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

Concept: A stationary wave (standing wave) is produced when two waves of the same frequency, amplitude, and wavelength travel in opposite directions and interfere with each other. In a stationary wave, two important points are formed:
• Node: A point where the displacement of the medium is always zero.
• Antinode: A point where the displacement of the medium is maximum. The arrangement of nodes and antinodes follows a regular pattern along the medium.

Step 1: Understand the spacing in a stationary wave. The distance between two successive nodes is: \[ \frac{\lambda}{2} \] Similarly, the distance between two successive antinodes is also: \[ \frac{\lambda}{2} \]

Step 2: Determine the distance between a node and the nearest antinode. Since a node lies midway between two antinodes, \[ \text{Distance between node and adjacent antinode} = \frac{\lambda}{4} \] Thus, the required distance is: \[ \boxed{\frac{\lambda}{4}} \]