Waves
Drag harmonic amplitudes and watch sine waves add up to square, sawtooth and triangle waves.
Drag the bars to set how much of each sine wave (harmonic) to add. Watch the waves combine into new shapes, or pick a preset like a square wave.
About the Fourier: Making Waves
Free fourier: making waves. Drag harmonic amplitudes and watch sine waves add up to square, sawtooth and triangle waves. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for physics, the fourier: making waves runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Drag harmonic amplitudes and watch sine waves add up to square, sawtooth and triangle waves. Use it to explore physics ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Fourier: Making Waves
- Use the controls to change Preset, Number of harmonics. The simulation reacts instantly.
- Pick an option such as Sine, Square, Sawtooth, Triangle to switch modes or load an example.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Press Square and add harmonics one by one.
- Try a sawtooth.
- Drag your own harmonics.
Key ideas you can learn
- Any repeating wave is a sum of sine waves.
- Higher harmonics have shorter wavelengths.
- A square wave needs many odd harmonics.
- More harmonics make a sharper shape.
Where this is used in the real world
Music synthesizers, MP3 compression, image processing and radio all use Fourier ideas.
Who is this simulation for?
Physics students in middle school, high school and first-year university, teachers who want a quick demonstration for the projector, and anyone revising for exams. It works well for flipped classrooms because students can explore before the lesson.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
What is a Fourier series?
A way to write a repeating function as the sum of sine and cosine waves of different frequencies.
Why does a square wave have overshoot?
Adding a finite number of harmonics causes ripples at sharp edges (the Gibbs phenomenon).
Is the Fourier: Making Waves free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Fourier: Making Waves work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.