Sound-driven liquid lens

This is a reduced-order visual approximation, not a calibrated reconstruction of Apple’s physical rig. It uses 24 rectangular-tank cosine modes selected around the drive frequency, plus low modes. Changing frequency selects a new basis and restarts the experiment. The forcing is a localized harmonic wavemaker, not a full model of vertically shaken Faraday waves.

Assumed tank: 0.24 × 0.16 m; depth 0.008 m. Illustrative oil-like constants: density 850 kg/m³, surface tension 0.03 N/m, kinematic viscosity 15 × 10⁻⁶ m²/s. Each mode follows q″ + 2βq′ + ω²q = ΓF cos(Ωt), with ω² = (gk + σk³/ρ)tanh(kd). Damping combines approximate viscous loss with empirical wall loss. Oscillators use an exact harmonic propagation step. Actuator gain is author-calibrated for small waves.

The renderer calculates surface normals from the mode gradients and refracts rays onto a flat wordmark plane using illustrative refractive indices 1.466, 1.470, and 1.474. Optical displacement is exaggerated 20×; softbox lighting and the chosen color dispersion are art direction. Acrylic geometry, glass interfaces, contact-line dynamics, nonlinear waves, and calibrated caustics are omitted. Playback is slowed to 0.15× and has no audio output.

Production path: use the same fluid parameters in a larger modal or free-surface solver; import a beveled transparent logo; path-trace refraction, reflections and caustics; render a high-frame-rate master for slow-motion playback. Use a compact GPU surface model for interaction and a pre-rendered fallback for low-power devices.

Sources: Apple Music’s official film · MIT surface-wave derivation · Physically Based Rendering: refraction and reflection.