a
\(y(x, t)=8.0 \sin \left(0.5 \pi x-4 \pi t-\frac{\pi}{4}\right)\)

Compare with a standard wave equation,

\(y=a \sin \left(\frac{2 \pi x}{\lambda}-\frac{2 \pi t}{T}+\phi\right)\)

we get \(\frac{2 \pi}{\lambda}=0.5 \pi\) or, \(\lambda=\frac{2 \pi}{0.5 \pi}=4 \mathrm{m}\)

\(\frac{2 \pi}{T}=4 \pi\) or \(, T=\frac{2 \pi}{4 \pi}=\frac{1}{2} \sec\)

\(v=1 / T=2 \mathrm{Hz}\)

Wave velocity, \(v=\lambda v=4 \times 2=8 \mathrm{m} / \mathrm{sec}\)