YOUR SOUND.
MADE VISIBLE.

A magnified, circular water well in a rigid surface: 6 mm across and 1 mm deep. Water at approximately 20°C: density 998 kg/m³, surface tension 0.0728 N/m, kinematic viscosity 1.004 × 10⁻⁶ m²/s; gravity 9.81 m/s². The idealized wall and bottom are impermeable. The contact line moves freely with a 90° contact angle and zero radial surface slope.

We use linear, small-amplitude capillary–gravity modes: Jₘ(αr/R) cos[m(θ−θ₀)], with J′ₘ(α) = 0 and k = α/R. Their natural frequencies satisfy ω² = (gk + γk³/ρ) tanh(kh). The complex response sums 70 modes: angular orders 0–9 and seven nonzero radial roots each. The uniform mode is excluded to conserve water volume.

Your measured pitch drives an idealized harmonic point-pressure force at 0.39 of the radius and angle 0.35 radians. Modal decay is approximated by β = 2νk² + 0.012ωₙ; response denominators are ωₙ² − ω² + 2iβω. This damping is not calibrated to a real vessel. The model omits detailed wall losses, nonlinear waves, splashes, and vertically driven Faraday instabilities. It does not simulate how your voice would transmit force into a real pool.

The water is magnified, its response normalized, and visible slopes enhanced. Fine lines trace equal-response levels at 10%, 24%, and 46% of the peak displacement amplitude; they are explanatory contours, not permanent nodes or light emitted by water. Broad lighting makes the full response visible, including at lower pitches. Motion plays in illustrative slow motion (approximately 0.27 cycles per second during input and 0.09 while idle) so the ripples can be seen; the actual detected frequency still determines the spatial response. Reflections, shadows, and edge highlights are artistic lighting, not measured optical effects. Transitions blend steady-state responses; this is not a transient fluid solver or a validated laboratory simulation. Finite mode and rendering resolution limit precision.

Before microphone use, the idle field uses a fixed 220 Hz demonstration input. While listening, silence or an uncertain pitch gently returns the field toward the demonstration response. Stop Microphone releases access and holds the last pattern. Sing a steady note to drive the model again. No microphone data is used until you activate it. Your audio is never uploaded or stored.

Water-wave dispersion · MIT
Contact-line and damping assumptions · Bongarzone & Gallaire
YIN pitch estimator · de Cheveigné & Kawahara