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At the risk being rebuffed, I would suggest that the "information"
carried by the sound wave is in the pressure depiction. Consider two
sources (speakers) which are distance L apart and driven by a common
source. Place a detector/microphone directly between the speakers at
L/2. Ignore reflected waves; consider only direct waves. Would you
detect no sound or maximum sound? Many students say none because
they are thinking displacement waves and the displacements cancel.
The experiment (as best as I can do it in the intro lab) says maximum
indicating to me that the pressure is the better thing to consider
for a sound wave. This conclusion is supported by a minimum when I
move the microphone to a pressure node/displacement antinode.
There should be a way to visualize this with
mechanical waves