A three-dimensional air-adsorbing structure for use in a volume in which there is a time-varying acoustic field. The structure has a three-dimensional, unitary, skeletal, porous scaffold having scaffold openings distributed within its volume, where the scaffold openings make up at least about 50% of the volume of the scaffold, air-adsorbing material particles, and a hydrophobic binder that couples air-adsorbing material particles to each other to form agglomerates and couples particles and agglomerates to the scaffold. The structure has structure openings in the agglomerates and structure openings between agglomerates, such structure openings being open to the outside environment, wherein the cumulative volume of the structure openings that have an apparent diameter larger than about 0.01 microns as measured by mercury porosimetry is at least about 40% of the volume of the air-adsorbing structure, and the cumulative volume of the structure openings that have an apparent diameter larger than about 5 microns as measured by mercury porosimetry is at least about 15% of the volume of the air-adsorbing structure.