# Compute impulse response of a cavity for sound waves

Given a (closed or not) surface and a point emitting a spherical sound wave, how can I calculate the wave amplitude in any point of space, considering reflections on this surface ?

The idea is to determine the response of the cavity to a dirac impulse, for use in convolution reverb afterwards (and also mainly because the question interests me). The main idea is answering the question "If I am at this point of the cavity and say 'Hello World', what echo will I hear ?".

Remembering some lessons on waves some years ago, I tried to go with Huygens-Fresnel principle, by computing the value of wave after exaclty 1, 2, 3 etc.. reflexions and summing up everything, but I couldn't find out how to properly formulate it in this case.

Going deeper into Wikipedia, the Kirchhoff integral theorem, but my attempts to use it where quite unsuccessful as well.

Is there some formula of this kind that would stand for my problem (and maybe that could be exactly resolved in cases with a lot of symmetries), or should I just get down to the wave equation and compute numerically the value (and thus, how should it be done with a dirac impulse as initial conditions) ?