Question

The phase velocity of a wave described by the equation $\psi = \psi_0 \sin (kx + \omega t + \frac{\pi}{2})$ is

• A. $\frac{x}{t}$
• B. $\frac{\psi_0}{\omega}$
• C. $\frac{\omega}{k}$
• D. $\frac{\pi}{2k}$
• E. $\psi_0$

Hint:

Phase velocity is always $\omega/k$, independent of phase constant.

Answer 1

The Correct Option is C

Concept:
Phase velocity: \[ v = \frac{\omega}{k} \]

Step 1: Identify wave form.
Given: \[ \psi = \psi_0 \sin(kx + \omega t + \phi) \]

Step 2: Compare with standard form.
Phase velocity depends only on $\omega$ and $k$. \[ v = \frac{\omega}{k} \]