  Perturbed Kerr black holes emit gravitational radiation, which (for the
practical purposes of gravitational-wave astronomy) consists of a superposition
of damped sinusoids termed quasi-normal modes. The frequencies and
time-constants of the modes depend only on the mass and spin of the black hole
- a consequence of the no-hair theorem. It has been proposed that a measurement
of two or more quasi-normal modes could be used to confirm that the source is a
black hole and to test if general relativity continues to hold in ultra-strong
gravitational fields. In this paper we propose a practical approach to testing
general relativity with quasi-normal modes. We will also argue that the
relative amplitudes of the various quasi-normal modes encode important
information about the origin of the perturbation that caused them. This helps
in inferring the nature of the perturbation from an observation of the emitted
quasi-normal modes. In particular, we will show that the relative amplitudes of
the different quasi-normal modes emitted in the process of the merger of a pair
of nonspinning black holes can be used to measure the component masses of the
progenitor binary.
