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Wave Motion: Theory and Application

J. Billingham and A. C. King
Format
Book
Published
Cambridge : Cambridge University Press, c2000.
Language
English
ISBN
0521632579, 0521634504 (pbk.)
Contents
  • Part 1 Linear Waves 5
  • 1 Basic Ideas 7
  • 2 Waves on a Stretched String 17
  • 2.1 Derivation of the Governing Equation 17
  • 2.2 Standing Waves on Strings of Finite Length 20
  • 2.3 D'Alembert's Solution for Strings of Infinite Length 26
  • 2.4 Reflection and Transmission of Waves by Discontinuities in Density 29
  • 2.4.1 A Single Discontinuity 29
  • 2.4.2 Two Discontinuities: Impedance Matching 31
  • 3 Sound Waves 36
  • 3.1 Derivation of the Governing Equation 36
  • 3.2 Plane Waves 40
  • 3.3 Acoustic Energy Transmission 42
  • 3.4 Plane Waves In Tubes 45
  • 3.5 Acoustic Waveguides 50
  • 3.5.1 Reflection of a Plane Acoustic Wave by a Rigid Wall 50
  • 3.5.2 A Planar Waveguide 51
  • 3.5.3 A Circular Waveguide 53
  • 3.6 Acoustic Sources 57
  • 3.6.1 Acoustic Source 58
  • 3.6.2 Energy Radiated by Sources and Plane Waves 62
  • 3.7 Radiation from Sources in a Plane Wall 64
  • 4 Linear Water Waves 74
  • 4.1 Derivation of the Governing Equations 74
  • 4.2 Linear Gravity Waves 78
  • 4.2.1 Progressive Gravity Waves 78
  • 4.2.2 Standing Gravity Waves 85
  • 4.2.3 Wavemaker 87
  • 4.2.4 Extraction of Energy from Water Waves 91
  • 4.3 Effect of Surface Tension: Capillary--Gravity Waves 94
  • 4.4 Edge Waves 97
  • 4.5 Ship Waves 99
  • 4.6 Solution of Initial Value Problems 104
  • 4.7 Shallow Water Waves: Linear Theory 109
  • 4.7.1 Reflection of Sea Swell by a Step 112
  • 4.7.2 Wave Amplification at a Gently Sloping Beach 114
  • 4.8 Wave Refraction 117
  • 4.8.1 Kinematics of Slowly Varying Waves 118
  • 4.8.2 Wave Refraction at a Gently Sloping Beach 121
  • 4.9 Effect of Viscosity 123
  • 5 Waves in Elastic Solids 130
  • 5.1 Derivation of the Governing Equation 130
  • 5.2 Waves in an Infinite Elastic Body 132
  • 5.2.1 One-Dimensional Dilatation Waves 133
  • 5.2.2 One-Dimensional Rotational Waves 134
  • 5.2.3 Plane Waves with General Orientation 134
  • 5.3 Two-Dimensional Waves in Semi-infinite Elastic Bodies 135
  • 5.3.1 Normally Loaded Surface 135
  • 5.3.2 Stress-Free Surface 137
  • 5.4 Waves in Finite Elastic Bodies 143
  • 5.4.1 Flexural Waves in Plates 144
  • 5.4.2 Waves in Elastic Rods 148
  • 5.4.3 Torsional Waves 150
  • 5.4.4 Longitudinal Waves 155
  • 5.5 Excitation and Propagation of Elastic Wavefronts 156
  • 5.5.1 Wavefronts Caused by an Internal Line Force in an Unbounded Elastic Body 157
  • 5.5.2 Wavefronts Caused by a Point Force on the Free Surface of a Semi-infinite Elastic Body 161
  • 6 Electromagnetic Waves 173
  • 6.1 Electric and Magnetic Forces and Fields 173
  • 6.2 Electrostatics: Gauss's Law 177
  • 6.3 Magnetostatics: Ampere's Law and the Displacement Current 179
  • 6.4 Electromagnetic Induction: Farady's Law 180
  • 6.5 Plane Electromagnetic Waves 182
  • 6.6 Conductors and Insulators 186
  • 6.7 Reflection and Transmission at Interfaces 189
  • 6.7.1 Boundary Conditions at Interfaces 189
  • 6.7.2 Reflection by a Perfect Conductor 191
  • 6.7.3 Reflection and Refraction by Insulators 194
  • 6.8 Waveguides 199
  • 6.8.1 Metal Waveguides 199
  • 6.8.2 Weakly Guiding Optical Fibres 202
  • 6.9 Radiation 208
  • 6.9.1 Scalar and Vector Potentials 208
