Resonance tube
A tube with a speaker at one end and a movable piston at the other. Standing waves form only at resonant lengths where an integer number of half-wavelengths (open tube) or odd quarter-wavelengths (closed tube) fit. Particles pile up at pressure nodes — exactly what sand does in a real Kundt's tube.
August Kundt invented this apparatus in 1866 to measure the speed of sound in various gases. A speaker (or vibrating rod) generates sound waves that travel down a tube. If the tube length matches a resonant condition, standing waves form and particles of cork dust or lycopodium powder collect at the pressure nodes.
For a tube open at both ends, pressure is free to fluctuate at each end (pressure antinodes), and the resonant frequencies are fn = n · v / (2L) for n = 1, 2, 3, … — the full harmonic series.
For a tube closed at one end, the closed end is a displacement node (pressure antinode) and the open end is a displacement antinode (pressure node). Only odd harmonics resonate: fn = (2n−1) · v / (4L) for n = 1, 2, 3, …
The speed of sound depends on temperature according to v = 331.3√(1 + T/273.15) m/s, where T is in degrees Celsius. At 20°C, v ≈ 343 m/s. Higher temperature means higher speed, which shifts all resonant frequencies upward.
In the visualization, particles drift toward pressure nodes (where pressure oscillation is zero but displacement oscillation is maximum). The standing wave pattern is shown as both a displacement wave and a pressure wave, with their quarter-wavelength phase offset.