Question

Phase difference between a node and an adjacent antinode in a stationary wave is:

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

Hint:

In stationary waves, nodes have zero amplitude, while antinodes have maximum amplitude. The phase difference progresses systematically along the wave.

Answer 1

The Correct Option is B

Step 1: A stationary wave results from the interference of two identical waves traveling in opposite directions. 
Step 2: The phase difference (\( \Delta \phi \)) between a node (where displacement is zero) and an adjacent antinode (where displacement is maximum) is given by: \[ \Delta \phi = \frac{\pi}{2} { rad}. \] This indicates that the particle at an antinode is a quarter cycle ahead of the particle at the node. \bigskip