Physics

Chladni figures

Sand collects along the nodal lines of a vibrating plate.

Actual application image

What happens

Explore prescribed analytic nodal patterns and watch model sand collect near their nodes. Square patterns combine cosine modes; circular patterns use Bessel membrane modes. Change the mode numbers, mix or morph patterns, and scatter the sand again. This is an illustration of nodal figures, not an elastic-plate eigenmode solver; grain motion is stochastic and does not resolve individual impacts.

Equations used in the module

Equations
w = cos(nπx/L) cos(mπy/L) ± cos(mπx/L) cos(nπy/L)
w = J_n(j_ns r/R) cos(nθ); J_n(j_ns) = 0
w = 0

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