Question

If a progressive wave is represented as $y=2\sin \pi \left(\begin{array}{c}\frac{t}{2}-\frac{x}{4}\end{array}\right)$ where x is in metre and t is in second, then the distance travelled by the wave in 5 s is

• A. 5m
• B. 10m
• C. 25m
• D. 32m

Answer 1

Answer: (B)

10m

Given that the progressive wave ,

$y=3\sin \pi \left(\begin{array}{c}\frac{t}{2}-\frac{x}{4}\end{array}\right)$
$=3\sin \left(\begin{array}{c}\frac{\pi t}{2}-\frac{\pi x}{4}\end{array}\right)$
We know the standard equation of progressive wave,

$y=r\sin \frac{2\pi }{\lambda }(vt-x)$

or
$y=r\sin \left(\begin{array}{c}\frac{2\pi vt}{\lambda }-\frac{2\pi x}{\lambda }\end{array}\right)$
We have, $\frac{2\pi v}{\lambda }=\frac{\pi }{2}$ or $v=\frac{\lambda }{4}$
and $\frac{2\pi }{\lambda }=\frac{\pi }{4}$ or $\lambda =8m$
$\therefore v=\frac{8}{4}=2m/s$

we know that the distance coverd by the wave is $d=vt$
So, the distance travelled by wave in t second $=2\times 5=10m$