A tube of length L filled with air supports a longitudinal standing wave: air molecules oscillate back and forth along the tube's axis instead of side to side. Each end forces a boundary condition on that motion — a closed end is rigid, so air can't move there (a displacement node, but a pressure antinode since molecules pile up against the wall); an open end lets air move freely, so it's a displacement antinode and a pressure node.
Those two conditions together only let certain wavelengths fit. A tube closed at both ends or open at both ends resonates at every harmonic: fn = n·c/(2L), n = 1, 2, 3, …. A tube closed at one end and open at the other only fits a quarter wave plus whole half-waves, so it resonates at odd harmonics only: fn = (2n−1)·c/(4L), n = 1, 2, 3, ….
The dots show air molecules bunching into compressions (bright) and thinning into rarefactions (dark) as they're pushed by whichever mode is nearest the driving frequency; the response curve below sums every mode the current tube supports, so its peaks mark the resonant frequencies for this length and end combination.
- Closed end — wall or piston; air velocity is forced to zero there.
- Open end — free to the atmosphere; pressure stays near ambient there.
This is the flat 2D companion to the 3D sound-wave-tube simulation: the same Kundt's-tube resonance physics, viewed as a single cross-section along the tube's axis.