A flat rectangular chamber of width Lx and depth Lz supports standing sound waves whose pressure pattern must fit the walls exactly. Only certain frequencies do this — the room's modes — given by f(nx,nz) = (c/2)·√((nx/Lx)² + (nz/Lz)²), where c ≈ 343 m/s is the speed of sound and nx, nz are non-negative integers (not both zero).
The heatmap shows the pressure pattern cos(nxπx/Lx)·cos(nzπz/Lz) of whichever mode is closest to the current driving frequency, brightened when the source frequency actually excites it. The response curve below sums a narrow bell curve around every mode's frequency, so the peaks mark exactly which drive frequencies make the chamber "boom" — the same room-mode math that makes small rooms and studios sound uneven at bass frequencies.
- Axial mode — pressure varies along one axis only (nx=0 or nz=0).
- Oblique mode — pressure varies along both axes at once.
This is the flat 2D companion to the 3D acoustic-resonance-chamber simulation: the same room-mode physics, reduced from a 3D box to one horizontal cross-section so the whole standing-wave field is visible at a glance.