MHT CET · Physics · Waves and Sound
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
- A \(300 \mathrm{~m} / \mathrm{s}\)
- B \(400 \mathrm{~m} / \mathrm{s}\)
- C \(500 \mathrm{~m} / \mathrm{s}\)
- D \(600 \mathrm{~m} / \mathrm{s}\)
Answer & Solution
Correct Answer
(C) \(500 \mathrm{~m} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
\(\therefore \quad\) 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 \(\mathrm{v}=\frac{\omega}{\mathrm{k}}\)
\(
\begin{aligned}
& \mathrm{v}=\frac{10 \pi}{0.02 \pi} \\
& \mathrm{v}=500 \mathrm{~m} / \mathrm{s}
\end{aligned}
\)
\(
\begin{aligned}
& \mathrm{k}=\frac{2 \pi}{\lambda} \\
& \mathrm{k}=0.02 \pi \\
& \omega=10 \pi
\end{aligned}
\)
\(\therefore \quad\) Velocity of wave is \(\mathrm{v}=\frac{\omega}{\mathrm{k}}\)
\(
\begin{aligned}
& \mathrm{v}=\frac{10 \pi}{0.02 \pi} \\
& \mathrm{v}=500 \mathrm{~m} / \mathrm{s}
\end{aligned}
\)
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