Question

A progressive wave of frequency \( 50\,\text{Hz} \) is travelling with velocity \( 350\,\text{m s}^{-1} \) through a medium. The change in phase at a given point in a time interval of \( 0.01\,\text{s} \) is

• A. \( \dfrac{\pi}{2} \,\text{rad} \)
• B. \( \pi \,\text{rad} \)
• C. \( \dfrac{\pi}{4} \,\text{rad} \)
• D. \( \dfrac{3\pi}{2} \,\text{rad} \)

Hint:

Phase change depends only on frequency and time, not on wave velocity.

Answer 1

The Correct Option is B

Step 1: Write expression for angular frequency.
\[ \omega = 2\pi f \]
Step 2: Substitute given frequency.
\[ \omega = 2\pi \times 50 = 100\pi \,\text{rad s}^{-1} \]
Step 3: Write phase change formula.
\[ \Delta \phi = \omega \Delta t \]
Step 4: Calculate phase change.
\[ \Delta \phi = 100\pi \times 0.01 = \pi \]
Step 5: Conclusion.
The change in phase is \( \pi \,\text{rad} \).