Compressions and Rarefactions in longitudinal waves

[Ali_94]

I know this may seem quite trivial but I just want to make sure, do the compressions in a longitudinal wave represent the highest displacement, in a transverse wave this is known as the crest, and do rarefactions represent the equivalent of troughs in longitudinal waves?
Thank you in advance

 

[Gordianus]

Yes, they do. You can send a longitudinal wave down a loooong spring and directly see alternate compression and expansion zones

 

[AlephZero]

In a longitudinal wave the amount of compression or rarefaction depends on the gradient of the displacement, $\partial u / \partial x$.

For a sinusiodal wave the maximum and minimum pressures occurs where the displacement is zero. The pressure change is zero where the displacement is a maximum.

See this animation: http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html - It's probably easiest to see if you set the "Form of tube" to "both ends closed". You can flip the graph to show either pressure or displacement.