The Foundations of Acoustics

Historical Introduction.- I. Equations and Units.- II. Complex Notation and Symbolic Methods.- III. Analytic Functions: Their Integration and the Delta Function.- IV. Fourier Analysis.- V. Advanced Fourier Analysis.- VI. The Laplace Transform.- VII. Integral Transforms and the Fourier Bessel Series.- VIII. Correlation Analysis.- IX. Wiener's Generalized Harmonic Analysis.- X. Transmission Factor, Filters, and Transients ("Küpfmüller's Theory").- XI. Probability Theory, Statistics, and Noise.- XII. Signals and Signal Processing.- XIII. Sound.- XIV. The One-Dimensional Wave Equation and Its Solutions.- XV. Reflection and Transmission of Plane Waves at Normal Incidence.- XVI. Plane Waves in Three Dimensions.- XVII. Sound Propagation in Ideal Channels and Tubes.- XVIII. Spherical Waves, Sources, and Multipoles.- XIX. Solution of the Wave Equation in General Spherical Coordinates.- XX. Problems of Practical Interest in General Spherical Coordinates.- XXI. The Wave Equation in Cylindrical Coordinates and Its Applications.- XXII. The Wave Equation in Spheroidal Coordinates and Its Solutions.- XXIII. The Helmholtz Huygens Integral.- XXIV. Huygens Principle and the Rubinowicz-Kirchhoff Theory of Diffraction.- XXV. The Sommerfeld Theory of Diffraction.- XXVI. Sound Radiation of Arrays and Membranes.- XXVII. The Green's Functions of the Helmholtz Equation and Their Applications.- XXVIII. Self and Mutual Radiation Impedance.- Tables.- I. Elementary Functions.- II. Trigonometric Functions.- III. Hyperbolic Functions.- IV. Harmonic and Hyperbolic Functions of Complex Argument.- V. The Inverse Harmonic and Hyperbolic Functions.- VI. Legendre Polynomials and Surface Harmonics.- VII. The Solutions of the Wave Equation.- VIII. Properties of the Bessel Functions.- IX. Spheroidal Functions.- X. The Gamma Function.- XI. The Lommel Functions of Two Variables.- References.- 1. Early History of Acoustics.- 1. Equations and Units.- 2. Complex Notation and Symbolic Methods.- 3. Analytic Functions; Their Integration and the Delta Function.- Chapters 4, 5. Fourier Analysis.- Chapters 6, 7. The Laplace Transform and Transform Theory.- 8. Correlation and Correlation Analysis.- 9. Wiener's Generalized Harmonic Analysis.- 10. Transmission Factors, Filters, and Transients.- 11. Probability, Theory, Statistics, and Noise.- 12. Signals and Signal Processing.- Chapters 13 to 17. Sound and Simple Sound Fields; Transmission and Reflection; Channels.- 16. Channels and Ducts. (See also Literature Chapters 20, 21.).- 17. Acoustic Impedances and Their Measurement.- 17. Horns.- 17. (Supplementary Literature.) Plates..- Chapters 18, 28. Radiation Impedance.- 18. Simple Spherical Sound Propagation, Sources, Dipoles and Quadrupoles.- 19. The Wave Equation in Spherical Coordinates and Its Solutions, Applications of the Theory.- Chapters 20, 21. The Wave Equation in Cylindrical Coordinates and Its Applications (See also Literature Chapter 17.).- 22. The Wave Equation in Spheroidal Coordinatesand Its Solutions.- 23. The Helmholtz-Huygens Integral (See also Literature Chapters 24, 25.).- Chapters 24, 25. Diffraction.- 26. Sound Radiation of Arrays and Membranes. (See also Literature Chapters 24, 25.).- 27. The Green's Function and Its Application. (See also Literature Chapters 17, 20, 21, 22.).- 28. Radiation Impedance. (See Literature Chapter 18.).- List of Symbols.

"This book provides a comprehensive treatment of a number of topics in acoustics and the mathematics of acoustics. It is well organized and clearly written. It clearly leans heavily to the mathematics ... . In summary, I would say that this is an excellent foundation for the mathematics of acoustics and a great reference for the mathematics applicable to particular problems in acoustics." (James K. Thompson, Noise News International, Vol. 24 (4), December, 2016)