Theory of acoustic eigenmodes in parabolic cylindrical enclosures

We present an exact method for calculating eigenmodes and eigenfrequencies for an acoustic enclosure (AE) defined by two confocal parabolic cylinders and two plane surfaces using parabolic cylinder coordinates. Rigid-wall boundary conditions are assumed; however, the model can easily be extended to include the more general case with mixed boundary conditions. A discussion of eigenmode symmetry properties and mode frequency dependence on AE shape is given. The latter problem is addressed by considering a series of symmetrical and asymmetrical AEs having the same volume.