When an air column is set into vibrations, the distance between two consecutive nodes of the resultant wave is

Analyze the question: It asks about the distance between two consecutive nodes in a stationary (standing) wave formed in an air column.

Concept: When an air column vibrates, the original wave and its reflection travel in opposite directions and combine to form a stationary wave. This wave has:

• Nodes (N): points of zero displacement (minimum vibration)
• Antinodes (A): points of maximum displacement

Step-by-step reasoning:

1. Between a node and the next antinode, the distance is λ/4.
2. Between an antinode and the next node, the distance is another λ/4.
3. So the distance from one node to the next consecutive node is:

λ/4 + λ/4 = λ/2

The same is true for two consecutive antinodes, which are also λ/2 apart.

You can also check this with a standing wave on a string: the pattern repeats every full wavelength, and within that one wavelength there are exactly two nodes, so they are separated by λ/2.

Answer: The distance between two consecutive nodes is half of the wavelength, which is option B.

Exam tip: Remember "N to N = λ/2, A to A = λ/2, N to A = λ/4." Questions on stationary waves, resonance tubes, and Melde's experiment often rely on these three facts.