A simple and straightforward setup, creating a wave visualization utilizing the principle of the Fourier-series. The number of circles (unit vectors), and the path they draw, is adjustable. Multiple versions of style (like a math visualization scheme) presented for render.

Video demo here, here, here, here, here and (MathVis example) here.

New version added to downloads, with vertical displacement example. 

The file is optimized for and rendered in Eevee (Render Viewport animation). Of course, you can set up any renderer you wish.

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NOTE

-(Since it is a concept demonstration, it is kept as simple as possible.) The GeoNodes trees are kept clean for easier readability and have detailed explanations. Everything is built from the base. The point of these setups is to provide a base core of the concept, node from node, instead of contracting all into node groups with exposed settings, which makes everything harder to read and dissect.

You can embellish, refine as you wish based on the core or realize your own ideas.

-Read the text description, it has a lot of useful info !

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Recommended blends -

The Wire

Kinetica

The Surface Voronizer