2D rectangular cavity · standing wave modes · Chladni-like pressure patterns
A rectangular acoustic cavity of dimensions L_x × L_y supports standing wave resonance modes. The pressure field for mode (m,n) is:
p(x,y,t) = cos(mπx/Lx) · cos(nπy/Ly) · cos(2πf_mn·t)
with resonance frequency: f_mn = (c/2) √((m/Lx)² + (n/Ly)²)
These are the acoustic modes of a room, a musical instrument body, or any hard-walled cavity. The node lines (zero pressure) correspond to Chladni patterns — places where sand would accumulate if the cavity were vibrating. Mode (1,0) is the fundamental; higher modes create complex interference patterns.