# The Flaming Oscilloscope: The Physics of Rubens’ Flame Tube

The flame tube, first described in 1905 by Heinrich Rubens and Otto Krigar-Menzel as a novel acoustics teaching apparatus, is a mesmerizing thing to behold. It is at once an early analogue to the oscilloscope, illustrating the nature of sound waves, and an alluring manipulation of fire that appeals to the pyromaniac in all of us.

I had a chance to play with a flame tube over the holidays and had great fun blasting Wagner down the length of the tube and watching the row of flames dance in unison. But more than a cool background to music, the flame tube also highlights some simple physics of waves in a pipe.

The typical setup is a long, metal pipe drilled along its length with a row of small holes. One end of the pipe is closed except for an attachment to a propane gas tank and the other end is filled with a speaker. You can probably guess what happens next.

The pipe is filled with propane and the holes are lit on fire, creating a row of individual golden flames down the length of the pipe. The magic happens when the sound is turned up, created either from a function generator at a single pitch (frequency) or from a song.

 Flame tube diagram. Credit: Image courtesy of Klaus Seiersen / Fysikbasen.dk
Initially I tried singing into a microphone to find a resonance frequency, but the function generator turned out to be much more accurate and easier on the ears. Even better was watching the flames jump in time to Wagner’s “Ride of the Valkyries”. Fire seemed a fitting medium to the song.

This film, created by Jeff Ryan at the University of Portland, shows a flame tube dancing to music by Journey, Beethoven, and the Phantom of the Opera. Look out for the resonant notes which cause distinct wave patterns along the tube.

#### Standing Waves in a Pipe

Sound travels by compressing air in a moving longitudinal pressure wave. To demonstrate this visually, few setups are more memorable than Rubens and Krigar-Menzel’s flame tube. Traveling pressure waves in the tube combine to form standing waves at certain resonant frequencies, determined by the length of the tube.

 Standing wave. Credit: Public domain
 Flames following the acoustic standing waves in a pipe.

The gas inside the flame tube follows the pressure wave and leaks out of the holes in a wave pattern. Therefore the flames also appear wave-like, depending on which holes are leaking the most gas.

The same tube can hold a range of different standing waves, each with an integer number of wavelengths. The more wavelengths fit inside the tube (i.e. the shorter the wavelength), the higher the frequency, by this equation

where c is the speed of sound in the gas, λ is the wavelength, and f is the frequency (or pitch) of the sound wave.

Therefore the speed of sound in propane can be measured simply by measuring the wavelength of the flames with a ruler and recording the frequency of the function generator.

 Measuring the wavelength of a standing wave. Function generator frequency: 830 Hz. Wavelength: 40 cm.

For a particular pitch at 830 Hz in the flame tube, I measured a wavelength of 40 cm, and therefore a speed of sound of 332 meters per second. For comparison, the speed of sound in air is about 340 m/s at room temperature, and the text book value of the speed of sound in propane is 258 m/s. So my rough measurement is reasonable, given the basic setup and unknown variables like air temperature.

Of course, real experimental setups are rarely neat, and studies have shown that flame tubes at low frequencies give very different speeds of sound than at higher frequencies, perhaps due to low frequency limitations of the speaker. A mixture of gases or changes in temperature within the tube can also cause the speed of sound to differ from the textbook value.

Today, Rubens’ flame tube is mostly used as an enticing physics demonstration in classrooms, and rarely as a scientific instrument (modern equipment like the oscilloscope are more accurate and certainly easier to set up). But for sheer visual impact, it’s a hard one to beat.

A recent music video featured the flame tube and other acoustic demos to create an impressive combination of art and science.

By Tamela Maciel, also known as “pendulum”