Discussion
The number of nodes and antinodes in a guitar string vibrating in the third harmonic is:
Answer: B
The string has 4 nodes and 3 antinodes.
A string fixed at both ends vibrating in its nth harmonic has n loops. Each loop has one antinode at its middle, and the nodes are at the ends and between loops, giving n + 1 of them. For n = 3: 3 antinodes and 4 nodes.
5 nodes and 4 antinodes is the fourth harmonic, 3 nodes and 2 antinodes the second, and 2 nodes with 3 antinodes is impossible for a string fixed at both ends.
Shortcut: in the nth harmonic of a string fixed at both ends there are n antinodes and n + 1 nodes, so the answer can be read off without a sketch.
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