Uniform approximations for the natural modes and frequencies of spindle- shaped acoustical resonators (Q1110414)

The authors consider the wave propagation in elongated acoustic bodies obtained by a small deformation of a body of infinite length, with a nonzero cross section. Separating the longitudinal variable and using the spectral decomposition for the two-dimensional Laplace operator in the cross section for both the Dirichlet and the Neumann condition on the wall of the waveguide, the authors obtain a second-order ordinary differential equation for the expansion coefficients. This equation serves to develop a uniform expansion for the natural modes for the prolate acoustical resonator.