Q140 / 160 · TS EAMCET 2023 (12 May Shift 1) · Physics
A wave is given by the equation $y=(0.02) \sin (\pi x-8 \pi t)$ then the velocity of the wave is ( $y$ and $x$ are in metre and $\mathrm{t}$ is in second)
- A$16 \mathrm{~ms}^{-1}$
- B$2 \mathrm{~ms}^{-1}$
- Correct answerC$8 \mathrm{~ms}^{-1}$
- D$18 \mathrm{~ms}^{-1}$
Solution
A wave is given by
$\mathrm{y}=0.02 \sin (\pi \mathrm{x}-8 \pi \mathrm{t})$
Compare with
$\begin{aligned}
& \mathrm{y}=\mathrm{A} \sin (\mathrm{kx}-\omega \mathrm{t}) \\
& \mathrm{k}=\pi, \omega=8 \pi
\end{aligned}$
Velocity, $\mathrm{v}=\frac{\omega}{\mathrm{k}}=\frac{8 \pi}{\pi}=8 \mathrm{~m} / \mathrm{s}$
Hence, the correct answer is option: 'C'.