I had a student start a research project on Rijke tubes several years ago.
He quickly came across the Scientific American article that Leigh
mentioned and that was pretty much the end of the project. I don't recall
the details (and am willing to confess that I was weak on them even at the
time) but here's what I carried away:
Gravity causes convection and creates a physical distinction between
velocity in the upward and downward direction. The fundamental resonance
mode involves pressure variations and velocity variations of varying phase
and amplitude along the length of the tube. (Draw cycles of pressure
variation versus velocity variation at different positions to see this.)
The net power transfer from heat source to resonant mode in this
thermo-acoustic engine is determined by a product of the pressure
variations and velocity variations averaged over a cycle of the resonant
mode. This product is zero at the ends where there is no pressure
variation and also in the middle where there is no velocity variation. It
is maximized at the quarter length positions, but the phase relationship
at the upper position is opposite that at the lower position. The phase
relationship with the heat source at the lower position causes energy
input into (and thus growth of) the fundamental mode while the upper
position produces damping. Thus, the tube will work with the screen
anywhere in the lower half and it works best with the screen a quarter of
the way up from the bottom.
John
P.S. Lest anybody think that I think the above is an *adequate*
explanation, please know that I do not!
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A. John Mallinckrodt email: mallinckrodt@csupomona.edu
Professor of Physics voice: 909-869-4054
Cal Poly Pomona fax: 909-869-5090
Pomona, CA 91768 office: Building 8, Room 223
web: http://www.sci.csupomona.edu/~mallinckrodt/