The equation y = A ^2(kx - ω t) characterizes a wave motion with

Given equation of the wave is $y = A \sin^2(kx - \omega t)$

Using the trigonometric identity $\sin^2 \theta = \dfrac{1 - \cos 2\theta}{2}$, we get:

$y = \dfrac{A}{2} [1 - \cos(2kx - 2\omega t)]$

$y = \dfrac{A}{2} - \dfrac{A}{2} \cos(2kx - 2\omega t)$

This represents a wave superimposed on a constant displacement of $\dfrac{A}{2}$.

The amplitude of the wave is the magnitude of the coefficient of the cosine term, which is $\dfrac{A}{2}$.

The angular frequency of the wave is $\omega' = 2\omega$.

The frequency of the wave is $f = \dfrac{\omega'}{2\pi} = \dfrac{2\omega}{2\pi} = \dfrac{\omega}{\pi}$.