Many aspects of modern physics rely on an understanding of Fourier series, both for the synthesis and the analysis of waveforms.

 

• Daniel Russell of Penn State offers this set of animations showing the Fourier composition of some common waveforms

https://www.acs.psu.edu/drussell/Demos/Fourier/Fourier.html

 

• This simulator from PhET enables interactive construction of waves from components. It also offers a game mode for student activities.

https://phet.colorado.edu/en/simulation/legacy/fourier

 

• This simulator from Falstad pairs well with the Russell animations and the PhET simulator, as it is designed for analysis rather than synthesis – you can input a standard wave form and show the breakdown of it into sine and cosine components. This simulator also allows filters to be applied.

http://www.falstad.com/fourier/