Acoustics-A Textbook for Engineers and Physicists

List of Examples Preface 7 Radiation from Vibrating Bodies7.1 Spherical Harmonics7.1.1 Separation of Variables7.1.2 Description of the Pressure Field7.1.3 Arbitrary Spatial Dependence7.2 Radiation from a Spherical Body7.2.1 Analysis7.2.2 Important Limits7.2.3 Symmetry Plane 7.2.4 Interaction with an Elastic Spherical Shell 7.3 Radiation from an Infinite Cylinder7.3.1 Separation of Variables7.3.2 Transverse Dependence-Cylindrical Bessel Functions7.3.3 Radiation due to a Helical Surface Wave7.3.4 Axially Periodic Surface Vibration 7.3.5 Finite Length Effects 7.4 Kirchhoff-Helmholtz Integral Theorem7.4.1 Derivation for an Acoustic Cavity7.4.2 Acoustic Radiation into an Exterior Domain7.5 Numerical Methods for Radiation from Arbitrary Objects7.5.1 Source Superposition7.5.2 Boundary Element Method7.5.3 Finite Element Method7.6 Homework Exercises 8 Radiation from a Source in a Baffle8.1 The Rayleigh Integral8.2 Farfield Directivity8.2.1 Cartesian Coordinate Description8.2.2 Farfield of a Piston Transducer8.3 Axial Dependence for a Circular Transducer8.4 An Overall Picture of the Pressure Field8.5 Radiation Impedance of a Circular Piston8.6 Time Domain Rayleigh Integral8.7 Homework Exercises 9 Modal Analysis of Waveguides9.1 Propagation in a Horn9.1.1 The Webster Horn Equation9.1.2 Exponential Horn9.1.3 Group Velocity9.1.4 WKB Solution for an Arbitrary Horn9.2 Two-Dimensional Waveguides9.2.1 General Solution9.2.2 Rigid Walls9.2.3 Interpretation9.2.4 Flexible Walls9.2.5 Orthogonality and Signal Generation9.3 Three-Dimensional Waveguides9.3.1 General Analytical Procedure9.3.2 Rectangular Waveguide9.3.3 Circular Waveguide9.4 Homework Exercises 10 Modal Analysis of Enclosures10.1 Fundamental Issues10.1.1 Wall-Induced Signals10.1.2 Source Excitation10.2 Frequency-Domain Analysis Using Forced Cavity Modes10.2.1 Rectangular Enclosures10.2.2 Spherical Cavities10.2.3 Cylindrical Enclosures10.3 Analysis Using Natural Cavity Modes10.3.1 Equations Governing Cavity Modes10.3.2 Orthogonality10.3.3 Analysis of the Pressure Field10.3.4 Rectangular Cavity10.3.5 Cylindrical Cavity10.3.6 Spherical Cavity10.4 Approximate Methods10.4.1 The Rayleigh Ratio and Its Uses10.4.2 Dowell's Approximation10.5 Homework Exercises"div> 11 Geometrical Acoustics11.1 Basic Considerations: Wavefronts and Rays11.1.1 Field Equations for an Inhomogeneous Fluid11.1.2 Reflection and Refraction of Rays11.2 Propagation in a Vertically Stratified Medium11.2.1 Snell's Law for Vertical Heterogeneity11.2.2 Intensity and Focusing Factor11.3 Arbitrary Heterogeneous Fluids11.3.1 Ray Tracing Equations11.3.2 Amplitude Dependence11.4 Fermat's Principle11.5 Homework Exercises 12 Scattering12.1 Background12.2 Scattering by Heterogeneity12.2.1 General Equations12.2.2 The Born Approximation12.3 Rayleigh Scattering Limit12.3.1 The Rayleigh Limit of the Born Approximation12.3.2 Mismatched Heterogeneous Region12.3.3 Scattering from a Rigid Body12.4 Measurements and Metrics12.5 High Frequency Approximation12.6 Scattering from Spheres12.6.1 Stationary Spherical Scatterer12.6.2 Scattering by an Elastic Spherical Shell12.7 Homework Exercises 13 Nonlinear Acoustic Waves13.1 Riemann's Solution for Plane Waves13.1.1 Analysis13.1.2 Interpretation13.1.3 Boundary and Initial Conditions13.1.4 Equations of State13.1.5 Quantitative Evaluations13.2 Effects of Nonlinearity13.2.1 Harmonic Generation13.2.2 Shock Formation13.2.3 Propagation of Weak Shocks13.3 General Analytical Techniques13.3.1 A Nonlinear Wave Equation13.3.2 Frequency Domain Formulation13.3.3 Regular Perturbation Series Expansion13.3.4 Method of Strained Coordinates13.4 Multidimensional Systems13.4.1 Finite Amplitude Spherical Wave13.4.2 Waves in Cartesian Coordinates13.5 Further Studies 13.6 Homework Exercises Appendix A: Curvilinear CoordinatesA.1 Spherical CoordinatesA.1.1 GradientA.1.2 LaplacianA.1.3 Velocity and AccelerationA.2 Cylindrical CoordinatesA.2.1 TransformationsA.2.2 GradientA.2.3 LaplacianA.2.4 Velocity and Acceleration Index