y=3 π ((t)/(2)-(x)/(4)) represents an equation of a progressive...

The given equation of a progressive wave is $y=3 \sin \pi\left(\frac{t}{2}-\frac{x}{4}\right)=3 \sin 2 \pi\left(\frac{t}{4}-\frac{x}{8}\right)$ The standard equation of a progressive wave is $y=y_0 \sin 2 \pi\left(\frac{t}{T}-\frac{x}{\lambda}\right)$ Comparing these two equations, we get $T=4 \mathrm{~s}, \quad \lambda=8 \mathrm{~m}$ $\therefore$ Velocity of wave, $v=\frac{\lambda}{T}=\frac{8}{4}=2 \mathrm{~ms}^{-1}$ Distance travelled by wave in time $t$ is $s=v t$ or $\quad s=2 \times 5=10 \mathrm{~m}$