  • 6.9.2 Electric Dipole 210
  • 6.9.3 Far Field of a Localised Current Distribution 212
  • 6.9.4 Centre Fed Linear Antenna 213
  • Part 2 Nonlinear Waves 219
  • 7 Formation and Propagation of Shock Waves 221
  • 7.1 Traffic Waves 221
  • 7.1.1 Derivation of the Governing Equation 221
  • 7.1.2 Small Amplitude Disturbances of a Uniform State 224
  • 7.1.3 Nonlinear Initial Value Problem 226
  • 7.1.4 Speed of the Shock 236
  • 7.2 Compressible Gas Dynamics 239
  • 7.2.1 Some Essential Thermodynamics 239
  • 7.2.2 Equations of Motion 243
  • 7.2.3 Construction of the Characteristic Curves 245
  • 7.2.4 Rankine--Hugoniot Relations 249
  • 7.2.5s Detonations 256
  • 8 Nonlinear Water Waves 269
  • 8.1 Nonlinear Shallow Water Waves 269
  • 8.1.1 Dam Break Problem 270
  • 8.1.2 A Shallow Water Bore 275
  • 8.2 Effect of Nonlinearity on Deep Water Gravity Waves: Stokes' Expansion 280
  • 8.3 Korteweg-de Vries Equation for Shallow Water Waves: the Interaction of Nonlinear Steepening and Linear Dispersion 285
  • 8.3.1 Derivation of the Korteweg-de Vries Equation 287
  • 8.3.2 Travelling Wave Solutions of the KdV Equation 290
  • 8.4 Nonlinear Capillary Waves 298
  • 9 Chemical and Electrochemical Waves 308
  • 9.1 Law of Mass Action 310
  • 9.2 Molecular Diffusion 314
  • 9.3 Reaction-Diffusion Systems 315
  • 9.4 Autocatalytic Chemical Waves with Unequal Diffusion Coefficients* 326
  • 9.4.1 Existence of Travelling Wave Solutions 327
  • 9.4.2 Asymptotic Solution for [delta] << 1 330
  • 9.5 Transmission of Nerve Impulses: the Fitzhugh-Nagumo Equations 334
  • 9.5.1 Fitzhugh-Nagumo Model 339
  • 9.5.2 Existence of a Threshold 342
  • 9.5.3 Travelling Waves 343
  • Part 3 Advanced Topics 355
  • 10 Burgers' Equation: Competition between Wave Steepening and Wave Spreading 357
  • 10.1 Burgers' Equation for Traffic Flow 357
  • 10.2 Effect of Dissipation on Weak Shock Waves in an Ideal Gas 362
  • 10.3 Simple Solutions of Burgers' Equation 369
  • 10.3.1 Travelling Waves 369
  • 10.3.2 Asymptotic Solutions for v << 1 370
  • 11 Diffraction and Scattering 378
  • 11.1 Diffraction of Acoustic Waves by a Semi-infinite Barrier 379
  • 11.1.1 Preliminary Estimates of the Potential 380
  • 11.1.2 Pre-transform Considerations 383
  • 11.1.3 Fourier Transform Solution 385
  • 11.2 Diffraction of Waves by an Aperture 391
  • 11.2.1 Scalar Diffraction: Acoustic Waves 391
  • 11.2.2 Vector Diffraction: Electromagnetic Waves 394
  • 11.3 Scattering of Linear, Deep Water Waves by a Surface Piercing Cylinder 399
  • 12 Solitons and the Inverse Scattering Transform 405
  • 12.1 Korteweg-de Vries Equation 406
  • 12.1.1 Scattering Problem 406
  • 12.1.2 Inverse Scattering Problem 410
  • 12.1.3 Scattering Data for KdV Potentials 416
  • 12.1.4 Examples: Solutions of the KdV Equation 418
  • 12.2 Nonlinear Schrodinger Equation 424
  • 12.2.1 Derivation of the Nonlinear Schrodinger Equation for Plane Electromagnetic Waves 424
  • 12.2.2 Solitary Wave Solutions of the Nonlinear Schrodinger Equation 431
  • 12.2.3 Inverse Scattering Transform for the Nonlinear Schrodinger Equation 435
  • Appendix 1 Useful Mathematical Formulas and Physical Data 451
  • A1.1 Cartesian Coordinates 451
  • A1.2 Cylindrical Polar Coordinates 451
  • A1.3 Spherical Polar Coordinates 452
  • A1.4 Some Vector Calculus Identities and Useful Results for Smooth Vector Fields 453
  • A1.5 Physical constants 454.
