2D Drum Modes

Circular drum: Bessel eigenmodes J_m(χ_{mn}r/R)cos(mθ), Chladni nodal patterns

(0,1)
Mode (m,n)
Frequency (rel)
0.0
Time
off
Superposition
Select mode (m,n) — angular, radial nodes
+
nodal (Chladni)
J_m(χ_{m,n} r/R)cos(mθ)cos(ωt). Zeros of J_m give nodal circles; azimuthal index m gives nodal diameters. Chladni patterns: sand collects at nodes. Superpose two modes to create complex beating patterns.