Question

A traveling wave is described by the equation \(y(x,t) = [0.05sin(8x-4t)]\) m
The velocity of the wave is [All the quantities are in SI unit]

• A. \(4\text{ ms}^{-1}\)
• B. \(2\text{ ms}^{-1}\)
• C. \(0.5\text{ ms}^{-1}\)
• D. \(8\text{ ms}^{-1}\)

Hint:

Compare with \(\sin(kx-\omega t)\); speed is \(\omega/k\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A travelling wave is \(y = A\sin(kx-\omega t)\), and its speed is \(v = \frac{\omega}{k}\).

Step 2: Compare:
Here \(k = 8\) rad/m and \(\omega = 4\) rad/s.
\[ v = \frac{4}{8} = 0.5\ \text{m/s} \]

Step 3: Other options:
\(4\) m/s is just \(\omega\), \(8\) m/s is just \(k\), and \(2\) m/s would come from \(k/\omega\) inverted incorrectly.

Final Answer:
The wave speed is \(0.5\) m/s, option (C). \[ \boxed{0.5\ \text{m/s}} \]