Question:
The displacement of a progressive wave is given by \( y = 0.5 \sin(100t - 2x) \), where x and y are in meters and t is in seconds. The velocity of the wave is:
The displacement of a progressive wave is given by \( y = 0.5 \sin(100t - 2x) \), where x and y are in meters and t is in seconds. The velocity of the wave is:
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For \( \sin(at - bx) \), wave speed is always:
\[
v = \frac{a}{b}
\]
Updated On: Jun 10, 2026
- \( 25\,\text{m s}^{-1} \)
- \( 50\,\text{m s}^{-1} \)
- \( 100\,\text{m s}^{-1} \)
- \( 200\,\text{m s}^{-1} \)
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The Correct Option is B
Solution and Explanation
Concept:
A progressive wave is represented as:
\[
y = A \sin(\omega t - kx)
\]
Wave speed is given by:
\[
v = \frac{\omega}{k}
\]
Step 1: Identify parameters Comparing: \[ y = 0.5 \sin(100t - 2x) \] We get: \[ \omega = 100,\quad k = 2 \]
Step 2: Compute wave speed \[ v = \frac{\omega}{k} = \frac{100}{2} \] \[ v = 50\,\text{m s}^{-1} \]
Step 1: Identify parameters Comparing: \[ y = 0.5 \sin(100t - 2x) \] We get: \[ \omega = 100,\quad k = 2 \]
Step 2: Compute wave speed \[ v = \frac{\omega}{k} = \frac{100}{2} \] \[ v = 50\,\text{m s}^{-1} \]
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