A simple theory of Rijke tube oscillation

A simple theory of Rijke tube oscillation is preseated based on mathematical re- alization of Rayleigh’s qualitative explanation of the mechanism of Rijke tube. This is done by assuming a single point of high temperature in an otherwise uniform tube and the sound source produced when cold air flows passing this point. The wave equation thus obtained is then rigorously solved. It is found that the Rijke tube oscillation is a feedback system. There is no feedback nor oscillation when the hot spot is at a node or antinode in the tube. The mean flow is necessary for the oscillation, the particle velocity of which is proportional to the mean velocity, and the ratio is proportional to the gauze temperature when the later is low and the feedback does not affect much the magnitude of the particle velocity When the temperature is high, the feedback increases rapidly and the particle velocity might grow to several or even tens of time of the mean velocity and almost indefinitely when the heaer temperature is high enough. Otherwise the growth is rather slow, when the mean flow or high temperature is first applied. The oscillations stop immediately when the mean flow is stopped. If the mean flow is controlled by a valve or a paddle at one end of the tube, an interesting sound is produced.