A wave disturbance in a medium is described by $y(x,t)=0.02\cos (50\pi t+\pi /2)\cos \left(10\pi x\right)$
Where 'x' and ' y 'are in metre and 't ' in seconds 

 $y=2a\cos (\omega t+\varphi )\cos \left(Kx\right)$ comparison with given equation gives 
$\begin{array}{l}K=\frac{2\pi }{\lambda }=10\pi \Rightarrow \lambda =\frac{1}{5}m=0.2m\\ \omega =2\pi f=50\pi \Rightarrow f=25\mathrm{Hz}\\ \therefore v=5{\mathrm{ms}}^{-1}\\ \text{ At }\mathrm{x}=0.15\mathrm{m}\\ \cos (10\pi \times 0.15)=\cos \left(1.5\pi \right)=0\text{ for all }t\\ \text{ At }x=0.3\\ \cos (10\pi \times 0.3)=\cos 3\pi =-1\text{ for all }t\\ \end{array}$