Question

$y=3\sin \pi (\frac{t}{2}-\frac{x}{4})$ 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

• A. 10 m
• B. 5 m
• C. 32 m
• D. 8 m

Answer 1

Answer: (A)

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
$T=4s,\lambda =8m$
$\therefore$ Velocity of wave,
$v=\frac{\lambda }{T}=\frac{8}{4}=2m{s}^{-1}$
Distance travelled by wave in time $t$ is
$s=vt$
or$s=2\times 5=10m$