Solution

Given that the progressive wave ,
$$y=3\sin \pi \begin{pmatrix}\dfrac{t}{2}-\dfrac{x}{4}\end{pmatrix}$$
$$=3\sin \begin{pmatrix}\dfrac{\pi t}{2}-\dfrac{\pi x}{4}\end{pmatrix}$$
We know the standard equation of progressive wave,
$$y=r\sin \dfrac{2\pi}{\lambda}(vt-x)$$
or
$$y=r\sin \begin{pmatrix}\dfrac{2\pi vt}{\lambda}-\dfrac{2\pi x}{\lambda}\end{pmatrix}$$
We have, $$\dfrac{2\pi v}{\lambda}=\dfrac{\pi}{2}$$ or $$v=\dfrac{\lambda}{4}$$
and $$\dfrac{2\pi}{\lambda}=\dfrac{\pi}{4}$$ or $$\lambda = 8m$$
$$\therefore v = \dfrac{8}{4}=2m/s$$
we know that the distance coverd by the wave is $$d=vt$$
So, the distance travelled by wave in t second $$=2\times 5=10m$$