The Ruben's Tube: Seeing Sound in a Line of Fire

What it is, and the demo that stops a lecture hall

A Ruben's tube (or standing-wave flame tube) is a rigid pipe — brass, copper or steel, typically 1–4 m long and 5–10 cm across — with a straight line of small holes (1–3 mm) drilled along the top at regular intervals. One end is capped by a loudspeaker or driven diaphragm; the other is fed flammable gas, usually propane or natural gas, through a fitting.

Run the demo in stages and the effect is theatrical:

• Gas only, no sound. Light the holes and you get a uniform row of small blue-orange flames, all the same height — the tube is simply a manifold at roughly constant pressure.
• Add a pure tone. Drive the speaker at a frequency whose half-wavelengths fit the tube, and the flames snap into a fixed pattern: tall plumes at regular positions, low flames between them, motionless as long as the tone holds.
• Sweep the frequency. As you raise the pitch the peaks bunch closer together; drop it and they spread apart. Hit a resonance and the pattern jumps to sharp, high contrast.

Feed in music instead of a pure tone and the whole line of fire dances — a crude but mesmerising real-time spectrum of the sound. What you are seeing is a longitudinal standing wave in the gas, made visible because the flame height tracks how much gas escapes each hole.

Standing waves: why the pattern stands still

The loudspeaker launches a sound wave down the gas column. The far end reflects it, and the returning wave superposes on the outgoing one. When the tube length L is a whole number of half-wavelengths, the two travelling waves lock into a standing wave — a pattern that oscillates in place but does not travel:

L = n·(λ/2),   n = 1, 2, 3 …

Because both ends are effectively closed (rigid cap / speaker face), each end is a displacement node and a pressure antinode. Between them the gas organises into fixed regions:

• Pressure antinodes — the pressure swings hardest here (high then low, once per cycle) but the gas itself barely moves back and forth. These sit at the ends and every λ/2 in from them.
• Pressure nodes — the pressure stays nearly constant, but the gas velocity is maximal; this is where the gas sloshes back and forth most violently. They lie a quarter-wavelength (λ/4) from each antinode.

The resonant frequencies follow directly from the wave-speed relation v = f·λ. With the speed of sound in propane around v ≈ 260 m/s (lower than air's 343 m/s because propane is heavier), a 2 m tube on its fundamental (n = 1, λ = 4 m) resonates near f = v/λ ≈ 65 Hz, and higher modes at integer multiples. The flames map out these fixed nodes and antinodes — that is why the fiery graph holds perfectly still.

The real mechanism: Bernoulli, not just "more pressure"

The tempting explanation is: high pressure pushes more gas out, so tall flames mark high-pressure points. That is wrong, and getting it right is what makes this demo a genuine physics puzzle.

The flame height is set by the time-averaged mass flow of gas leaking from each hole. Gas escaping a small orifice obeys a Bernoulli/Torricelli relation — the efflux speed depends on the square root of the pressure difference across the hole:

u ≈ √(2·Δp / ρ)  →   flow ∝ √Δp

Here ρ is the gas density and Δp is the (instantaneous) pressure inside minus atmospheric. Now the subtlety: the acoustic pressure oscillates, so we must average √(Δp) over a cycle. Because the square-root function is concave, the average of √(p₀ + p̃·cos ωt) is lower where the fluctuation amplitude p̃ is large. In the standard low-amplitude regime the outcome is:

• Pressure nodes (velocity antinodes) — pressure steady, the vigorous back-and-forth gas motion boosts net efflux → tall flames.
• Pressure antinodes — big pressure swings, but the concave √ average and the reduced mean throughput → short flames.

So, counter-intuitively, the flame peaks usually mark the pressure nodes / velocity antinodes. Crucially, the spacing between adjacent peaks is still exactly λ/2, so you read off the wavelength correctly regardless of which feature you're measuring. Rubens and Krigar-Menzel used exactly this to measure sound wavelengths in 1905.

The numbers: wavelengths, speeds and what you'll measure

The Ruben's tube is a real measuring instrument, and the arithmetic is friendly. Suppose you drive a 2 m tube filled with propane (v ≈ 260 m/s) at 500 Hz. The wavelength is λ = v/f = 260/500 ≈ 0.52 m, so adjacent flame peaks sit about λ/2 ≈ 26 cm apart, and you'd see roughly 7–8 peaks along the pipe. Push to 1000 Hz and the spacing halves to ~13 cm; the flames crowd together into a fine comb.

