Formulas of Acoustics

Cover......Page 1
Formulas of Acoustics (Second Edition)......Page 4
9783540768326......Page 5
Preface to the first edition, abbreviated......Page 6
Preface to the second edition......Page 7
Contents......Page 8
Contributors......Page 20
A Conventions......Page 21
B.1 Fundamental Differential Equations......Page 25
B.2 Material Constants of Air......Page 28
B.3 General Relation for Field Admittance and Intensity......Page 31
B.4 Integral Relations......Page 32
B.5 Green’s Functions and Formalism......Page 33
B.6 Orthogonality of Modes in a Duct with Locally Reacting Walls......Page 39
B.7 Orthogonality of Modes in a Duct with Bulk Reacting Walls......Page 40
B.8 Source Conditions......Page 41
B.10 Principles of Superposition......Page 42
B.11 Hamilton’s Principle......Page 45
B.13 Vector and Tensor Formulation of Fundamentals......Page 46
B.14 Boundary Condition at a Moving Boundary......Page 58
B.15 Boundary Conditions in Liquids and Solids......Page 59
B.16 Corner Conditions......Page 60
B.17 Surface Wave at Locally Reacting Plane......Page 61
B.18 Surface Wave Along a Locally Reacting Cylinder......Page 62
B.19 Periodic Structures, Admittance Grid......Page 64
B.20 Plane Wall with Wide Grooves......Page 68
B.21 Thin Grid on Half-Infinite Porous Layer......Page 70
B.22 Grid of Finite Thickness with Narrow Slits on Half-Infinite Porous Layer......Page 73
B.23 Grid of Finite Thickness with Wide Slits on Half-Infinite Porous Layer......Page 76
References......Page 78
C.1 Fundamentals of Equivalent Networks......Page 79
C.2 Distributed Network Elements......Page 85
C.3 Elements with Constrictions......Page 91
C.5 Chain Circuit......Page 93
C.6 Partition Impedance of Orifices......Page 94
References......Page 146
D.1 Plane Wave Reflection at a Locally Reacting Plane......Page 147
D.2 Plane Wave Reflection at an Infinitely Thick Porous Layer......Page 149
D.3 Plane Wave Reflection at a Porous Layer of Finite Thickness......Page 150
D.4 Plane Wave Reflection at a Multilayer Absorber......Page 152
D.5 Diffuse Sound Reflection at a Locally Reacting Plane......Page 153
D.7 Sound Reflection and Scattering at Finite-Size Local Absorbers......Page 156
D.8 Uneven, Local Absorber Surface......Page 161
D.9 Scattering at the Border of an Absorbent Half-Plane......Page 162
D.10 Absorbent Strip in a Hard Baffle Wall, with Far Field Distribution......Page 164
D.11 Absorbent Strip in a Hard Baffle Wall, as a Variational Problem......Page 166
D.12 Absorbent Strip in a Hard Baffle Wall, with Mathieu Functions......Page 168
D.13 Absorption of Finite-Size Absorbers, as a Problem of Radiation......Page 173
D.14 A Monopole Line Source Above an Infinite, Plane Absorber; Integration Method......Page 174
D.15 A Monopole Line Source Above an Infinite, Plane Absorber; with Principle of Superposition......Page 182
D.16 A Monopole Point Source Above a Bulk Reacting Plane, Exact Forms......Page 185
D.17 A Monopole Point Source Above a Locally Reacting Plane, Exact Forms......Page 187
D.18 A Monopole Point Source Above a Locally Reacting Plane, Exact Saddle Point Integration......Page 190
D.19 A Monopole Point Source Above a Locally Reacting Plane, Approximations......Page 193
D.20 A Monopole Point Source Above a Bulk Reacting Plane, Approximations......Page 199
References to Part D......Page 203
E.1 Plane Wave Scattering at Cylinders......Page 205
E.2 Plane Wave Scattering at Cylinders and Spheres......Page 208
E.3 Multiple Scattering at Cylinders and Spheres......Page 218
E.4 Cylindrical Wave Scattering at Cylinders......Page 219
E.5 Cylindrical or Plane Wave Scattering at a Corner Surrounded by a Cylinder......Page 221
