Question

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

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

Hint:

Phase change equals angular frequency times the time interval.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
At a given point, the phase of a travelling wave changes with time as \(\Delta\phi = \omega\Delta t = 2\pi f\Delta t\). The wave speed is not needed here.

Step 2: Compute:
\[ \Delta\phi = 2\pi\times50\times0.01 = \pi\ \text{rad} \]

Step 3: Check:
The period is \(T = \dfrac1{50} = 0.02\) s, so 0.01 s is half a period. Half a period corresponds to a phase change of \(\pi\). Option (C). The other options are \(\tfrac14\), \(\tfrac12\) and \(\tfrac32\) of that.

Final Answer:
0.01 s is half a period, a phase change of pi. \[ \boxed{\text{(C) }\pi\ \text{rad}} \]