Question

A progressive wave of frequency 50 Hz is travelling with velocity 350 m/s through a medium. The change in phase at a given time interval of 0.01 second is

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

Hint:

Phase change over time at a fixed point: \(\Delta \phi = \omega \Delta t = 2\pi f \Delta t\). Frequency in Hz gives cycles per second; multiply by time to get cycles, then by \(2\pi\) for radians.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
A wave has frequency \(f = 50\ \text{Hz}\) and velocity \(v = 350\ \text{m/s}\). We need the phase change \(\Delta \phi\) over a time interval \(\Delta t = 0.01\ \text{s}\) at a fixed position.

Step 2: Key Formula or Approach:
Phase change is given by \(\Delta \phi = 2\pi f \Delta t\).

Step 3: Detailed Explanation:
Substitute the values: \[ \Delta \phi = 2\pi (50)(0.01) = 2\pi (0.5) = \pi\ \text{rad}. \]

Step 4: Final Answer:
The change in phase is \(\pi\) radians, which is option (C).