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Q.
$y=3 \sin \pi (\frac {t}{2}-\frac {x}{4})$ represents an equation of a progressive wave, where $t$ is in second and $x$ is in metre. The distance travelled by the wave in $5$ seconds is
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
$T=4 s , \lambda=8\, m$
$\therefore $ Velocity of wave,
$v=\frac{\lambda}{T}=\frac{8}{4}=2\, ms ^{-1}$
Distance travelled by wave in time $t$ is
$s=v t$
or$\,\,\,\,s=2 \times 5=10 \,m$