Caption: An animation dynamically illustrating the 2nd harmonic or 1st overtone of standing waves (specifically, standing sound waves) in air in an simplified musical pipe.
One full wavelength is shown. You can tell this because there are 3 nodes and 2 anti-nodes with oscillations going in opposite directions.
Features:
Transverse sound waves as well as longitudinal sound waves occur in solids.
Transverse sound waves CANNOT exist in fluids when they are sufficiently ideal since shearing forces (i.e., "sideways" forces) do NOT exist in ideal fluids.
That there are 3 nodes shows that one full wavelength is shown: one complete up-and-down cycle for the oscillation. The "up" is motion to the right; the "down" is motion to the left.
But we notice their oscillations in the obvious rarefactions and compressions of the displayed cartoon air molecules.
Saying 90° out of phase is equivalent saying 1/4 wavelength out of phase.
Density oscillates in phase with pressure. Thus, the two thermodynamic variables have their nodes and anti-nodes in the same places.
In real wind instruments, there are holes somewhere to let sound (i.e., sound waves) escape.