Description
475 p., [3] p. of plates : ill. ; 23 cm.
Notes
Includes bibliographical references and index.
Technical Details
  • Access in Virgo Classic
  • Staff View

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    g| Part 1 t| Linear Waves g| 5 -- g| 1 t| Basic Ideas g| 7 -- g| 2 t| Waves on a Stretched String g| 17 -- g| 2.1 t| Derivation of the Governing Equation g| 17 -- g| 2.2 t| Standing Waves on Strings of Finite Length g| 20 -- g| 2.3 t| D'Alembert's Solution for Strings of Infinite Length g| 26 -- g| 2.4 t| Reflection and Transmission of Waves by Discontinuities in Density g| 29 -- g| 2.4.1 t| A Single Discontinuity g| 29 -- g| 2.4.2 t| Two Discontinuities: Impedance Matching g| 31 -- g| 3 t| Sound Waves g| 36 -- g| 3.1 t| Derivation of the Governing Equation g| 36 -- g| 3.2 t| Plane Waves g| 40 -- g| 3.3 t| Acoustic Energy Transmission g| 42 -- g| 3.4 t| Plane Waves In Tubes g| 45 -- g| 3.5 t| Acoustic Waveguides g| 50 -- g| 3.5.1 t| Reflection of a Plane Acoustic Wave by a Rigid Wall g| 50 -- g| 3.5.2 t| A Planar Waveguide g| 51 -- g| 3.5.3 t| A Circular Waveguide g| 53 -- g| 3.6 t| Acoustic Sources g| 57 -- g| 3.6.1 t| Acoustic Source g| 58 -- g| 3.6.2 t| Energy Radiated by Sources and Plane Waves g| 62 -- g| 3.7 t| Radiation from Sources in a Plane Wall g| 64 -- g| 4 t| Linear Water Waves g| 74 -- g| 4.1 t| Derivation of the Governing Equations g| 74 -- g| 4.2 t| Linear Gravity Waves g| 78 -- g| 4.2.1 t| Progressive Gravity Waves g| 78 -- g| 4.2.2 t| Standing Gravity Waves g| 85 -- g| 4.2.3 t| Wavemaker g| 87 -- g| 4.2.4 t| Extraction of Energy from Water Waves g| 91 -- g| 4.3 t| Effect of Surface Tension: Capillary--Gravity Waves g| 94 -- g| 4.4 t| Edge Waves g| 97 -- g| 4.5 t| Ship Waves g| 99 -- g| 4.6 t| Solution of Initial Value Problems g| 104 -- g| 4.7 t| Shallow Water Waves: Linear Theory g| 109 -- g| 4.7.1 t| Reflection of Sea Swell by a Step g| 112 -- g| 4.7.2 t| Wave Amplification at a Gently Sloping Beach g| 114 -- g| 4.8 t| Wave Refraction g| 117 -- g| 4.8.1 t| Kinematics of Slowly Varying Waves g| 118 -- g| 4.8.2 t| Wave Refraction at a Gently Sloping Beach g| 121 -- g| 4.9 t| Effect of Viscosity g| 123 -- g| 5 t| Waves in Elastic Solids g| 130 -- g| 5.1 t| Derivation of the Governing Equation g| 130 -- g| 5.2 t| Waves in an Infinite Elastic Body g| 132 -- g| 5.2.1 t| One-Dimensional Dilatation Waves g| 133 -- g| 5.2.2 t| One-Dimensional Rotational Waves g| 134 -- g| 5.2.3 t| Plane Waves with General Orientation g| 134 -- g| 5.3 t| Two-Dimensional Waves in Semi-infinite Elastic Bodies g| 135 -- g| 5.3.1 t| Normally Loaded Surface g| 135 -- g| 5.3.2 t| Stress-Free Surface g| 137 -- g| 5.4 t| Waves in Finite Elastic Bodies g| 143 -- g| 5.4.1 t| Flexural Waves in Plates g| 144 -- g| 5.4.2 t| Waves in Elastic Rods g| 148 -- g| 5.4.3 t| Torsional Waves g| 150 -- g| 5.4.4 t| Longitudinal Waves g| 155 -- g| 5.5 t| Excitation and Propagation of Elastic Wavefronts g| 156 -- g| 5.5.1 t| Wavefronts Caused by an Internal Line Force in an Unbounded Elastic Body g| 157 -- g| 5.5.2 t| Wavefronts Caused by a Point Force on the Free Surface of a Semi-infinite Elastic Body g| 161 -- g| 6 t| Electromagnetic Waves g| 173 -- g| 6.1 t| Electric and Magnetic Forces and Fields g| 173 -- g| 6.2 t| Electrostatics: Gauss's Law g| 177 -- g| 6.3 t| Magnetostatics: Ampere's Law and the Displacement Current g| 179 -- g| 6.4 t| Electromagnetic Induction: Farady's Law g| 180 -- g| 6.5 t| Plane Electromagnetic Waves g| 182 -- g| 6.6 t| Conductors and Insulators g| 186 -- g| 6.7 t| Reflection and Transmission at Interfaces g| 189 -- g| 6.7.1 t| Boundary Conditions at Interfaces g| 189 -- g| 6.7.2 t| Reflection by a Perfect Conductor g| 191 -- g| 6.7.3 t| Reflection and Refraction by Insulators g| 194 -- g| 6.8 t| Waveguides g| 199 -- g| 6.8.1 t| Metal Waveguides g| 199 -- g| 6.8.2 t| Weakly Guiding Optical Fibres g| 202 -- g| 6.9 t| Radiation g| 208 -- g| 6.9.1 t| Scalar and Vector Potentials g| 208 -- g| 6.9.2 t| Electric Dipole g| 210 -- g| 6.9.3 t| Far Field of a Localised Current Distribution g| 212 -- g| 6.9.4 t| Centre Fed Linear Antenna g| 213 -- g| Part 2 t| Nonlinear Waves g| 219 -- g| 7 t| Formation and Propagation of Shock Waves g| 221 -- g| 7.1 t| Traffic Waves g| 221 -- g| 7.1.1 t| Derivation of the Governing Equation g| 221 -- g| 7.1.2 t| Small Amplitude Disturbances of a Uniform State g| 224 -- g| 7.1.3 t| Nonlinear Initial Value Problem g| 226 -- g| 7.1.4 t| Speed of the Shock g| 236 -- g| 7.2 t| Compressible Gas Dynamics g| 239 -- g| 7.2.1 t| Some Essential Thermodynamics g| 239 -- g| 7.2.2 t| Equations of Motion g| 243 -- g| 7.2.3 t| Construction of the Characteristic Curves g| 245 -- g| 7.2.4 t| Rankine--Hugoniot Relations g| 249 -- g| 7.2.5s t| Detonations g| 256 -- g| 8 t| Nonlinear Water Waves g| 269 -- g| 8.1 t| Nonlinear Shallow Water Waves g| 269 -- g| 8.1.1 t| Dam Break Problem g| 270 -- g| 8.1.2 t| A Shallow Water Bore g| 275 -- g| 8.2 t| Effect of Nonlinearity on Deep Water Gravity Waves: Stokes' Expansion g| 280 -- g| 8.3 t| Korteweg-de Vries Equation for Shallow Water Waves: the Interaction of Nonlinear Steepening and Linear Dispersion g| 285 -- g| 8.3.1 t| Derivation of the Korteweg-de Vries Equation g| 287 -- g| 8.3.2 t| Travelling Wave Solutions of the KdV Equation g| 290 -- g| 8.4 t| Nonlinear Capillary Waves g| 298 -- g| 9 t| Chemical and Electrochemical Waves g| 308 -- g| 9.1 t| Law of Mass Action g| 310 -- g| 9.2 t| Molecular Diffusion g| 314 -- g| 9.3 t| Reaction-Diffusion Systems