An acoustic core has a plurality of cell walls formed of an additive-manufacturing material and a resonant space defined by the plurality of cell walls. At least some of the resonant cells have a multitude of sound-attenuating protuberances formed of the additive-manufacturing material of the cell walls protruding into the resonant space with a random or semi-random orientation and/or size. The sound-attenuating protuberances may be formed by orienting an additive-manufacturing tool with respect to a toolpath to form a contour of a workpart, in which the toolpath includes a plurality of overlapping toolpath passes configured so as to intentionally introduce an amount of additive-manufacturing material to the workpart that exceeds a domain occupied by the contour. As the amount of additive-manufacturing material intentionally introduced exceeds the domain occupied by the contour, a portion of the additive-manufacturing material may incidentally form the plurality of sound-attenuating protuberances.