Three-Dimensional Acoustic Field Visualization in Microgravity: Eliminating Gravitational Bias from Cymatic Pattern Formation

On a vibrating plate, particles settle onto the plate and map its nodal lines. Inside a resonating volume of air or liquid, the sound field is three-dimensional, but under gravity a particle medium sinks or rises unless the acoustic force is large enough to hold it. Most cymatic experiments are therefore shaped by gravity, and the full three-dimensional particle patterns of a resonating volume have rarely been observed in an unbiased medium.

We propose a sealed-container experiment conducted under microgravity, initially via parabolic flight and subsequently aboard an orbital platform, to remove gravitational bias and observe the three-dimensional particle patterns of a resonating sphere. For a rigid spherical chamber driven by four transducers at tetrahedral vertices, standard acoustics predicts:

a single particle shell at the first radially symmetric resonance (ka = 4.493), at a radius that depends on the particle medium;
two and three nested shells at the next radial resonances (ka = 7.725 and 10.904), which are not harmonics of the first;
four, twelve and twenty-four particle clusters with tetrahedral and cubic symmetry near the shell mode and at the l = 3 and l = 4 resonances;
two-frequency patterns equal to the sum of the single-frequency patterns.
These predictions follow from standard acoustic theory and were checked against a numerical model of the chamber.

Version 1.1 (15 September 2026) corrects the premise that plate patterns are cross-sections of a three-dimensional field, replaces Predictions 1 to 4, and corrects the target frequency band, the particle media table, and the flight protocol. Version 1.0 placed the first shell at the fundamental frequency, put nested shells at harmonics, and predicted Platonic, toroidal, and quasicrystalline patterns. No experimental data existed for either version. Version 1.0 remains available unchanged. Model code: https://eequalsicsquared.com/cymatics-model.js