Question:
A progressive wave is given by the equation \(Y=0.07\sin(6x-3t)\) m. The velocity of the wave is (all quantities are in SI units)
A progressive wave is given by the equation \(Y=0.07\sin(6x-3t)\) m. The velocity of the wave is (all quantities are in SI units)
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Compare the given equation with y = A sin(kx - wt) and use v = w/k.
Updated On: Nov 13, 2026
- 6 m/s
- 3 m/s
- 2 m/s
- 0.5 m/s
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
A wave travelling along +x is written as \( y = A\sin(kx - \omega t) \), and its speed is \( v = \frac{\omega}{k} \).
Step 2: Identify the Constants
Comparing with \( Y = 0.07\sin(6x - 3t) \): \( k = 6 \) rad/m and \( \omega = 3 \) rad/s.
Step 3: Calculation
\( v = \frac{\omega}{k} = \frac{3}{6} = 0.5 \) m/s.
Step 4: Compare the options
The velocity 0.5 m/s is option (D).
Final Answer:
The wave velocity is 0.5 m/s. \[ \boxed{\text{(D) }0.5\ \text{m/s}} \]
A wave travelling along +x is written as \( y = A\sin(kx - \omega t) \), and its speed is \( v = \frac{\omega}{k} \).
Step 2: Identify the Constants
Comparing with \( Y = 0.07\sin(6x - 3t) \): \( k = 6 \) rad/m and \( \omega = 3 \) rad/s.
Step 3: Calculation
\( v = \frac{\omega}{k} = \frac{3}{6} = 0.5 \) m/s.
Step 4: Compare the options
The velocity 0.5 m/s is option (D).
Final Answer:
The wave velocity is 0.5 m/s. \[ \boxed{\text{(D) }0.5\ \text{m/s}} \]
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