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Comment by jasallen | Hacker News Reader

Relative to the frame of reference, it seems to me the sparse particles would be travelling closer to the speed of the craft than the dense particles.

The "density front" travels at exactly the speed of sound, but it consists of nearly static particles (not static from the frame of reference, from the frame of reference they are moving backward at nearly the speed of sound), these static particles are the relevant V.

The sparse particles just in front of the dense ones are accelerating to get more sparse. From the perspective of the reference frame, they are therefore moving 'backward' at slightly less than the speed of sound, making there relative velocity closer to that of the reference frame. So lower density and lower velocity. and that doesn't even account for additional compression which I don't even know enough to do armchair reasoning on.

So, I'm the farthest thing from an expert, but this is why it doesn't seem to make sense to me.

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Stare at this thing for a while:

http://www.acs.psu.edu/drussell/Demos/waves/Lwave-v8.gif

In all seriousness though I'm going through your post to see if you've found a gaping problem =). I don't think there can be different density velocity ratios at any point of displacement in the wave's reference frame because the same net number of particles has to pass through each point or you start making a permanent buildup on one side or the other of that point, which you can't do because in the reference frame of the still air that point is moving at the speed of sound.

A moving point passes by the same number of unique particles at the speed of sound as it would if it were going the speed of turtle (if you ignore thermal dispersion).

"the same net number of particles has to pass through each point"

Agreed: the corollary to the "the sparse particles just in front of the dense ones" is the "sparse ones just behind the next wave of dense ones", which are, in fact, decelerating, or moving backward even closer to the speed of sound than the dense ones relative to the reference frame. So individual particles oscillate back and forth, but net effect is no movement (to the reference frame of the average speed of the particles, which is a third reference frame :-) )

Surely that animation exaggerates how little net molecule displacement occurs. I'm not sure what would cause many of the molecules to reverse direction while in the low-pressure part of the wave.

The pressure (also density) maximum is the velocity maximum.

Shouldn't you put the front of the craft at the pressure minimum and the back of the craft at the pressure maximum? Then the wave would be pushing you along.

The wave won't push you along at the speed of sound; at any point on the wave from the wave's reference frame (the speed of sound) there is a net flow of particles heading the opposite direction, unless your amplitude gets so high that average particle velocity in some places starts to exceed the speed of sound, in which case you don't have a sound wave anymore I don't think.

I agree about the particles moving in the waves frame, but what you are talking about is drag, I think. The pressure gradient still produces a net force on the object. How big it is compared with other forces, such as drag, I have no idea.

If you are talking about the gradient I think you are, any effect it has it can minimized to nearly nonexistent by increasing the wavelength.

Wouldn't the velocity maximum be 90 degrees out of phase with respect to the density? (in steady-state standing-wave operation)

Actually you just explained his idea, no?

The difference between the dense particles just behind the craft with maximal drag and sparse particles just in front, means a pressure differential pushing the vehicle forward

No, that would be a mechanic to provide thrust, which is not what he was describing.

Sure, some thrust. The idea here is to find the sweet spot where enough thrust is provided to balance against the drag.. right?

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