About Fourier: Making Waves
Add up sines or cosines to make waves of different shapes. Discover how changing the amplitudes of different harmonics changes the sound you hear. Play the Wave Game and combine harmonics to match a target waveform. Construct wave packets and explore the effects of changing the spacing between Fourier components and wave packet width.
How to play Fourier: Making Waves
Everything is hands-on: drag, click and experiment — the simulation reacts instantly. Add up sines or cosines to make waves of different shapes.
Questions & answers
- What is Fourier: Making Waves?
- Fourier: Making Waves is a free interactive simulation from PhET Interactive Simulations (University of Colorado Boulder) that you can play right in your browser on crumble.lol — no downloads and no sign-up. Add up sines or cosines to make waves of different shapes. Discover how changing the amplitudes of different harmonics changes the sound you hear.
- What can kids learn from Fourier: Making Waves?
- It helps kids explore: explain qualitatively how sines and cosines add up to produce arbitrary periodic functions. recognize that each fourier component corresponds to a sinusoidal wave with a different wavelength or period. describe sounds in terms of sinusoidal waves. compare and contrast waves in space and waves in time. recognize that wavelength and period do not correspond to specific points on the graph but indicate the length/time between two consecutive troughs, peaks, or any other corresponding points. relate the mathematical notation of a fourier series to its graphical representation and determine which aspect of the graph is described by each of the symbols in the equation. recognize that λ & t and k & ω are analogous, but not the same. translate an equation from summation notation to expanded notation. recognize that the width of a wave packet in position space is inversely related to the width of a wave packet in fourier space. explain how the heisenberg uncertainty principle results from the properties of waves. recognize that the spacing between fourier components is inversely related to the spacing between wave packets, and that a continuous distribution of fourier components leads to a single wave packet.
- What age is Fourier: Making Waves good for?
- It is designed for high school up to university, and curious kids outside that range can absolutely enjoy poking around it too.
- Is Fourier: Making Waves free to play?
- Yes — Fourier: Making Waves is completely free on crumble.lol and runs fully in your browser on computers and tablets.