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it's slightly less wrong, as far as i can see - http://www.acooke.org/cute/HyperloopW0.html

I read your post, but I don't understand why the first link can't work. Is there a problem with a wave propagating along the tube with essentially infinite envelope? Here's a nice animation:

http://www.acoustics.org/press/151st/WaveVectorDemosmall.gif

In other words: decompose the standing wave into its forward and backward components and just keep the forward one. This is not the same thing as the air having a net velocity, so you don't bleed all your energy into friction with the walls. (You'll still lose some energy as the sound wave is naturally damped by friction due to the residual motion of the air molecules, but this might not be a large effect.)

you may be right; perhaps i have only remembered solutions with boundary conditions that would not allow such a solution. i will try to think things through again and perhaps do the maths. thanks.

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