Longitudinal standing waves in gas

[Karol]

Homework Statement

In the uppermost drawing is a propagating wave. the distance between two successive high pressure areas, as seen in the picture, is the wavelength [itex]\lambda[/itex], but in the drawing just underneath it, the Kunt pipe, the distance between two successive heaps of cork is [itex]\lambda/2[/itex], why?
The Kunt pipe is filled with thin cork powder and when there are standing waves the cork piles in the nodes, denoted N in the drawing.
I understand the distance between two successive nodes is [itex]\lambda/2[/itex] in transverse waves, but why in longitudinal waves? the mechanism is different.
And what's the mechanism? is a molecule swinging back and forth between two nodes, the third drawing from above? the nodes, i understand, are high pressure areas. the molecules don't move in them so the cork piles there.
In the 2 lowest drawings i ask if the high pressure areas change place each half period time between the nodes.

Homework Equations

The velocity of waves: [itex]\lambda=u/f[/itex]

The Attempt at a Solution

If my explanation is right and the molecules on each side of each node, a high pressure area, oscillate in opposite directions and if the nodes change places as in the lowest drawings then there is a difference between the successive nodes and that explains the [itex] \lambda/2[/itex] distance.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?