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Two boundary value problems for the Helmholtz equation in a semi-infinitestrip are considered. The main feature of these problems is that, in additionto the function and its normal derivative on the boundary, the functionals ofthe boundary conditions possess tangential derivatives of the second and fourthorders. Also, the setting of the problems is complimented by certain edgeconditions at the two vertices of the semi-strip. The problems model wavepropagation in a semi-infinite waveguide with membrane and plate walls. Atechnique for the exact solution of these fluid-structure interaction problemsis proposed. It requires application of two Laplace transforms with respect toboth variables with the parameter of the second transform being a certainfunction of the first Laplace transform parameter. Ultimately, this methodyields two scalar Riemann-Hilbert problems with the same coefficient anddifferent right-hand sides. The dependence of the existence and uniquenessresults of the physical model problems on the index of the Riemann-Hilbertproblem is discussed.

Helmholtz equation in a semi-infinite strip with impedance boundary conditions of the third and fifth orders