2D wave equation: ∂²u/∂t² = c²∇²u, solved by finite differences.
Normal modes: u_{mn}(x,y,t) = sin(mπx/L)·sin(nπy/L)·cos(ω_{mn}t), ω_{mn}=cπ√(m²+n²)/L.
Chladni figures: sand accumulates where displacement is zero (nodal lines). Mode buttons excite standing waves directly.