E.6 Plane Wave Scattering at a Hard Screen......Page 228
E.7 Cylindrical or Plane Wave Scattering at a Screen with an Elliptical Cylinder Atop......Page 229
E.8 Uniform Scattering at Screens and Dams......Page 234
E.9 Scattering at a Flat Dam......Page 243
E.10 Scattering at a Semicircular Absorbing Dam on Absorbing Ground......Page 246
E.11 Scattering in Random Media, General......Page 250
E.12 Function Tables for Monotype Scattering......Page 258
E.13 Sound Attenuation in a Forest......Page 262
E.14 Mixed Monotype Scattering in Random Media......Page 264
E.15 Multiple Triple-Type Scattering in Random Media......Page 268
E.16 Plane Wave Scattering at Elastic Cylindrical Shell......Page 280
E.17 Plane Wave Backscattering by a Liquid Sphere......Page 283
E.18 Spherical Wave Scattering at a Perfectly Absorbing Wedge......Page 284
E.19 Impulsive Spherical Wave Scattering at a Hard Wedge......Page 286
E.20 Spherical Wave Scattering at a Hard Screen......Page 288
E.21 Spherical Wave Scattering at a Cone......Page 290
E.22 Polar Mode Numbers at a Soft Cone......Page 295
E.23 Polar Mode Numbers at a Hard Cone......Page 299
E.24 Scattering at a Cone with Axial Sound Incidence......Page 302
References......Page 305
F.1 Definition of Radiation Impedance and End Corrections......Page 307
F.2 Some Methods to Evaluate the Radiation Impedance......Page 309
F.3 Spherical Radiators......Page 311
F.4 Cylindrical Radiators......Page 315
F.5 Piston Radiator on a Sphere......Page 317
F.6 Strip-Shaped Radiator on Cylinder......Page 319
F.7 Plane Piston Radiators......Page 321
F.9 Narrow Strip-Shaped, Field-Excited Radiator......Page 329
F.10 Wide Strip-Shaped, Field-Excited Radiator......Page 331
F.11 Wide Rectangular, Field-Excited Radiator......Page 333
F.12 End Corrections......Page 336
F.13 Piston Radiating Into a Hard Tube......Page 347
F.14 Oscillating Mass of a Fence in a Hard Tube......Page 348
F.15 A Ring-Shaped Piston in a Baffle Wall......Page 349
F.17 Directivity of Radiator Arrays......Page 350
F.18 Radiation of Finite Length Cylinder......Page 355
F.19 Monopole and Multipole Radiators......Page 357
F.20 Plane Radiator in a Baffle Wall......Page 359
F.22 Radiation of Plates with Special Excitations......Page 364
References......Page 365
G.1 Structure Parameters of Porous Materials......Page 367
G.2 Theory of the Quasi-homogeneous Material......Page 370
G.3 Rayleigh Model with Round Capillaries......Page 372
G.4 Model with Flat Capillaries......Page 374
G.5 Longitudinal Flow Resistivity in Parallel Fibres......Page 376
G.6 Longitudinal Sound in Parallel Fibres......Page 378
G.7 Transversal Flow Resistivity in Parallel Fibres......Page 380
G.8 Transversal Sound in Parallel Fibres......Page 390
G.9 Effective Wave Multiple Scattering in Transversal Fibre Bundle......Page 401
G.10 Biot’s Theory of Porous Absorbers......Page 405
G.11 Empirical Relations for Characteristic Values of Fibre Absorbers......Page 414
G.12 Characteristic Values from Theoretical Models Fitted to Experimental Data......Page 419
References......Page 422
H Compound Absorbers......Page 423
H.1 Absorber of Flat Capillaries......Page 424
H.2 Plate with Narrow Slits......Page 427
H.3 Plate with Wide Slits......Page 431
H.4 Dissipationless Slit Resonator......Page 435
H.5 Resonance Frequencies and Radiation Loss of Slit Resonators......Page 439
H.6 Slit Array with Viscous and Thermal Losses......Page 440
H.7 Slit Resonator with Viscous and Thermal Losses......Page 446
H.8 Free Plate with an Array of Circular Holes, with Losses......Page 449
H.9 Array of Helmholtz Resonators with Circular Necks......Page 455
H.10 Slit Resonator Array with Porous Layer in the Volume, Fields......Page 457
