The Clink: Acoustic Resonance of a Toast Glass (2D)

Glass Geometry

Wall thickness 1.5 mm

Bowl radius 3.5 cm

Glass height 9.0 cm

Liquid fill level 20%

Material

Live Readouts

Fundamental f₀

— Hz

Note (approx.)

—

Stiffness/density √(E/ρ)

— m/s

Decay Q (ring length)

—

How it works

This 2D edition shows the same real thin-shell resonance from two flat views instead of a 3D shell: a side cross-section of the glass's wall profile and liquid level, and a top-down ring that traces the fundamental "elliptical breathing" mode shape directly — the rim's radius plotted against angle, the way an engineer would sketch mode (n=2) of a vibrating shell.

f₀  ≈  K · (thickness / radius²) · √(E / ρ)  /  (1 + β·height/radius)
then  f  =  f₀ / √(1 + liquid-mass-ratio)

Thicker walls and smaller radii raise the pitch; taller shells and more liquid lower it — the same scaling a real cylindrical shell follows, and the same trick behind tuning a wine glass with water. Lead crystal's lower stiffness/density ratio drops its pitch slightly versus ordinary glass, and its lower internal damping is why crystal glasses ring so much longer after a clink.

Clicking the glass excites the mode: the top-down ring visibly stretches into an ellipse and decays exponentially while a real oscillator pair (fundamental + first harmonic) plays through Web Audio at the computed frequency.

Glass wall / rim mode Liquid fill

click glass to clink · drag to pan · scroll to zoom