A panel is provided for attenuating noise. This panel includes a porous first skin, a second skin and a core, which is connected between the porous first skin and the second skin. The core includes a corrugated body and a plurality of stringer bodies. The corrugated body includes a plurality of corrugations configured from at least a plurality of baffles and a plurality of porous septums. Each of the corrugations includes a respective one of the baffles and a respective one of the porous septums. A first of the corrugations forms a first channel that extends laterally between a first of the baffles and a first of the porous septums. The stringer bodies are spaced longitudinally along the first channel. Each of the stringer bodies includes a first sidewall disposed within the first channel and configured to fluidly isolate longitudinally adjacent portions of the first channel from one another.