Mixing Sines

Harmonics and their amplitudes

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Harmonics $\sin nx$ (for whole numbers $n$) all repeat every $2\pi$.
• Adding harmonics with different amplitudes makes new periodic shapes.
• A Fourier series is such a sum, possibly with infinitely many terms.

Steps

1. Harmonics
2. Match the target
3. Harmonics of a string
4. Same period
5. Period of a mixture
6. Only harmonics