Resonance in Open and Closed Pipes
A system exhibiting resonance oscillates with a large amplitude. This occurs at the frequency of a fundamental mode or a multiple thereof, which is one of its harmonics (or overtones). The graphic shows a pipe containing air with either closed or open ends. Sine waves represent standing waves with specified wavelengths and frequencies. Nodes are points of zero amplitude while antinodes are points of maximum amplitude. A closed end is a node and an open end is an antinode, which is essential in explaining how wind instruments work.
The wavelengths and frequencies for resonance in air columns for a pipe of length moving at the speed of sound are: with one open end, and , for odd; and with two open ends, and , for even.
See the Wikipedia entry for Resonance.