The equation of wave motion is $\mathrm{Y}=5 \sin (10 \pi \mathrm{t}$ $-0.02 \pi x+\pi / 3)$ where $x$ is in…
The equation of wave motion is $\mathrm{Y}=5 \sin (10 \pi \mathrm{t}$ $-0.02 \pi x+\pi / 3)$ where $x$ is in metre and $t$ in second. The velocity of the wave is
$300 \mathrm{~m} / \mathrm{s}$
$400 \mathrm{~m} / \mathrm{s}$
$500 \mathrm{~m} / \mathrm{s}$
$600 \mathrm{~m} / \mathrm{s}$
Solution
$\therefore \quad$ Equation of Wave: $\mathrm{y}=\mathrm{A} \sin (\mathrm{kx}-\omega \mathrm{t}+\phi)$ Value of $\mathrm{k}$ :
$\begin{aligned}
& \mathrm{k}=\frac{2 \pi}{\lambda} \\
& \mathrm{k}=0.02 \pi \\
& \omega=10 \pi
\end{aligned}$
$\therefore \quad$ Velocity of wave is $\mathrm{v}=\frac{\omega}{\mathrm{k}}$
$\begin{aligned}
& \mathrm{v}=\frac{10 \pi}{0.02 \pi} \\
& \mathrm{v}=500 \mathrm{~m} / \mathrm{s}
\end{aligned}$