The radiation of sound through the open end of a cylindrical or conical pipe of any cross section, or through a hole in a plane wall, is analyzed theoretically. The scattering of a sound wave by the end of a rod or slab is also treated. Only the case in which the wavelength λ is large compared with a typical radial dimensionaof the opening or of the end, is considered. The method of matched asymptotic expansions is employed. Results on end corrections and reflection coefficients previously obtained by Helmholtz, Rayleigh, and Bazer and Karp using intuitive arguments are recovered and verified. Agreement is found with the exact results of Levine and Schwinger and Vainstein, and with the smalla/λ results of Lesser and Lewis, in the cases they treated. In addition various new results are obtained.