Apparatus and methods for using acoustic radiation forces to order particles suspended in a host liquid are described. The particles may range in size from nanometers to millimeters, and may have any shape. The suspension is placed in an acoustic resonator cavity, and acoustical energy is supplied thereto using acoustic transducers. The resulting pattern may be fixed by using a solidifiable host liquid, forming thereby a solid material. Patterns may be quickly generated; typical times ranging from a few seconds to a few minutes. In a one-dimensional arrangement, parallel layers of particles are formed. With two and three dimensional transducer arrangements, more complex particle configurations are possible since different standing-wave patterns may be generated in the resonator. Fabrication of periodic structures, such as metamaterials, having periods tunable by varying the frequency of the acoustic waves, on surfaces or in bulk volume using acoustic radiation forces, provides great flexibility in the creation of new materials. Periodicities may range from millimeters to sub-micron distances, covering a large portion of the range for optical and acoustical metamaterials.