TRAPPED ACOUSTIC MODES

A constructive proof is given for the existence of trapped acoustic modes in the vicinity of a strip of length 2a parallel to, and midway between, the bounding lines of a two-dimensional waveguide. The modes, which are shown to exist for sufficiently large a, satisfy Neumann conditions on the strip and the bounding lines and a Dirichlet condition on the midline outside the strip, and may be either symmetric or antisymmetric about a line through the centre of, and perpendicular to, the strip. When a is large, the equation determining the wavenumber of the modes reduces to that proposed by Evans and Linton (1991) using nonrigorous arguments.