Figures
Sixteen ways a plate can be still
Classic square figures by their mode numbers, three point-driven resonances of the reference plate, and three free-disc modes.
Swap the sand for light powder: it creeps to the antinodes and draws each figure’s negative.
Square · eigenmode
(1, 2) −
The lowest mismatched pair. Sand holds the diagonals and clears the corners.
211 Hz on the reference plate
Square · eigenmode
(1, 3) +
The plus sign keeps both diagonals as mirrors. A cross through the centre, with arcs closing off the corners.
422 Hz on the reference plate
Square · eigenmode
(2, 3) −
Two half-waves against three. The figure leans, then locks onto the diagonal.
548 Hz on the reference plate
Square · eigenmode
(2, 4) −
An even pair. Nested cells with a diagonal seam cutting through them.
843 Hz on the reference plate
Square · eigenmode
(1, 4) −
The widest mismatch at low order. Long nodal bands bow toward the free edges.
717 Hz on the reference plate
Square · eigenmode
(3, 5) −
A denser lattice. Ridges of sand narrow as the wavenumber climbs.
1,433 Hz on the reference plate
Square · eigenmode
(2, 5) +
Plus sign, mirrored diagonals. Broad cells alternate across the full width.
1,223 Hz on the reference plate
Square · eigenmode
(4, 6) −
High order, tight grid. The grains take noticeably longer to settle.
2,192 Hz on the reference plate
Square · eigenmode
(3, 6) −
Three against six. The doubled ratio reads as stripes crossed by a diagonal.
1,897 Hz on the reference plate
Square · eigenmode
(5, 7) −
The finest square figure here. The lines crowd so closely that the sand needs a slow, steady settle to keep them apart.
3,120 Hz on the reference plate
Square · point-driven
242 Hz
The first modelled centre-driven resonance of the reference plate. Several modes share the sum.
242 Hz on the reference plate
Square · point-driven
523 Hz
Second resonance. One mode dominates the sum and the lines go sharp.
523 Hz on the reference plate
Square · point-driven
744 Hz
Third resonance, crowded by its neighbours. Small drive shifts change the figure.
744 Hz on the reference plate
Disc · eigenmode
2 diameters · 0 circles
Two nodal diameters, no circles. The simplest figure a free disc will hold.
90 Hz on the reference plate
Disc · eigenmode
0 diameters · 1 circle
One nodal circle at 0.68 of the radius, no diameters. A single still ring inside a moving disc.
155 Hz on the reference plate
Disc · eigenmode
3 diameters · 1 circle
Three diameters and one circle. Chladni’s law scores it (3 + 2)² = 25 against 4 for two bare diameters; the exact ratio is nearer ten — the law is a guide, not a table.
904 Hz on the reference plate
