Acoustic response of a rectangular cavity with orifices.

The acoustic response of a rectangular cavity to excitation through waveguides terminating at orifices in the cavity walls is analyzed. Acoustic pressure is expressed by eigenfunctions satisfying Neumann boundary conditions as well as by those satisfying Dirichlet ones. The change in boundary condition from wall to orifice is included by appeal to Lagrange undetermined multipliers. The acoustic consequences of an orifice may be summarized as follows. Resonances of the cavity with zero impedance orifices are higher than those of the cavity without orifices. In particular, the low-order mode (0,0,0) has zero frequency for the simple cavity but appears at finite frequency for a range of orifice impedance. Within a narrow range of orifice impedance, every resonance displays great sensitivity to impedance change. Qualitatively, orifices reproduce the effect of a uniform change in wall impedance. A gap between the speaker diaphragm and a waveguide reproduces these orifice-generated effects.