← Labs
2D Wave Equation Explorer
u_tt = c²∇²u — click to excite, watch normal modes and Chladni patterns
Membrane — click to excite
Wave speed c:
1.0
Damping:
0.002
Domain:
Square
Circular
Mode excite:
m=1,n=1
m=1,n=2
m=2,n=2
m=2,n=3
Clear
Chladni Pattern (nodal lines)
Mode (m,n):
1,1
1,2
2,1
2,2
2,3
1,3
Chladni patterns: sand accumulates at nodal lines (zero displacement). Normal mode ψ_{mn}(x,y) = sin(mπx/L)·sin(nπy/L). Frequency ω_{mn} = cπ√(m²+n²)/L.
Frequency Spectrum
ω₁₁ = cπ√2/L | ω₁₂ = cπ√5/L | ω₂₂ = cπ√8/L