g| 315 -- g| 9.4 t| Autocatalytic Chemical Waves with Unequal Diffusion Coefficients* g| 326 -- g| 9.4.1 t| Existence of Travelling Wave Solutions g| 327 -- g| 9.4.2 t| Asymptotic Solution for [delta] << 1 g| 330 -- g| 9.5 t| Transmission of Nerve Impulses: the Fitzhugh-Nagumo Equations g| 334 -- g| 9.5.1 t| Fitzhugh-Nagumo Model g| 339 -- g| 9.5.2 t| Existence of a Threshold g| 342 -- g| 9.5.3 t| Travelling Waves g| 343 -- g| Part 3 t| Advanced Topics g| 355 -- g| 10 t| Burgers' Equation: Competition between Wave Steepening and Wave Spreading g| 357 -- g| 10.1 t| Burgers' Equation for Traffic Flow g| 357 -- g| 10.2 t| Effect of Dissipation on Weak Shock Waves in an Ideal Gas g| 362 -- g| 10.3 t| Simple Solutions of Burgers' Equation g| 369 -- g| 10.3.1 t| Travelling Waves g| 369 -- g| 10.3.2 t| Asymptotic Solutions for v << 1 g| 370 -- g| 11 t| Diffraction and Scattering g| 378 -- g| 11.1 t| Diffraction of Acoustic Waves by a Semi-infinite Barrier g| 379 -- g| 11.1.1 t| Preliminary Estimates of the Potential g| 380 -- g| 11.1.2 t| Pre-transform Considerations g| 383 -- g| 11.1.3 t| Fourier Transform Solution g| 385 -- g| 11.2 t| Diffraction of Waves by an Aperture g| 391 -- g| 11.2.1 t| Scalar Diffraction: Acoustic Waves g| 391 -- g| 11.2.2 t| Vector Diffraction: Electromagnetic Waves g| 394 -- g| 11.3 t| Scattering of Linear, Deep Water Waves by a Surface Piercing Cylinder g| 399 -- g| 12 t| Solitons and the Inverse Scattering Transform g| 405 -- g| 12.1 t| Korteweg-de Vries Equation g| 406 -- g| 12.1.1 t| Scattering Problem g| 406 -- g| 12.1.2 t| Inverse Scattering Problem g| 410 -- g| 12.1.3 t| Scattering Data for KdV Potentials g| 416 -- g| 12.1.4 t| Examples: Solutions of the KdV Equation g| 418 -- g| 12.2 t| Nonlinear Schrodinger Equation g| 424 -- g| 12.2.1 t| Derivation of the Nonlinear Schrodinger Equation for Plane Electromagnetic Waves g| 424 -- g| 12.2.2 t| Solitary Wave Solutions of the Nonlinear Schrodinger Equation g| 431 -- g| 12.2.3 t| Inverse Scattering Transform for the Nonlinear Schrodinger Equation g| 435 -- g| Appendix 1 t| Useful Mathematical Formulas and Physical Data g| 451 -- g| A1.1 t| Cartesian Coordinates g| 451 -- g| A1.2 t| Cylindrical Polar Coordinates g| 451 -- g| A1.3 t| Spherical Polar Coordinates g| 452 -- g| A1.4 t| Some Vector Calculus Identities and Useful Results for Smooth Vector Fields g| 453 -- g| A1.5 t| Physical constants g| 454.
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    a| Wave-motion, Theory of.
    700
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    a| King, A. C.
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    a| QA927 .B539 2000 w| LC i| X004474331 l| STACKS m| SCI-ENG t| BOOK
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