Question

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

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

Hint:

Visualizing the sine wave helps greatly: nodes are at \( 0, \lambda/2, \lambda \) and antinodes are at the peaks \( \lambda/4, 3\lambda/4 \).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A stationary wave, or standing wave, forms when two identical waves travel in opposite directions and superimpose.
This creates points of zero displacement called nodes and points of maximum displacement called antinodes.

Step 2: Key Formula or Approach:
The approach is to use the standard geometric properties of a standing wave pattern.
We know that the distance between two consecutive nodes is \( \lambda/2 \), where \( \lambda \) is the wavelength.

Step 3: Detailed Explanation:
In a standing wave, a full wavelength \( \lambda \) covers two complete vibrating loops.
Nodes occur at positions where the waves destructively interfere completely.
The distance separating two consecutive nodes is exactly half of a wavelength, or \( \lambda/2 \).
Antinodes occur exactly halfway between two consecutive nodes, where constructive interference is maximum.
Therefore, the distance from a node to the very next adjacent antinode is half of the distance between two nodes.
This distance is calculated as \( \frac{1}{2} \times \left(\frac{\lambda}{2}\right) = \frac{\lambda}{4} \).

Step 4: Final Answer:
The distance between a node and an adjacent antinode is \( \lambda/4 \).