7.2.3 Symmetry Plane
7.2.4 Interaction with an Elastic Spherical Shell
7.3 Radiation from an Infinite Cylinder
7.3.1 Separation of Variables
7.3.2 Transverse Dependence-Cylindrical Bessel Functions
7.3.3 Radiation due to a Helical Surface Wave
7.3.4 Axially Periodic Surface Vibration
7.3.5 Finite Length Effects
7.4 Kirchhoff-Helmholtz Integral Theorem
7.4.1 Derivation for an Acoustic Cavity
7.4.2 Acoustic Radiation into an Exterior Domain
7.5 Numerical Methods for Radiation from Arbitrary Objects
7.5.1 Source Superposition
7.5.2 Boundary Element Method
7.5.3 Finite Element Method
7.6 Homework Exercises
8 Radiation from a Source in a Baffle
8.1 The Rayleigh Integral
8.2 Farfield Directivity
8.2.1 Cartesian Coordinate Description
8.2.2 Farfield of a Piston Transducer
8.3 Axial Dependence for a Circular Transducer
8.4 An Overall Picture of the Pressure Field
8.5 Radiation Impedance of a Circular Piston
8.6 Time Domain Rayleigh Integral
8.7 Homework Exercises
9 Modal Analysis of Waveguides
9.1 Propagation in a Horn
9.1.1 The Webster Horn Equation
9.1.2 Exponential Horn
9.1.3 Group Velocity
9.1.4 WKB Solution for an Arbitrary Horn
9.2 Two-Dimensional Waveguides
9.2.1 General Solution
9.2.2 Rigid Walls9.2.3 Interpretation
9.2.4 Flexible Walls
9.2.5 Orthogonality and Signal Generation
9.3 Three-Dimensional Waveguides
9.3.1 General Analytical Procedure
9.3.2 Rectangular Waveguide
9.3.3 Circular Waveguide
9.4 Homework Exercises
10 Modal Analysis of Enclosures
10.1 Fundamental Issues
10.1.1 Wall-Induced Signals
10.1.2 Source Excitation
10.2 Frequency-Domain Analysis Using Forced Cavity Modes
10.2.1 Rectangular Enclosures
10.2.2 Spherical Cavities
10.2.3 Cylindrical Enclosures
10.3 Analysis Using Natural Cavity Modes
10.3.1 Equations Governing Cavity Modes
10.3.2 Orthogonality
10.3.3 Analysis of the Pressure Field
10.3.4 Rectangular Cavity
10.3.5 Cylindrical Cavity
10.3.6 Spherical Cavity
10.4 Approximate Methods
10.4.1 The Rayleigh Ratio and Its Uses
10.4.2 Dowell’s Approximation
10.5 Homework Exercises<
11 Geometrical Acoustics
11.1 Basic Considerations: Wavefronts and Rays
11.1.1 Field Equations for an Inhomogeneous Fluid
11.1.2 Reflection and Refraction of Rays
11.2 Propagation in a Vertically Stratified Medium
11.2.1 Snell’s Law for Vertical Heterogeneity
11.2.2 Intensity and Focusing Factor
11.3 Arbitrary Heterogeneous Fluids
11.3.1 Ray Tracing Equations
11.3.2 Amplitude Dependence
11.4 Fermat’s Principle
11.5 Homework Exercises
12 Scattering
12.1 Background
12.2 Scattering by Heterogeneity
12.2.1 General Equations
12.2.2 The Born Approximation
12.3 Rayleigh Scattering Limit
12.3.1 The Rayleigh Limit of the Born Approximation
12.3.2 Mismatched Heterogeneous Region
12.3.3 Scattering from a Rigid Body
12.4 Measurements and Metrics
12.5 High Frequency Approximation
12.6 Scattering from Spheres
12.6.1 Stationary Spherical Scatterer
12.6.2 Scattering by an Elastic Spherical Shell
12.7 Homework Exercises
13 Nonlinear Acoustic Waves
13.1 Riemann’s Solution for Plane Waves
13.1.1 Analysis
13.1.2 Interpretation
13.1.3 Boundary and Initial Conditions
13.1.4 Equations of State
13.1.5 Quantitative Evaluations
13.2 Effects of Nonlinearity
13.2.1 Harmonic Generation
13.2.2 Shock Formation
13.2.3 Propagation of Weak Shocks
13.3 General Analytical Techniques
13.3.1 A Nonlinear Wave Equation
13.3.2 Frequency Domain Formulation
13.3.3 Regular Perturbation Series Expansion
13.3.4 Method of Strained Coordinates
13.4 Multidimensional Systems
13.4.1 Finite Amplitude Spherical Wave
13.4.2 Waves in Cartesian Coordinates
13.5 Further Studies
13.6 Homework Exercises
Appendix A: Curvilinear Coordinates
A.1 Spherical Coordinates
A.1.1 Gradient
A.1.2 Laplacian
A.1.3 Velocity and Acceleration
A.2 Cylindrical Coordinates
A.2.1 Transformations
A.2.2 Gradient
A.2.3 Laplacian
A.2.4 Velocity and Acceleration
Index