You mean a sound wave traveling inside a pipe getting reflected back from open end? Mathematically, what you get is a boundary conditions P=constant at the end, which means reflection is the only possible solution. But that might not help you. You probably want to picture what actually happens with the moving air.
Imagine a pressure wave approaching the end of the pipe. The way the pressure wave travels is by compressing air ahead of it and decompressing air behind it, so you end up with an area of lower pressure behind the wave. Imagine that pressure wave reaching the open end. The high pressure zone almost immediately disperses (turning into a spherical wave outside the pipe) but that still leaves the low pressure zone inside the pipe. That pulls some air back into the pipe from outside, which keeps moving inside the pipe by inertia, and basically launches a wave in reverse.