A sound insulation device for mounting in a tubular part, in particular a motor vehicle bodywork part, the device comprising a partitioning insert, a cord of a composition that is thermally expandable so as to form a foam, said cord being fitted to the periphery of the insert, retaining means for holding the cord on the insert prior to expansion of the cord, and means for encouraging the cord to expand towards the inside wall of the tubular part, wherein the cord is formed by being extruded in rectilinear manner without any particular shaping, and wherein the cord retaining means are integrally molded with the partitioning insert and also serve to shape the extruded cord around the periphery of the partitioning insert.