In this paper a method is described of measuring the acoustic impedance of a sample of material forming one boundary of a shallow cylindrical cavity, by determining the sound pressure produced when a known volume current is injected into the cavity from a high impedance source. The volume current is effectively determined by observing the pressure when the cavity is rigidly terminated. The use of a ring source suppresses the first radial mode of the cavity and extends the frequency limit set by uniformity of pressure by at least an octave.Secondary effects due to the finite impedance of the source and microphone and heat losses at the walls have been evaluated. The method appears to be simple, rapid, and precise.