In the case of a pipe, one end of the pipe is necessarily open. Whether the other end is open affects the frequencies that can form a standing wave. A node must occur at a closed end, and an antinode must occur at an open end.
If both ends of the pipe are open, the pipe is designated an open pipe. Since an antinode occurs at both ends, the math involved is similar to a fixed string, in which case a node occurs at both ends.
If one end of the pipe is closed, the pipe is designated closed. In this case, a node occurs at one end of the pipe and an antinode occurs at the other end. The wave must therefore complete at least one quarter cycle of the wavelength (the shortest distance from node to antinode) in the length of the pipe yielding the same values for a string fixed at one end.
