Developing an amplitude compensation method for obtaining high-resolution acoustic directivities from played musical instruments

ORAL

Abstract

When considering the acoustic radiation of a source, far-field directivity patterns are useful graphical representation of sound propagation in a given direction and frequency. Directivity measurements of played musical instruments present several experimental challenges, including the need for musicians to play consistently and reproducibly. Some researchers have chosen to implement fixed, limited-element microphone arrays surrounding instruments for rough directivity assessments. Unfortunately, with practical numbers of microphones, this approach limits spatial resolution and field decomposition bandwidth. Higher-resolution data may be obtained with a given microphone count by rotating a musician in sequential azimuthal angle increments under a fixed semicircular microphone array. The musician plays a selected note sequence with each increment, but corrections must be made for playing variability. For 5$^\circ$ resolution this results in 2664 measurements with M=37 in the polar angle $\theta$ and N=72 in the azimuthal angle $\phi$. This paper explores the development of an amplitude compensation method that utilizes reference microphones that are fixed in the rotating reference frame. By approximating the reference and arc microphones as the input and outputs of an LTI system, transfer functions, $\hat{H}_{MN}$, may be computed. The resulting set of $\hat{H} _{MN}$ are invariable under scalar changes in amplitude that are identical at both the reference and arc microphone positions. An experimental validation using a source with random variations in amplitude will be presented.

–

Authors

  • Nicholas J. Eyring II

    Brigham Young University

  • Benjamin Bloom

    Department of Physics, University of Arizona, Tucson, AZ, National Institute for Materials Science, Tsukuba, Japan, The University of Electro-Communications, Tokyo, Langmuir Laboratory, New Mexico Tech, The University of Arizona, Brigham Young University, Department of Physics Colorado State University, Colorado School of Mines, National Renewable Energy Laboratory, University of Colorado Boulder, Principal Investigator, Graduate Student, Colorado State University, SSRL, SLAC, Department of Chemistry and Biochemistry, Brigham Young University, Department of Physics and Astronomy, Brigham Young University, National Tsing Hua University, Hsinchu, Taiwan, Colorado State Univ, JILA, University of Colorado at Boulder, NIST, JILA, University of Colorado at Boulder, Heinrich-Heine-Universitat, Department of Physics, University of Colorado Denver, Denver, CO 80217, Biomedical Engineering, University of Texas at Austin, Austin, TX, The University Centre in Svalbard, Utah State University, Utah Valley University, New Mexico State University, The George Washington University Nuclear Physics Research Group, Institute for Nuclear Physics at the Johannes Gutenberg University of Mainz, None, Colorado State Engineering Research Center, St. Petersburg Electrotechnical University in Saint Petersburg, Russia, University of California San Diego, Argonne National Laboratory, Los Alamos National Laboratory, Imperial College London, Space Dynamics Lab, Utah State University, Physics and CASS, Utah State University, Department of Chemistry, Colorado State University, Fort Collins, CO 80523, Department of Physics, Colorado State University, Fort Collins, CO 80523, Dept. of Electrical, Computer, and Energy Engineering, University of Colorado at Boulder, Dept. of Physics and Astronomy, University of Denver, CU Boulder, RASEI, NREL, University of Colorado, Rutgers, UTK, Joint Institute for Heavy Ion Research \& ORNL, University of Guelph, Insitituto de Estructura de la Materia, University of Toronto, INFN Laboratori Nazionali del Sud, University of York, University of Surrey, TRIUMF, Simon Frasier University, Universdad de Sevilla, Simon Fraser University, Univ of Utah, Univ of Wyoming, New Mexico Tech, GLOBALFOUNDRIES, IBM Systems and Technology Group, IBM Research Division, Irvine Valley College, University of Colorado - Boulder, Department of Physics, Arizona State University, Tempe, AZ, Department of Physics, New Mexico State University, Las Cruces, NM, Department of Physics, University of Michigan, Flint, MI, High Altitude Observatory, JILA, University of Colorado

  • Benjamin Bloom

    Department of Physics, University of Arizona, Tucson, AZ, National Institute for Materials Science, Tsukuba, Japan, The University of Electro-Communications, Tokyo, Langmuir Laboratory, New Mexico Tech, The University of Arizona, Brigham Young University, Department of Physics Colorado State University, Colorado School of Mines, National Renewable Energy Laboratory, University of Colorado Boulder, Principal Investigator, Graduate Student, Colorado State University, SSRL, SLAC, Department of Chemistry and Biochemistry, Brigham Young University, Department of Physics and Astronomy, Brigham Young University, National Tsing Hua University, Hsinchu, Taiwan, Colorado State Univ, JILA, University of Colorado at Boulder, NIST, JILA, University of Colorado at Boulder, Heinrich-Heine-Universitat, Department of Physics, University of Colorado Denver, Denver, CO 80217, Biomedical Engineering, University of Texas at Austin, Austin, TX, The University Centre in Svalbard, Utah State University, Utah Valley University, New Mexico State University, The George Washington University Nuclear Physics Research Group, Institute for Nuclear Physics at the Johannes Gutenberg University of Mainz, None, Colorado State Engineering Research Center, St. Petersburg Electrotechnical University in Saint Petersburg, Russia, University of California San Diego, Argonne National Laboratory, Los Alamos National Laboratory, Imperial College London, Space Dynamics Lab, Utah State University, Physics and CASS, Utah State University, Department of Chemistry, Colorado State University, Fort Collins, CO 80523, Department of Physics, Colorado State University, Fort Collins, CO 80523, Dept. of Electrical, Computer, and Energy Engineering, University of Colorado at Boulder, Dept. of Physics and Astronomy, University of Denver, CU Boulder, RASEI, NREL, University of Colorado, Rutgers, UTK, Joint Institute for Heavy Ion Research \& ORNL, University of Guelph, Insitituto de Estructura de la Materia, University of Toronto, INFN Laboratori Nazionali del Sud, University of York, University of Surrey, TRIUMF, Simon Frasier University, Universdad de Sevilla, Simon Fraser University, Univ of Utah, Univ of Wyoming, New Mexico Tech, GLOBALFOUNDRIES, IBM Systems and Technology Group, IBM Research Division, Irvine Valley College, University of Colorado - Boulder, Department of Physics, Arizona State University, Tempe, AZ, Department of Physics, New Mexico State University, Las Cruces, NM, Department of Physics, University of Michigan, Flint, MI, High Altitude Observatory, JILA, University of Colorado