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Inverse Chladni patterns: New surprises in a classic experiment

Collaboration with the University of Twente, The Netherlands,
sponsored by a research grant from FOM: "Newton vs. Stokes: Competing forces in granular matter".

Inverse Chladni patterns, i.e., grains collecting at the anti-nodes (instead of at the nodes) of a resonating
horizontal plate, were traditionally believed to occur only for particles light enough to be carried along by
the air currents induced by the vibrating plate. Thus it comes as a surprise that there is yet a second mechanism
leading to inverse Chladni patterns: When the acceleration of the resonating plate remains below g, all grains
spontaneously roll towards the anti-nodes, irrespective of their size and even in the absence of air. See Publ. 80.

The new mechanism, illustrated in the pictures below, is a subtle one and has escaped detection for more than
two centuries in countless demonstrations of this classic high school experiment.



(a) Top view of a flexible plate resonating in its 2x2 mode at 50 Hz. The amplitude of the oscillation is 0.40 mm, meaning
that the maximum acceleration of the plate is 4g. After a few seconds the bouncing particles - originally distributed uniformly
over the plate - have collected at the nodal lines, forming a standard Chladni pattern.

(b) The same plate at the smaller amplitude of 0.09 mm (maximum acceleration 0.9 g). The particles no longer bounce, but
instead roll over the surface of the plate, and collectively migrate towards the anti-nodes. The process is slower than the
former one: it takes about a minute before the inverse Chladni pattern has formed.

The rightmost picture shows Ernst Chladni himself, around 1800, performing at the Palace of Thurn und Taxis in Regensburg.

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