a
(a) The given equation can be \(x\) written as

\(y = \frac{A}{2}\cos \,\left( {4\pi nt - \frac{{4\pi x}}{\lambda }} \right) + \frac{A}{2}\)    \(\left( \because cos^2 \theta = \frac{{1+ cos2\theta}}{{2}}  \right)\)

Hence amplitude \( = \frac{A}{2}\) and frequency \( = \frac{\omega }{{2\pi }} = \frac{{4\pi n}}{{2\pi }} = 2n\)

and wave length \( = \frac{{2\pi }}{k} = \frac{{2\pi }}{{4\pi /\lambda }} = \frac{\lambda }{2}\).