In a transverse wave the particles of the medium vibrate about their mean positions in a direction perpendicular to the direction of wave propagation.
Here, the particle velocity is given by $ \frac{dy}{dt}$ and wave velocity is given by $ \frac{dx}{dt}$. Hence, the angle between particle velocity and wave velocity ma transverse wave is $ \frac{\pi}{2}$
Displacement current is a quantity appearing in Maxwell’s equations. Displacement current definition is defined in terms of the rate of change of the electric displacement field (D). It can be explained by the phenomenon observed in a capacitor.