John Stuart Reid proposes that sound is not actually a wave, as has been thought for centuries, but a “bubble” and that this is what creates the amazing patterns we see captured with cymatics.
In his article, The Physics of Sound, Reid says that sound has previously been thought to travel as a wave because of the graphical, wave-based representation we have used to capture sound visibly in the past…

“The graphical representation of sound ‘waves’ in the past is why the term ’sound waves’ is used, causing the false impression that sound travels as a wave.”

…but that cymatics allows us to realize that the true form of sound is actually spherical, or bubble-like, in nature.

Journal of Cymatics: Cymatics Scientist Says Sound is a Bubble, Not a Wave

(Thanks Wes!)