The Clink: Acoustic Resonance of a Toast Glass

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

A toast glass rings like a thin vibrating shell, not a plucked string. Its walls behave like a curved elastic plate: bending stiffness grows with the cube of wall thickness while mass grows only linearly with it, and stretching the same wall over a wider radius makes it floppier still. Thin-plate/shell vibration theory collapses this into one clean scaling law for the fundamental "elliptical breathing" mode (the same n=2 rim mode a wine glass sings in):

f₀  ≈  K · (thickness / radius²) · √(E / ρ)  /  (1 + β·height/radius)
E  = Young's modulus (stiffness)   ρ = density
K, β = mode-shape / shell-length constants

Thicker walls and smaller bowls raise the pitch; taller, floppier walls lower it, exactly as a real cylindrical shell's circumferential mode softens as it gets longer. Lead crystal has a lower E/ρ ratio than ordinary soda-lime glass, so it rings a shade lower — and its lead content damps internal friction less, giving crystal glasses their famously long, singing decay (higher Q) compared to the shorter "clank" of everyday glass.

Filling the glass loads the shell with extra vibrating mass without adding any stiffness — the wall still bends the same way, it just has more to move — so the frequency drops as f₀/√(1 + added-mass ratio). This is the real mechanism behind the classic "tune a wine glass by adding water" trick.

Clicking the glass excites this fundamental mode plus its first harmonic with an exponentially decaying envelope, rendered as a genuine elliptical deformation of the rim and played back through Web Audio at the computed frequency.

Glass shell (click to clink) Liquid fill

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

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