Using the continuity conditions of the tangential component of the magnetic flux density and of the electric field at the core-metal and metal-medium boundaries and the Drude model for a noble metal, we give the equations relating the plasmonic eigenfrequency and decay rate, the nanoshell's geometric parameters and the indices of refraction of the core and the embedding medium. We find the range of frequencies to which the hole-to-sphere ratio can be tuned. (C) 2012 Elsevier B.V. All rights reserved.