The Foundations of Acoustics - Eugen Skudrzyk

The Foundations of Acoustics

Basic Mathematics and Basic Acoustics

(Autor)

Buch | Softcover
XXVIII, 790 Seiten
2012 | 1. Softcover reprint of the original 1st ed. 1971
Springer Wien (Verlag)
978-3-7091-8257-4 (ISBN)
181,89 inkl. MwSt
Research and scientific progress are based upqn intuition coordinated with a wide theoretical knowledge, experimental skill, and a realistic sense of the limitations of technology. Only a deep insight into physical phenomena will supply the necessary skills to handle the problems that arise in acoustics. The acoustician today needs to be well acquainted with mathematics, dynamics, hydrodynamics, and physics; he also needs a good knowledge of statistics, signal processing, electrical theory, and of many other specialized subjects. Acquiring this background is a laborious task and would require the study of many different books. It is the goal of this volume to present this background in as thorough and readable a manner as possible so that the reader may turn to specialized publications or chapters of other books for further information without having to start at the preliminaries. In trying to accomplish this goal, mathematics serves only as a tool; the better our understanding of a physical phenomenon, the less mathematics is needed and the shorter and more concise are our computa tions. A word about the choice of subjects for this volume will be helpful to the reader. Even scientists of high standing are frequently not acquainted with the fundamentals needed in the field of acoustics. Chapters I to IX are devoted to these fundamentals. After studying Chapter I, which dis cusses the units and their relationships, the reader should have no difficulty converting from one system of units to any other.

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)

Erscheint lt. Verlag 7.1.2012
Zusatzinfo XXVIII, 790 p.
Verlagsort Vienna
Sprache englisch
Maße 170 x 244 mm
Gewicht 1385 g
Themenwelt Naturwissenschaften Physik / Astronomie Allgemeines / Lexika
Schlagworte acoustics
ISBN-10 3-7091-8257-3 / 3709182573
ISBN-13 978-3-7091-8257-4 / 9783709182574
Zustand Neuware
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