An aircraft auxiliary power unit sound attenuation apparatus includes a perforated body having a center aperture through which exhaust fluid passes, a backing member outwardly offset from the perforated body, a plurality of connecting members coupling the perforated body to the backing member to form a locally reacting sound attenuation member having a plurality of channels spanning outwardly from the perforated body to the backing member, and a bulk absorber disposed in each of the plurality of channels where the bulk absorber is in fluid communication with the exhaust fluid, where the locally reacting sound attenuation member is in fluid communication with an auxiliary power unit of an aircraft so that the plurality of channels are oriented in a direction crossing a pressure drop direction of an exhaust fluid flow passing through the center aperture and each channel circumscribes the center aperture.