A panel is provided for attenuating sound. This panel includes a perforated first skin, a second skin and a core. The core forms a plurality of cavities vertically between the perforated first skin and the second skin. The core includes an array of corrugations that include a first baffle, a second baffle and a first septum. The cavities include a first cavity formed longitudinally between the first baffle and the second baffle. The first cavity is fluidly coupled with perforations in the first skin. The first septum extends from the first skin and the first baffle to the second skin and the second baffle. The first septum divides the first cavity into fluidly coupled sub-cavities. At least one element of the panel includes at least one first rib and at least one second rib, the first rib extends along a first trajectory and the second rib extends along a second trajectory that is non-parallel with the first trajectory.