Sound radiation from an acoustic source typically exhibits directional behavior, as is the case for the human voice, musical instruments, and loudspeakers, to name just a few. The necessity of directional data for many applications, such as sound source modeling, microphone placement, room acoustical design, and auralization, motivates directivity measurements. However, these measurements require careful understanding and implementation to produce the most meaningful results. Accordingly, this dissertation addresses several topics relevant to directivity theory, measurement, processing, and application. It first expands and amends previously published concepts of an acoustic source center and demonstrates the close relationship between the center and a source's far-field directional response. This relationship subsequently leads to an acoustic centering method that improves source placements within directivity measurement arrays. The dissertation then addresses several measurement considerations, including the required numbers of sampling positions for directivity measurements, quadrature rules applicable to standardized dual-equiangular sampling schemes, and a source's far-field response from arbitrarily shaped microphone arrays. Selected directivity results for the human voice and musical instruments illustrate applications of the developed measurement theories for procuring high-resolution results over a sphere. Compiled voice and musical instrument directivities now appear in an open-source database for use in room acoustical modeling, microphone placements, and other applications. To better elucidate and help predict sound source radiation, this work proposes several theoretical models, including equivalent point-source models, low-frequency radiation from a radially vibrating cap set on a rigid spherical shell with a circular aperture, and radiation from a vibrating cap on a rigid sphere with imposed mode shapes. Finally, this dissertation presents two microphone placement methods for audio and other applications. The first method approximates the measurement of a source's sound power spectrum through a single-channel measurement; the second considers microphone placement for maximum perceived loudness. The work's various developments, results, and conclusions will assist researchers and practitioners in better evaluating, predicting, and applying sound source directivities for many uses.



College and Department

Physical and Mathematical Sciences; Physics and Astronomy



Date Submitted


Document Type





directivity, sound radiation, musical instruments, acoustics, speech, modeling, microphone placement