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Natural Frequencies and Standing Wave Patterns:
A standing wave pattern is characterized by the presence of nodes and antinodes that are always present at the same position along the medium. The fundamental frequency or first harmonic has the smallest possible number of nodes and antinodes. The standing wave patterns for the other harmonics - second, third, fourth, etc. - have an increasing number of nodes and antinodes.
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At the open ends of an air column, air is free to vibrate back and forth. Thus, the open ends are vibrational antinodes. When the air column is forced to resonate, the ends become antinodes. Each consecutive antinode must be separated by a node. So for the lowest possible frequency (fundamental or first harmonic), there must be one node between the two ends. 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 two antinodes (on the ends) and one node, then the second harmonic has three antinodes (two of which are at the ends of the air column) and two nodes. The third harmonic has four antinodes and three nodes. The fourth harmonic has five antinodes and four nodes. The fifth harmonic has ... - and so on.
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Length-Wavelength Relationship:
A standing wave pattern shows a unique relationship between the wavelength of the waves that create the pattern and a length measured along the medium between two points on the pattern. Every nodal position on the pattern is separated from the next adjacent nodal position by one-half of a wavelength. Similarly, every antinodal position on the pattern is separated from the next adjacent antinodal position by one-half of a wavelength.
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