Explore the Fourier: Making Waves
Drag harmonic amplitudes and watch sine waves add up to square, sawtooth and triangle waves. Free, no signup, runs in your browser.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
See it in action
The Fourier: Making Waves with sample data entered and the result showing.
What is the Fourier: Making Waves?
Drag harmonic amplitudes and watch sine waves add up to square, sawtooth and triangle waves. It runs in your browser, so a change to a setting or a drag on an object shows up at once.
Music synthesizers, MP3 compression, image processing and radio all use Fourier ideas.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
Any repeating wave is a sum of sine waves.
Higher harmonics have shorter wavelengths.
A square wave needs many odd harmonics.
Press Square and add harmonics one by one.
Try a sawtooth.
Drag your own harmonics.
Used for
Pick one to see how it fits.
Physics learners
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.
Try it freeTeachers
For teachers: project the Fourier: Making Waves on the board, let students predict the result, then run it together and test this: Try a sawtooth. For students: change one thing at a time and write down what changes.
Try it freeHow it compares
A plain look at this tool next to the usual alternative.
| This simulation | Textbook diagram | |
|---|---|---|
| Interactive | Drag, tap and change settings | Fixed picture |
| Install | Nothing to install | Not needed |
| Cost | Free to use | Depends on the book |
Questions people ask
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. The Fourier: Making Waves is free, needs no signup or download and runs in your web browser. It is part of the Physics group of AZRS simulations.
Does the Fourier: Making Waves work on a phone or tablet?
Yes. The Fourier: Making Waves takes touch input as well as mouse input, so you can use its 2 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.
How do I use the Fourier: Making Waves?
1. In the Fourier: Making Waves, use the controls to change Preset, Number of harmonics. The simulation reacts instantly. 2. In the Fourier: Making Waves, pick an option such as Sine, Square, Sawtooth, Triangle to switch modes or load an example. 3. Start with this experiment: Press Square and add harmonics one by one. Drag any glowing handle, object or slider with your mouse or finger and the Fourier: Making Waves responds in real time. 4. Change one setting at a time and watch which readout moves, then compare it with this idea: Any repeating wave is a sum of sine waves.
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Try the Fourier: Making Waves now
Drag harmonic amplitudes and watch sine waves add up to square, sawtooth and triangle. Free to use.
Try it free