Question

In a stationary wave, the distance between a node and the adjacent antinode is:

• A. $\lambda$
• B. $\lambda/2$
• C. $\lambda/4$
• D. $2\lambda$

Hint:

Stationary Wave Distances: Node to node = $\lambda/2$ Antinode to antinode = $\lambda/2$ Node to adjacent antinode = $\lambda/4$

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A stationary (standing) wave is formed by the interference of two waves of the same frequency and amplitude traveling in opposite directions. It consists of nodes (points of zero displacement) and antinodes (points of maximum displacement).
Step 2: Detailed Explanation:
1. In a full wavelength (\(\lambda\)), the wave repeats its pattern.
2. The distance between two consecutive nodes or two consecutive antinodes is half a wavelength (\(\lambda/2\)).
3. A node and the immediately following antinode represent the distance from a zero point to a peak. This is exactly half the distance between two nodes.
4. Therefore, the distance is: \[ \frac{1}{2} \times \frac{\lambda}{2} = \frac{\lambda}{4} \]
Step 4: Final Answer
The distance is \(\lambda/4\).