Rijka

Rijka breathes fire into a glowing pipe, and it roars back a single pure tone.

The Physics

In 1859 P. L. Rijke put a hot metal gauze inside a vertical tube open at both ends and heard it sing loudly. The sound stops when the tube is laid horizontal and the upward air flow stops. Rayleigh gave the reason in 1878: an acoustic oscillation grows if heat is added where and when the pressure is high.

In an open–open tube the fundamental has a pressure node at each end. The drive is strongest with the gauze about a quarter of the way up from the bottom; a gauze in the upper half damps the sound instead. The same feedback causes dangerous combustion instability in rocket engines and gas turbines.

f ≈ c / 2L (loudest with the gauze at about L/4 from the bottom)

• f: tone frequency (Hz)
• c: speed of sound in the warm air (m/s)
• L: tube length (m)

Rijke, Ann. Phys. 183, 339 (1859); Rayleigh, “The explanation of certain acoustical phenomena”, Nature 18, 319 (1878).

Honest caveat: c is the warm-gas value, so the pitch depends on how hot the air is. Rijke used a hot gauze, not a flame; flame versions are variants.

On the shirt

Front: Rijka, the pixel-art character, with “SINGING HEAT”. Back: the Rijke tube, Rayleigh's criterion, the L/4 sweet spot, the tone formula and the 1859 and 1878 sources. Printed on a unisex tee.