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: Plan:
Use $\lambda$ and $T$.

Step 2: Steps:
$\lambda = \frac{2\pi}{k} = \frac{2\pi}{8} = \frac{\pi}{4}$ m and $T = \frac{2\pi}{\omega} = \frac{2\pi}{4} = \frac{\pi}{2}$ s.
$v = \frac{\lambda}{T} = \frac{\pi/4}{\pi/2} = 0.5$ m/s.

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