Note that the pressure variation leads the displacement by a quarter wavelength.
This is equivalent to
a phase shift of p/2 radians.
When the displacement is maximum or minimum the pressure variation is zero.
Why does pressure variation lead displacement by p/2?
Consider a fluid element
Piston
The element with wave
Volume of the element without wave
Displacement of left side
Displacement of right side
press the Pause/Play button if you want to Pause/Play
The pressure in the element is inversely proportional to the volume of the
element. The bigger the volume, the lower the pressure.
The
volume of the element is largest and the pressure variation is minimum
The
volume of the element is the same as that without wave and the pressure
variation is zero
The
volume of the element is smallest and the pressure variation is maximum
The volume of the element is the same as that
without wave and the pressure variation is zero