Onset and Mode Selection of Faraday Waves
A University of Groningen lab project on subharmonic response, onset acceleration, and spatial mode selection in glycerol-water mixtures.
Context
This investigation began as a first-year University of Groningen Physics Lab research project by Leonardo Miranda, Sam Bakker, Tsjeard Bron, and Mihnea Marcu, advised by Toms Ozoliņš. Our work was selected for presentation at the 2026 PAM Symposium as the best Physics research project.
Faraday waves appear when a liquid bath is driven vertically: above a critical acceleration, the flat surface gives way to standing patterns. The experiment gave us a compact way to test ideas about parametric resonance, dissipation, and the spatial modes allowed by a finite rectangular bath.
What we wanted to know
- Would the observed motion contain the harmonic and, especially, subharmonic frequencies predicted for parametrically forced waves?
- How would the onset acceleration change with driving frequency and the viscosity of glycerol-water mixtures?
- Would the reconstructed spatial patterns follow the gravity-capillary dispersion relation and the rectangular modes allowed by the bath?
How we investigated it
We mounted a glycerol-water bath on a mechanical wave driver, measured its vertical acceleration, and filmed a submerged one-millimetre dot grid from above. Refraction through the moving surface displaced the apparent dot positions. A custom Python pipeline tracked those displacements, projected them onto temporal frequencies, supported manual review of wave onset, and used free-surface synthetic schlieren to reconstruct signed surface height.
The work was collaborative. Sam developed the theoretical background and numerical instability model; Tsjeard connected theory and results and built the fluid-property tools; Mihnea developed most of the physical setup and methods as well as the Blender model; and I developed and published the analysis toolkit. Toms advised the project.
What we found
Across the tested mixtures, the strongest spectral bands occurred at half-integer multiples of the driving frequency. The subharmonic response was particularly clear, as expected for Faraday waves. The spatial results were similarly strong: reconstructed wavenumbers followed the dispersion relation and closely matched allowed rectangular modes. A fit of measured against expected wavenumber had slope 1.050 ± 0.020.
Maps of power at half the driving frequency exposed the nodes of the standing waves and complemented the signed height maps: one says where the repeated response is strongest, while the other preserves whether the surface is above or below its mean level.
The onset result was less conclusive. Measured onset acceleration generally increased with viscosity and driving frequency, but it was systematically overestimated, so exact agreement with theory could not be established. The apparatus was sensitive to tilt, camera pose, glare, delayed stabilization, and small changes between mixtures. The global-motion correction could also remove part of the real wave signal. We therefore treated every onset choice as a human-reviewed estimate rather than the output of an automatic detector.
What the experiment produced
Alongside the report, the project produced an open-source Python toolkit for frequency analysis, manual onset review, ray-traced surface reconstruction, spatial mode extraction, and reproducible publication figures. The complementary Project case study follows the mathematics and implementation from moving dots to spectra and signed height maps; the report contains the full scientific account.