Exciting resonant modes in a circle with five out of phase sources @NilsBerglund

Nils Berglund | Exciting resonant modes in a circle with five out of phase sources @NilsBerglund | Uploaded September 2024 | Updated October 2024, 1 hour ago.
Like several previous videos on this channel , this one shows waves in a circular cavity excited by pulsing sources in other, connected cavities. In this case, there are five sources, and unlike in previous simulations, the five sources are pulsing a fifth of a period out of phase. Some commenters suggested trying this, in the hope that it might lead to spiraling waves. This is not quite the case, but the resulting interference patterns are interesting nonetheless.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:32
In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, slightly averaged over a sliding time window.

Render time: 15 minutes 30 seconds
Compression: crf 23
Color scheme: Part 1 - Cividis by Jamie R. Nuñez, Christopher R. Anderton, Ryan S. Renslow
journals.plos.org/plosone/article?id=10.1371/journal.pone.0199239
Part 2 - Twilight by Bastian Bechtold
github.com/bastibe/twilight

Music: "Doorway" by Slenderbeats@slenderbodies

See also
https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ for more explanations (in French) on a few previous simulations of wave equations.

The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!

#wave #resonator

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