Question:
The equation of wave motion is \(Y = 6sin(12πt-0.02πx+\frac{π}{3})\) where x is in metre and time in second. The velocity of the wave is
The equation of wave motion is \(Y = 6sin(12πt-0.02πx+\frac{π}{3})\) where x is in metre and time in second. The velocity of the wave is
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Wave speed equals omega divided by k.
Updated On: Oct 1, 2026
- \(200\) m/s
- \(300\) m/s
- \(400\) m/s
- \(600\) m/s
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Compare with the standard form \(y = A\sin(\omega t - kx + \phi)\). The wave speed is \(v = \dfrac\omega k\).
Step 2: Read off the values:
\(\omega = 12\pi\) rad/s and \(k = 0.02\pi\) rad/m.
Step 3: Compute:
\[ v = \frac{12\pi}{0.02\pi} = 600\ \text{m/s} \]
Step 4: Check:
Option (D). The wave travels in the +x direction because the time and position terms have opposite signs. Options (A), (B), (C) would need \(\omega/k\) of 200, 300 or 400.
Final Answer:
v = omega over k = 12 pi / 0.02 pi. \[ \boxed{\text{(D) }600\ \text{m/s}} \]
Compare with the standard form \(y = A\sin(\omega t - kx + \phi)\). The wave speed is \(v = \dfrac\omega k\).
Step 2: Read off the values:
\(\omega = 12\pi\) rad/s and \(k = 0.02\pi\) rad/m.
Step 3: Compute:
\[ v = \frac{12\pi}{0.02\pi} = 600\ \text{m/s} \]
Step 4: Check:
Option (D). The wave travels in the +x direction because the time and position terms have opposite signs. Options (A), (B), (C) would need \(\omega/k\) of 200, 300 or 400.
Final Answer:
v = omega over k = 12 pi / 0.02 pi. \[ \boxed{\text{(D) }600\ \text{m/s}} \]
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