• Wavelength range. Over a usable audio band of ~50–1000 Hz in propane, λ runs from about 5 m down to 0.26 m — from "one broad hump" to "dozens of tight peaks."
• Gas matters. The speed of sound scales as √(γ·R·T/M). Heavier fuels (propane, M ≈ 44 g/mol) give a slower v and shorter λ than air; a tube run on hydrogen would show far coarser spacing.
• Drive power. A few watts of audio is plenty; the contrast comes from resonance, not brute loudness. On a well-tuned mode the peak-to-trough flame ratio is dramatic.
• Hole size and spacing. Rubens' original used ~100 holes of 2 mm along 4 m. Holes must be small compared to λ so each acts as a local pressure probe rather than venting the wave away.

Because you can measure λ with a ruler and know f from the generator, the tube yields the speed of sound in the fuel directly from v = f·λ — a legitimate lab result, not just a light show.

Step by step: how the fire draws the wave

Trace the chain of physics from the speaker cone to the flame tips:

• 1. Drive. A signal generator feeds a loudspeaker sealing one end; its cone pushes and pulls the gas column at frequency f.
• 2. Reflection. The sealed far end reflects the wave back along the tube.
• 3. Superposition. Outgoing and reflected waves add. At the right f, they form a standing wave with fixed pressure nodes and antinodes (constructive/destructive interference locked in space).
• 4. Local flow modulation. Each hole sees the local acoustic field. The time-averaged efflux — governed by the √(Δp) Bernoulli relation — varies smoothly along the tube.
• 5. Flame height. A hole passing more gas per second feeds a taller diffusion flame; one passing less burns short. The flame tips trace out the standing-wave envelope.
• 6. You measure. Ruler the distance between equivalent features; that's λ/2. Combine with f to get v.

The key insight: nothing about the flames travels. The standing wave is stationary, so the flame graph is stationary too — a frozen photograph of an oscillation happening thousands of times per second, held still by resonance.

History, uses and where you'll meet one

Heinrich Rubens (1865–1922) — better known to physicists for his far-infrared "residual ray" (Reststrahlen) measurements, whose blackbody data helped drive Max Planck to the quantum hypothesis in 1900 — built the flame tube with Otto Krigar-Menzel around 1905 to make acoustic wavelengths directly visible and measurable. It descended from Kundt's tube (1866), which used cork dust to reveal nodes, and it lives on today mainly as a spectacular teaching demonstration.

• Lecture halls and science museums. Its main modern role: a vivid intro to standing waves, normal modes and the difference between pressure and velocity in a sound wave.
• Music visualisation. Two-dimensional "pyro boards" — a grid of thousands of flames driven by loudspeakers — extend the idea into flickering, dancing surfaces synced to music, a staple of maker fairs and viral videos.
• Teaching the counter-intuitive. Precisely because the naïve "pressure = tall flame" story fails, it's a favourite for teaching careful reasoning about time-averages and Bernoulli flow.

It rarely appears as a metrology tool now — oscilloscopes and microphones do that job better — but as a way of feeling what a standing wave is, nothing beats a two-metre line of fire holding perfectly still.

Misconceptions, subtleties and safety

"Tall flames mark high pressure." The most common error. In the usual regime, tall flames mark pressure nodes (velocity antinodes), because time-averaged flow — via the concave √(Δp) law — peaks where the gas velocity, not the pressure, is greatest.

"The pattern always reads the same way." Not quite. At low static gas pressure or very high acoustic amplitude, the effect can reverse, with flame minima at the nodes. Detailed studies (e.g. Gee and colleagues) show the flame-height map depends on both drive level and mean flow. What never changes is the spacing: λ/2 between equivalent features.

"The flames are moving with the sound." They aren't. The standing wave is spatially fixed, so the envelope is fixed. Only when you feed complex, changing sound does the pattern visibly shift.

Safety is real, not decorative.

• You are burning flammable gas under mild pressure from a line of open flames — a job for a fume hood or well-ventilated space, never a closed room.
• Backfire and internal ignition are hazards; the tube must be robust and properly sealed, with a controlled fuel supply and shutoff.
• The metal gets hot; ignition should be careful and the whole apparatus purged and handled by people who know gas safety. This is a demonstration to admire, not a casual home build.

The Ruben's tube alongside other ways of making sound (and vibration) visible

Demonstration	What vibrates	What you see	Quantity read off
Ruben's tube	Gas column in a pipe	Row of flames, tall at velocity antinodes	Wavelength λ (ruler between peaks)
Kundt's tube (1866)	Air column in glass tube	Piles of cork dust / powder at nodes	λ from dust-pile spacing
Chladni plate	Metal plate surface	Sand collects on nodal lines	2-D modal (nodal) patterns
Standing wave on a string	Stretched string	Stationary loops (segments)	λ = 2L/n, harmonic number
Oscilloscope	Electrons in a beam	Waveform trace on a screen	Amplitude vs time