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 $8\, s$ 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 = 4 \, s $ and $\frac{2}{vT} = \frac{1}{4}$
or $v = \frac{8}{T} = \frac{8}{4} = 2 \, ms^{-1}$
$\therefore $ Distance travelled by wave is $8\, s$
$ =v \times t = 2 \times 8 = 16\, m$