Friday, June 24, 2016

more Chladni figures in R

Following on from an earlier post, the Chladni images here are made using a slightly modified version of the same R script (source here), which uses cosines instead of sines. If you imagine the square of the vibrating surface to be fixed at the center (as depicted below), using cosines seems the natural choice. When modeling standing waves, cosines are used to model open-ended pipes, while sines are used to model fixed-end strings.

Playing around with cosine-based formulas led to some images that seemed very close to Chadni's own diagrams, which can be found in an appendix to his book on Google books.

For a few of these I've uploaded the scripts that produced them.

Chladni image 40 b
Source here.

 Chladni image 41
Source here.

Chladni image 53
Source here.

Chladni image 58
Source here.

Chladni image 63
Source here.

And of course, many more are possible. Try a few yourself :)