The steady time-harmonic problem is reduced to a system of singular integral equations for determining the tractions generated at the interface between the plate and half space where a thin viscous couplant is applied. These equations are found to have different types of singular solutions depending on the parameter values. They are solved numerically for a specific set of physical parameters that includes a wide range of values of the couplant viscosity and incident wavelength. The reflected and transmitted powers are calculated and the reflected power is plotted as a function of incident wavelength for various values of couplant viscosity. The wavelengths at which resonances occur in these functions are found to be strongly dependent on the couplant.

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