Angular Distribution Analysis in Acoustics

The purpose of this book is to j.irEUR'~ 0l'l' a new technique for the experimental investigation of the free wave model sound field of acoustics. The technique is based on the use of spherical harmonic functions of angle. Acousticians frequently encounter random sound fields whose properties may be closely modelled by use of the "free wave" field. This model field is defined by two basic statistical properties: stationarity in time, and homogeneity in space. Stationarity means that any single order statistic measured by a microphone in the field will be independent of the time at which the recording is taken, while homogeneity means that the measurement will also be independent of the mic- phone's position in the field. Furthermore, second order statistics obtained from the measurements of two microphones will depend only on the time lapse between the two recordings, and the relative spatial separation of the micro­ phones, and not on the microphones' absolute positions in space and time. The free wave field may also (equivalently) be pictured as a collection of plane sound waves which approach an observation position from all angles. These are the "free waves" of the title, with no correlation between waves at different angles and frequencies, although there may exist an angle-dependant plane wave density function. This is a measure of the density of sound energy arriving from different angles. The free wave field has proved to be a simple but remarkably powerful model.

Contenu

1 Introduction.- 2 The Free Wave Sound Field.- 2.1 Introduction.- 2.2 Properties of the Free Wave Field.- 2.2.1 Homogeneous Sound Fields in Ducts.- 2.2.2 The Free Wave Field.- 2.3 Spectral Density Measurement in Free Wave Fields: Cook's Theorem.- 2.3.1 Architectural Acoustics.- 2.3.2 Cook's Theorem for a Diffuse Field.- 2.3.3 Cook's Theorem and Ocean Acoustics.- 2.4 Extension of Cook's Theorem for Anisotropic Fields.- 2.4.1 Anisotropic Fields.- 2.4.2 Interpretation of the Plane Wave Weighting Function: Energy Flow.- 2.4.3 Application to Duct Acoustics.- 2.5 Summary.- References.- Figures.- 3 Inference of the Plane Wave Weighting Function From Spectral Density Measurements.- 3.1 Introduction.- 3.2 Cook's Theorem and Nondiffuse Fields.- 3.2.1 Applications of Cook's Theorem.- 3.2.2 Criteria of Diffuseness.- 3.3 Inductive Weighting Analysis: Parametric Models.- 3.3.1 Inductive Weighting Analysis: Sea Noise.- 3.3.2 Inductive Weighting Analysis: Fan Noise.- 3.3.3 Inductive Weighting Analysis: Room Fields.- 3.3.4 The Use of Parametric Weighting Families.- 3.3.5 Cosine-Power Weighting.- 3.3.6 Strip Function Weightings.- 3.3.7 Computational Applications of Strip Weightings.- 3.4 Direct Weighting Analysis: Theoretical Inverse.- 3.4.1 Use of Theoretical Inverse.- 3.4.2 Practical Application.- 3.5 Direct Weighting Analysis: Wavenumber Spectra.- 3.5.1 Fundamental Properties.- 3.5.2 Wavenumber Spectra for Parametric Model Weighting.- 3.5.3 Truncation Effects.- 3.5.4 Practical Applications.- 3.6 Direct Weighting Analysis: Stationary Phase Approximation.- 3.7 Direct Weighting Analysis: Spherical Harmonic Expansions.- 3.7.1 Fundamental Properties.- 3.7.2 Harmonic Expansions of CCSD, Weighting.- 3.7.3 Fundamental Limitations.- 3.7.4 Practical Applications.- 3.8 Conclusions.- References.- Figures.- 4 The Spherical Harmonic Analysis of Free Wave Fields in Practice.- 4.1 Introduction.- 4.2 Formulation of the Harmonic Search Problem: Least Squares Fitting.- 4.2.1 Preliminary Formulation.- 4.2.2 Weighting Factor; Real and Imaginary Data Fitting.- 4.2.3 Regression Analysis: solution of problem.- 4.2.4 Regression Analysis: measures of statistical quality.- 4.2.5 Regression Analysis: collinearity.- 4.2.6 Summary.- 4.3 Harmonic Analysis of the Gravitational and Magnetic Fields of Planets.- 4.3.1 Geomagnetism.- 4.3.2 The Magnetic Fields of Jupiter and Saturn.- 4.3.3 The Earth's Gravitational Field.- 4.3.4 Summary.- 4.4 Development of Harmonic Search Procedure.- 4.4.1 Introduction.- 4.4.2 Basis of Development.- 4.4.3 Model Experiment Data.- 4.4.4 Design of Experiment: CCSD Sampling.- 4.4.5 Design of Variable Hoppers.- 4.4.6 Simple FS, BE Search Procedures.- 4.4.7 Stepwise Search Procedure.- 4.4.8 Statistical Properties of Results.- 4.4.9 Collinearity Safeguards.- 4.4.10 Origin of Collinearity.- 4.4.11 Final program.- 4.5 Development of Axisymmetric Harmonic Search Procedure.- 4.5.1 Simple FS Search Procedure.- 4.5.2 Stepwise Procedure: Collinearity Safeguards.- 4.6 Properties of Analysis Results.- 4.6.1 Results of Analysis.- 4.6.2 Sensitivity to data errors.- 4.7 Conclusions.- References.- Figures.- Tables.- 5 Summary.- Appendix A.- Appendix B.- Appendix C.