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A closed-end air column consists of a column of air that is open to the surrounding environment at one end and closed off (capped, covered, etc.) at the opposite end. At the open end, air is free to vibrate back and forth. Thus, the open end is a vibrational antinode. At the closed end, air is not free to vibrate back and forth. The closed end is a vibrational node. When the air column is forced to resonate, a standing wave is produced with an antinode at one end and a node at the other end. So for the lowest possible frequency (fundamental or first harmonic), there must be a single node and antinode. The standing wave patterns for the other harmonics have additional nodes and antinodes in comparison to the first harmonic). So if the first harmonic has one antinode and one node, then the third harmonic has two antinodes and two nodes. The fifth harmonic has three antinodes and three nodes. The seventh harmonic has four antinodes and four nodes. The ninth harmonic has ... - and so on.
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