A structural panel may be configured for attenuating noise. This panel includes a first skin, a second skin and a core forming a plurality of cavities vertically between the first skin and the second skin. The core may include a wall connected to and extending vertically between the first skin and the second skin. The wall may be laterally between and fluidly separate at least a first of the cavities from a second of the cavities. The wall may include a vertical stiffener. One or more perforations in the first skin may be fluidly coupled with the first of the cavities.