'Cymatics' is the science of visualizing audio frequencies.
When you play tones that match the resonant frequency of the tube, it forms high and low pressure zones of gas and this effects the height of the flame.
A metal tube filled with flammable gas, attached to a speaker. Different audio frequencies 409Hz, 490Hz and 564Hz form pressure waves in the gas, creating high and low flame shapes on top of the tube.
When you play a constant tone of, say 440 Hz (the musical note A), the flames will form a perfect sine wave.
Instructables | The Rubens' Tube: Soundwaves In Fire!
University of Minnesota | Trigonometry in Nature: Sinusoidal Waves as Sound