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:
Stationary waves (or standing waves) are formed by the superposition of two identical waves traveling in opposite directions.
A node is a point of minimum (zero) amplitude, while an antinode is a point of maximum amplitude.
Step 2: Detailed Explanation:
In a full wavelength \( \lambda \) of a stationary wave, there are two identical loops.
The distance between two consecutive nodes is \( \lambda/2 \).
The distance between two consecutive antinodes is also \( \lambda/2 \).
An antinode is located exactly halfway between two consecutive nodes.
Therefore, the distance between a node and its immediately adjacent antinode is exactly half of \( \lambda/2 \).
\[ \text{Distance} = \frac{\lambda/2}{2} = \frac{\lambda}{4} \]
Step 3: Final Answer:
The distance between a node and an adjacent antinode is \( \lambda/4 \).