A long enclosure being regarded as a waveguide in which the sound, generated by some source, may propagate, one is interested in a multimodal approach of the sound propagation within this waveguide, as it may be particularly adapted to take into account geometrical (cross-section, curvature) or physical (boundary condition) non-uniformities in the waveguide, as well as the radiation or continuity conditions at the extremities. A key point in such multimodal formulation is the choice of the basis of local transverse modes, on which the wave field is projected. In �classical� waveguides having a simple and bounded cross-section, a complete orthogonal basis of eigenmodes can be analytically obtained. The case of an open waveguide is more difficult, since no such a basis can be exhibited. However, an open resonator, as displays the cross-section of an open waveguide, is known to also exhibit resonant modes, with complex eigen-frequencies, owing to the radiative losses. In the present study it is shown how these modes, than can be numerically evaluated, can be used to establish a multimodal formulation in an open waveguide modelling a long rectangular enclosure.
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