Question

If the equation of a progressive wave is given as $y=a\sin \pi \left[\frac{t}{2}-\frac{x}{4}\right]$, where $x$ is in metres and t is in seconds, then the distance through which the wave moves in $8s$ is

• A. 2 m
• B. 16 m
• C. 4 m
• D. 8 m

Answer 1

Answer: (B)

Given, $y=a\sin \pi \left[\frac{t}{2}-\frac{x}{4}\right]$
Comparing it with standard equation
$y=a\sin \pi \left[\frac{2t}{T}-\frac{2x}{vT}\right]$
$\Rightarrow \frac{2}{T}=\frac{1}{2}$ or $T=4s$ and $\frac{2}{vT}=\frac{1}{4}$
or $v=\frac{8}{T}=\frac{8}{4}=2m{s}^{-1}$
$\therefore$ Distance travelled by wave is $8s$
$=v\times t=2\times 8=16m$