This letter explores the effect of the directivity of a source on time reversal acoustic focusing of energy. A single loudspeaker produces an airborne focus of sound in a reverberation chamber and in a classroom. Individual foci are created at microphone positions that surround the loudspeaker. The primary axis of the loudspeaker is then rotated and experiments are repeated to average out the room response. Focal amplitude, temporal quality of the foci, and spatial focusing quality are compared to determine the optimal angle to aim a directional source axis relative to the desired focal position.
Time reversal is a technique that may be used to achieve intentional sound focusing. The purpose of this presentation is to explore how intense the focus of airborne sound energy can be using time reversal. Experiments utilize loudspeakers and a single microphone placed in a reverberation chamber. Various frequency ranges and loudspeaker orientations are explored along with different types of loudspeakers in order to experimentally determine the optimum conditions for generating the loudest focus possible. The overall purpose of this study is to create an acoustic focus at nonlinear sound pressure levels in order to create a controllable source of nonlinear acoustic sound.
The tabulation of normal subgroups of 3D crystallographic space groups that are themselves 3D crystallographic space groups (csg's) is an ambitious goal, but would have a variety of applications. For convenience, such subgroups are referred to as `csg-normal' while normal subgroups of the crystallographic point group (cpg) of a crystallographic space group are referred to as `cpg-normal'. The point group of a csg-normal subgroup must be a cpg-normal subgroup. The present work takes a significant step towards that goal by tabulating the translational subgroups (a.k.a. sublattices) that are capable of supporting csg-normal subgroups. Two necessary conditions are identified on the relative sublattice basis that must be met in order for the sublattice to support csg-normal subgroups: one depends on the operations of the point group of the space group, while the other depends on the operations of the cpg-normal subgroup. Sublattices that meet these conditions are referred to as `normally supportive'. For each cpg-normal subgroup (excluding the identity subgroup 1) of each of the arithmetic crystal classes of 3D space groups, all of the normally supportive sublattices have been tabulated in symbolic form, such that most of the entries in the table contain one or more integer variables of infinite range; thus it could be more accurately described as a table of the infinite families of normally supportive sublattices. For a given pair of cpg-normal subgroup and normally supportive sublattice, csg-normal subgroups of the space groups of the parent arithmetic crystal class can be constructed via group extension, though in general such a pair does not guarantee the existence of a corresponding csg-normal subgroup.
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