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Abstract: Let Ω be an opened domain of with a boundary Γ. The problem numbered (1) in the text has a unique solution in , if , on a part of Γ the area S of which is different from zero and . ɛ is the damping of an elastic structure and ζ is the normalised acoustic impedance of the internal wall of the cavity. ɛ and are small parameters. Thanks to a proper modal expansion and a mean over a narrow band of wave number k, an integral relation between the trace of u on and g is built to the first order in and ɛ, using the residues theorem. It is not an equivalent equation to the problem, but just a step towards its resolution, which will be published in future papers. To cite this article: D. Brenot, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]