In the interior of an extended liquid a cyclic cavitation process can be set up by a focused acoustic wave field. A cluster of supercritical cavities is developed when the tensile strength of the liquid is exceeded. This occurs almost simultaneously in a confined region around the focal point where the sound speed rapidly vanishes when the cavities approach their critical size. As a consequence, the inner boundary condition for the acoustic field, carried by the single-phase liquid, changes from total reflection at the focal point without phase shift, as at a rigid wall, to reflection at the boundary of the cluster, which now forms a low-pressure two-phase kernel embedded in the single-phase liquid. The cluster is compliant to expansion waves but essentially rigid to compression waves. As soon as the cluster is formed its further development is determined jointly by the sound field and by the far field pressure of the liquid. The former first makes the cavities in the cluster grow and then contributes to its collapse, while the latter tends to bring about its collapse from the moment of cluster formation.