If both ends of the tube are open, the musical instrument is said to contain an open-end air column. The standing waves in a pipe open at both ends are analogous to the natural modes on a string. Because the pipe ends are open the natural mode has a maximum displacement of the air at the open ends, and a minimum pressure fluctuation at the open ends.  This makes sense, since the air is free to move at the open ends and the pressure cannot build up at the open end the way it can in the interior where the air is confined.  This gives the node (minimum) and anti-node (maximum) patterns for pressure and displacement (motion) for the sound wave in the open ended pipe.