To reduce the costs of construction, operation, maintenance, energy storage and grid connection, some devices for extracting energy from sea waves are likely to be installed on the coast. We study theoretically a single oscillating water column (OWC) installed at the tip of a long and thin breakwater. The linearized problems of radiation and scattering for a hollow cylinder with an open bottom are then solved by the usual method of eigenfunction expansions and integral equations. Since a thin breakwater is the limit of a wedge, an exact solution for the diffraction by a solid cylinder at the tip of a wedge is derived to facilitate the analysis. Following Sarmento & Falcão (J. Fluid Mech., vol. 150, 1985, pp. 467–485), power takeoff by Wells turbines is modelled by including air compressibility in the chamber above the water surface. The effects of air compressibility on the extraction efficiency is studied. It is shown that for this simple geometry the angle of incidence affects the waves outside the structure but not the extracted power.