Explanation

(b) 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 equation, we get
T=4s, λ=8m
∴ velocity of wave,
$v = \frac{\lambda}{T} = \frac{8}{4} = 2ms^{- 1}$
Distance travelled by wave in time t is
S=vt
Or s=2×5=10m