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If I may take a guess… I bet the frequency is jumping around as you hit resonance with cetain wavelength in the tube. I would guess that the wave propagates up the tube as the mic takes a sample. The rest of the energy bounces back down the tube combining with the new wave coming out of the speaker… This new wave then bounces back up into the mic again. As you change the slide you change the time the wave bounces back and forth in the tube causing different mixing effects. It would be interesting to graph what frequency you have vs the distance of the slide.
Strube
The acoustic resonance could very well be part of it. The really interesting thing though, is that as you change the length of the tube, you’re changing both the acoustically resonant frequencies, as well as the length of time it takes a signal to travel from the speaker to the microphone. It’s also possible that the amplifier circuit has resonances in that frequency range (although I tried to design against that).
Taking all that into account gets pretty complex, and the whole thing is really a pretty neat physics problem.