It's probably easiest to picture longitudinal (compression/rarefaction) waves by thinking of a spring. Have you seen a "Slinky"? That's a large soft spring on which it's easy to send longitudinal waves, and you can easily see the alternating bunched-up and spread-out parts of the spring.
The spring forces accelerate any part in between a bunched and a spread region toward the spread region. The bunched part pushes out and the stretched part pulls in. That works very much like the way tension in a string accelerates parts of the string, depending on how the angle of the string varies from place to place in a transverse string wave.
When you try to picture how air supports longitudinal waves, you can see that air acts like a spring in that when it's compressed its pressure goes up. It might seem tricky to imagine different parts of air pushing on each other, because air molecules can just move past each other. Over a big enough distance scale, they do bump into each other, however, and act just like springs. If you tried to make a very short-wavelength wave, shorter than the typical distance an air molecule travels before hitting another, it wouldn't propagate in air.
(published on 06/03/2009)