Standing Waves in an Air Column (2D)

This is the 2D-native counterpart to the 3D standing-wave string simulator. Instead of a transverse wave pinned at both ends of a string, it models a longitudinal sound wave resonating inside a pipe, where each end can independently be open (air free to move, a displacement antinode) or closed (air trapped, a displacement node). Switching between open–open, closed–closed and closed–open geometries changes which harmonics the pipe can sustain — every integer multiple for the first two, only odd multiples for a stopped pipe — and the mode-number, pipe-length and sound-speed sliders drive the exact quarter-wave and half-wave resonance formulas live, drawn as genuine 2D displacement and pressure envelopes with their nodes and antinodes marked, rather than a rendered 3D object.