The equation of a wave travelling on a string is y= 4sin $\frac{\pi }{2}\left(8t -\frac{x}{8}\right)$ . If x and y are in cm , then velocity of wave is :

The given equation can be  written as y= 4 sin $\left(4\pi t-\frac{\pi x}{16}\right)$

$$\begin{gathered} \Rightarrow \left(v\right) =\frac{co-efficient of t\left(\omega \right)}{co-efficient of x \left(K\right)} \\ \Rightarrow v= \frac{4\pi }{{\displaystyle \raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$16$}\right.}}=64 cm /sec along +x direction. \end{gathered}$$