Rubens' Tube Flame Pattern Calculator

Introduction: Rubens' Tube Standing-Wave Flames

A Rubens' tube makes an acoustic standing-wave pattern visible as a row of flames. The apparatus is a long perforated metal tube supplied with fuel and driven by sound; after the gas is ignited, changes in pressure along the tube alter the flames emerging from its holes. A steady tone can therefore produce a repeating high-and-low flame pattern. This calculator uses the tube length, tone frequency, and entered sound speed to estimate the wavelength, spacing, peak count, and a set of relative flame-height samples for that idealized pattern.

The Rubens' tube calculation begins with the sound wavelength $\lambda$. With excitation frequency $f$ and sound speed $v$, it uses $\lambda =\frac{v}{f}$. The calculator also reports the frequency associated with a half-wavelength across the entered tube length $L$: $L=\frac{\lambda }{2}$. It defines node spacing as $\frac{\lambda }{2}$ and estimates flame peaks with $\left(\lfloor \frac{2L}{\lambda }\rfloor +1\right)$. That last value is a count produced by the calculator’s half-wavelength rule, rather than a guarantee of the exact number of visible tall flames in a physical build.

For Rubens' tube planning, the wavelength is the key link between the selected tone and the scale of the pattern: increasing frequency shortens $\lambda$, while increasing the entered sound speed lengthens it. Real tubes can depart from this simple picture because of end conditions, gas flow, hole geometry, speaker coupling, and combustion. The results are most useful as a starting prediction to compare with a carefully controlled observation.

Rubens' Tube Nodes and Relative Flame Heights

For a Rubens' tube, this tool does more than return a wavelength: it samples a wave along the entered tube length at evenly spaced positions. At position $x$ measured from one end, its underlying signed wave sample is $P\left(x\right)=P_0\sin \left(\frac{2\pi x}{\lambda }\right)$. The displayed relative flame height is the absolute value of the corresponding sine sample, so every table value falls between zero and one. In other words, the output shows the magnitude of the modeled variation, not a measured flame height in centimetres.

That sampling method makes the Sample Points setting important for a Rubens' tube preview. More points add more locations to the output table and can make narrow changes in the modeled wave easier to inspect, but they do not alter wavelength, node spacing, fundamental frequency, or expected peak count. The table is particularly useful when comparing the model with the positions of the holes already drilled in a tube.

Rubens' Tube Demonstrations and Wave Learning

A Rubens' tube is widely used to turn an otherwise invisible sound field into a visual lesson about wavelength and resonance. Sweeping a tone source can change the spacing of the modeled pattern, while holding the tone steady provides a fixed arrangement to examine. The calculator expresses the same frequency–wavelength relationship in the rearranged form $f=\frac{v}{\lambda }$: for a chosen sound speed, higher frequencies correspond to shorter wavelengths and more closely spaced changes in the sampled pattern.

Any live Rubens' tube demonstration requires far more than the wave calculation. Fuel selection, gas regulation, leak testing, ignition procedures, ventilation, audience separation, fire control, and the construction of the tube and sound source all affect safety. This page does not model gas flow, combustion, sound pressure level, hole diameter, or the stability of flames. Use the output only to explore the idealized acoustic geometry, and follow applicable safety procedures and qualified supervision for any flame-based experiment.

How to use: Set Up a Rubens' Tube Pattern Estimate

To calculate a Rubens' tube pattern, enter the physical tube length in metres, the sound frequency in hertz, and the sound speed in metres per second. The calculator returns wavelength, the reported fundamental frequency $\frac{v}{2L}$, node spacing, and expected flame peaks. It then creates a position-by-position table using the requested number of sample points. Keep all three physical inputs in the units shown by the labels; mixing centimetres with metres or kilohertz with hertz will change the result substantially.

The following Rubens' tube table is consistent with the calculator’s sampling rule for a 1.2 m tube driven at 500 Hz with a sound speed of 343 m/s. Its wavelength is 0.686 m, and the listed heights are the rounded absolute sine samples at the five selected positions.

For this Rubens' tube setup, changing only the tone changes the wavelength and therefore shifts every sampled phase. Changing only the tube length leaves wavelength unchanged but changes the range of positions being sampled and the reported fundamental frequency. If a physical flame pattern does not resemble the idealized table, first verify the input units and tone frequency, then investigate the apparatus rather than treating the table as a combustion prediction.

Formula: Sound Speed and the Rubens' Tube Model

The Rubens' tube calculator accepts sound speed as an input, which lets the wavelength model be used with a speed appropriate to the conditions being considered. In an ideal-gas treatment, sound speed may be written as $v=\sqrt{\frac{\gamma RT}{M}}$, where $\gamma$ is the adiabatic index, $R$ is the gas constant, $T$ is absolute temperature, and $M$ is molar mass. The page does not calculate those quantities or infer a gas mixture; it simply uses the speed value supplied in the form.

For a Rubens' tube, the central model remains deliberately narrow: divide sound speed by frequency to find wavelength, halve that wavelength for node spacing, and evaluate equally spaced sine samples over the tube length. It is a useful way to reason about the geometry of a desired pattern before an experiment, artistic installation, or classroom discussion, but it cannot determine whether a particular speaker, tube, fuel system, or room will produce a clear pattern.

Worked example: checking a Rubens' Tube speed assumption

For a Rubens' tube comparison, enter a tube length and tone frequency, calculate the pattern, then change only Speed of Sound (m/s) and calculate again. A higher entered speed produces a longer wavelength and wider reported node spacing; comparing those outputs identifies how strongly that assumption affects the planned flame layout.

Rubens' Tube limitations and assumptions

This Rubens' tube calculator is an idealized standing-wave estimate, not a model of flame chemistry or a complete design review. Its output depends on correctly entered metres, hertz, metres per second, and sample count. Physical results can differ because the tube, holes, fuel delivery, acoustic driver, and boundary behavior are not represented, and the calculation is not a substitute for safe experimental procedures or expert assessment of a flame apparatus.