Final answer:
The correct answer is option a, which indicates that within one full wavelength of a standing wave, there can be 2 nodes and 3 antinodes or 2 antinodes and 3 nodes.
Step-by-step explanation:
The correct answer is option a. In a standing wave, nodes are points where the medium does not move, and antinodes are points where the medium moves with the greatest amplitude. Along one full wavelength of a standing wave, there are always one more node than there are antinodes.
This is because at each end of the wavelength, there must be a node, and between two nodes, there can only be one antinode. So, for every additional node, there is an additional segment and therefore an additional antinode.
Hence, if you have 2 nodes, there must be 1 antinode between them, but since a full wavelength needs to end with a node, this means there are actually 3 antinodes in total along that wavelength.
Alternatively, if you start with 2 antinodes, you must have 3 nodes for a full wavelength, because there must be nodes at each end with an antinode between every two nodes. Therefore, the first option is correct as it considers the proper distribution of nodes and antinodes within a standing wave pattern.