Using a recently developed perturbation theory for quasinormal modes (QNM's
), we evaluate the shifts in the real and imaginary parts of the QNM freque
ncies due to a quasistatic perturbation of the black hole spacetime. We sho
w the perturbed QNM spectrum of a black hole can have interesting features
using a simple model based on the scalar wave equation. [S0556-2821(99)0770
2-4].