Acoustics-A Textbook for Engineers and Physicists

<div>List of Examples</div><div><br></div><div>Preface</div><div><br></div><div>7 Radiation from Vibrating Bodies</div><div>7.1 Spherical Harmonics</div><div>7.1.1 Separation of Variables</div><div>7.1.2 Description of the Pressure Field</div><div>7.1.3 Arbitrary Spatial Dependence</div><div>7.2 Radiation from a Spherical Body</div><div>7.2.1 Analysis</div><div>7.2.2 Important Limits</div><div>7.2.3 Symmetry Plane<br><div>7.2.4 Interaction with an Elastic Spherical Shell&nbsp;</div><div>7.3 Radiation from an Infinite Cylinder</div><div>7.3.1 Separation of Variables</div><div>7.3.2 Transverse Dependence-Cylindrical Bessel Functions</div><div>7.3.3 Radiation due to a Helical Surface Wave</div><div>7.3.4 Axially Periodic Surface Vibration&nbsp;</div><div>7.3.5 Finite Length Effects&nbsp;</div><div>7.4 Kirchhoff-Helmholtz Integral Theorem</div><div>7.4.1 Derivation for an Acoustic Cavity</div><div>7.4.2 Acoustic Radiation into an Exterior Domain</div><div>7.5 Numerical Methods for Radiation from Arbitrary Objects</div><div>7.5.1 Source Superposition</div><div>7.5.2 Boundary Element Method</div><div>7.5.3 Finite Element Method</div><div>7.6 Homework Exercises</div><div><br></div><div>8 Radiation from a Source in a Baffle</div><div>8.1 The Rayleigh Integral</div><div>8.2 Farfield Directivity</div><div>8.2.1 Cartesian Coordinate Description</div><div>8.2.2 Farfield of a Piston Transducer</div><div>8.3 Axial Dependence for a Circular Transducer</div><div>8.4 An Overall Picture of the Pressure Field</div><div>8.5 Radiation Impedance of a Circular Piston</div><div>8.6 Time Domain Rayleigh Integral</div><div>8.7 Homework Exercises</div><div><br></div><div>9 Modal Analysis of Waveguides</div><div>9.1 Propagation in a Horn</div><div>9.1.1 The Webster Horn Equation</div><div>9.1.2 Exponential Horn</div><div>9.1.3 Group Velocity</div><div>9.1.4 WKB Solution for an Arbitrary Horn</div><div>9.2 Two-Dimensional Waveguides</div><div>9.2.1 General Solution</div><div>9.2.2 Rigid Walls9.2.3 Interpretation</div><div>9.2.4 Flexible Walls</div><div>9.2.5 Orthogonality and Signal Generation</div><div>9.3 Three-Dimensional Waveguides</div><div>9.3.1 General Analytical Procedure</div><div>9.3.2 Rectangular Waveguide</div><div>9.3.3 Circular Waveguide</div><div>9.4 Homework Exercises</div><div><br></div><div>10 Modal Analysis of Enclosures</div><div>10.1 Fundamental Issues</div><div>10.1.1 Wall-Induced Signals</div><div>10.1.2 Source Excitation</div><div>10.2 Frequency-Domain Analysis Using Forced Cavity Modes</div><div>10.2.1 Rectangular Enclosures</div><div>10.2.2 Spherical Cavities</div><div>10.2.3 Cylindrical Enclosures</div><div>10.3 Analysis Using Natural Cavity Modes</div><div>10.3.1 Equations Governing Cavity Modes</div><div>10.3.2 Orthogonality</div><div>10.3.3 Analysis of the Pressure Field</div><div>10.3.4 Rectangular Cavity</div><div>10.3.5 Cylindrical Cavity</div><div>10.3.6 Spherical Cavity</div><div>10.4 Approximate Methods</div><div>10.4.1 The Rayleigh Ratio and Its Uses</div><div>10.4.2 Dowell’s Approximation</div><div>10.5 Homework Exercises&lt;<div><br></div><div>11 Geometrical Acoustics</div><div>11.1 Basic Considerations: Wavefronts and Rays</div><div>11.1.1 Field Equations for an Inhomogeneous Fluid</div><div>11.1.2 Reflection and Refraction of Rays</div><div>11.2 Propagation in a Vertically Stratified Medium</div><div>11.2.1 Snell’s Law for Vertical Heterogeneity</div><div>11.2.2 Intensity and Focusing Factor</div><div>11.3 Arbitrary Heterogeneous Fluids</div><div>11.3.1 Ray Tracing Equations</div><div>11.3.2 Amplitude Dependence</div><div>11.4 Fermat’s Principle</div><div>11.5 Homework Exercises</div><div><br></div><div>12 Scattering</div><div>12.1 Background</div><div>12.2 Scattering by Heterogeneity</div><div>12.2.1 General Equations</div><div>12.2.2 The Born Approximation</div><div>12.3 Rayleigh Scattering Limit</div><div>12.3.1 The Rayleigh Limit of the Born Approximation</div><div>12.3.2 Mismatched Heterogeneous Region<div>12.3.3 Scattering from a Rigid Body</div><div>12.4 Measurements and Metrics</div><div>12.5 High Frequency Approximation</div><div>12.6 Scattering from Spheres</div><div>12.6.1 Stationary Spherical Scatterer</div><div>12.6.2 Scattering by an Elastic Spherical Shell</div><div>12.7 Homework Exercises</div><div><br></div><div>13 Nonlinear Acoustic Waves</div><div>13.1 Riemann’s Solution for Plane Waves</div><div>13.1.1 Analysis</div><div>13.1.2 Interpretation</div><div>13.1.3 Boundary and Initial Conditions</div><div>13.1.4 Equations of State</div><div>13.1.5 Quantitative Evaluations</div><div>13.2 Effects of Nonlinearity</div><div>13.2.1 Harmonic Generation</div><div>13.2.2 Shock Formation</div><div>13.2.3 Propagation of Weak Shocks</div><div>13.3 General Analytical Techniques</div><div>13.3.1 A Nonlinear Wave Equation</div><div>13.3.2 Frequency Domain Formulation</div><div>13.3.3 Regular Perturbation Series Expansion</div><div>13.3.4 Method of Strained Coordinates</div>13.4 Multidimensional Systems</div><div>13.4.1 Finite Amplitude Spherical Wave</div><div>13.4.2 Waves in Cartesian Coordinates</div><div>13.5 Further Studies<br><div>13.6 Homework Exercises</div><div><br></div><div>Appendix A: Curvilinear Coordinates</div><div>A.1 Spherical Coordinates</div><div>A.1.1 Gradient</div><div>A.1.2 Laplacian</div><div>A.1.3 Velocity and Acceleration</div><div>A.2 Cylindrical Coordinates</div><div>A.2.1 Transformations</div><div>A.2.2 Gradient</div><div>A.2.3 Laplacian</div><div>A.2.4 Velocity and Acceleration</div></div></div><div><br></div><div>Index</div></div>