The equation $\mathrm{y} = {\mathrm{Acos}}^2(2\mathrm{\pi nt}-2\mathrm{\pi }\frac{\mathrm{x}}{\mathrm{\lambda }})$ represents a wave with

The given equation can be x written as
 

$\mathrm{y} = \frac{\mathrm{A}}{2}\cos (4\mathrm{\pi nt}-\frac{4\mathrm{\pi x}}{\mathrm{\lambda }})+\frac{\mathrm{A}}{2}$

                                             $(\because {\cos }^2\mathrm{\theta } = \frac{1+\cos 2\mathrm{\theta }}{2})$

Hence amplitude = $\frac{\mathrm{A}}{2}$ and frequency = $\frac{\mathrm{\omega }}{2\mathrm{\pi }}$= $\frac{4\mathrm{\pi n}}{2\mathrm{\pi }}$= 2n 

and wavelength = $\frac{2\mathrm{\pi }}{\mathrm{k}} = \frac{2\mathrm{\pi }}{{\displaystyle \frac{4\mathrm{\pi }}{\mathrm{\lambda }}}} = \frac{\mathrm{\lambda }}{2}$