Discovered by Ernst Chladni (1787): sprinkle sand on a vibrating plate, and sand collects at nodal lines (where displacement = 0). For a square plate, modes are cos(mπx/L)cos(nπy/L) with frequency ∝ m²+n².
Each mode (m,n) of the square plate has displacement ψ(x,y) = cos(mπx)·cos(nπy). Nodal lines are where |ψ| < ε. Higher modes (larger m,n) create more complex patterns with higher frequencies: f_{mn} ∝ m²+n² for a square plate clamped at center.