H.11 Slit Resonator Array with Porous Layer in the Volume, Impedances......Page 464
H.12 Slit Resonator Array with Porous Layer on Back Orifice......Page 469
H.13 Slit Resonator Array with Porous Layer on Front Orifice......Page 472
H.14 Array of Slit Resonators with Subdivided Neck Plate......Page 476
H.15 Array of Slit Resonators with Subdivided Neck Plate and Floating Foil in the Gap......Page 477
H.16 Array of Slit Resonators Covered with a Foil......Page 482
H.17 Poro-elastic Foils......Page 485
H.18 Foil Resonator......Page 489
H.19 Ring Resonator......Page 491
H.20 Wide-Angle Absorber, Scattered Far Field......Page 494
H.21 Wide-Angle Absorber, Near Field and Absorption......Page 500
H.22 Tight Panel Absorber, Rigorous Solution......Page 505
H.23 Tight Panel Absorber, Approximations......Page 513
H.24 Porous Panel Absorber, Rigorous Solution......Page 516
References......Page 522
I.1 “Noise Barriers”......Page 523
I.2 Sound Transmission through a Slit in a Wall......Page 526
I.3 Sound Transmission through a Hole in a Wall......Page 531
I.4 Hole Transmission with Equivalent Network......Page 535
I.5 Sound Transmission through Lined Slits in a Wall......Page 537
I.6 Chambered Joint......Page 540
I.7 “Noise Sluice”......Page 541
I.8 Sound Transmissionßindexsound transmission through plates through Plates, Some Fundamentals......Page 545
I.9 Sound Transmission through a Simple Plate......Page 552
I.10 Infinite Double-Shell Wall with Absorber Fill......Page 558
I.11 Double-Shell Wall with Thin Air Gap......Page 560
I.12 Plate with Absorber Layer Behind......Page 561
I.13 Sandwich Panels......Page 562
I.14 Finite-Size Plate......Page 571
I.15 Single Plate across a Flat Duct......Page 575
I.16 Single Plate in a Wall Niche......Page 579
I.17 Strip-Shaped Wall in Infinite Baffle Wall......Page 584
I.18 Finite-Size Plate with a Front Side Absorber Layer......Page 587
I.19 Finite-Size Plate with a Back Side Absorber Layer......Page 590
I.20 Finite-Size Double Wall with an Absorber Core......Page 591
I.21 Plenum Modes......Page 594
I.22 Sound Transmission through Suspended Ceilings......Page 597
I.23 Office Fences......Page 602
I.24 Office Fences, with Second Principle of Superposition......Page 604
I.25 Infinite Plate Between Two Different Fluids......Page 607
I.26 Sandwich Plate with an Elastic Core......Page 609
I.27 Wall of Multiple Sheets with Air Interspaces......Page 611
References......Page 614
J.1 Flat Capillary with Isothermal Boundaries......Page 615
J.3 Circular Capillary with Isothermal Boundary......Page 618
J.4 Lined Ducts, General......Page 621
J.5 Modes in Rectangular Ducts with Locally Reacting Lining......Page 625
J.6 Least Attenuated Mode in Rectangular, Locally Lined Ducts......Page 627
J.7 Sets of Mode Solutions in Rectangular, Locally Lined Ducts......Page 633
J.8 Flat Duct with a Bulk Reacting Lining......Page 639
J.9 Flat Duct with an Anisotropic, Bulk Reacting Lining......Page 641
J.10 Mode Solutions in a Flat Duct with Bulk Reacting Lining......Page 643
J.11 Flat Duct with Unsymmetrical, Locally Reacting Lining......Page 645
J.12 Flat Duct with an Unsymmetrical, Bulk Reacting Lining......Page 648
J.13 Round Duct with a Locally Reacting Lining......Page 649
J.14 Admittance of Annular Absorbers Approximated with Flat Absorbers......Page 663
J.15 Round Duct with a Bulk Reacting Lining......Page 665
J.16 Annular Ducts......Page 667
J.17 Duct with a Cross-Layered Lining......Page 670
J.18 Single Step of Duct Height and/or Duct Lining......Page 678
J.19 Sections and Cascades of Silencers, no Feedback......Page 691
J.20 A Section with Feedback Between Sections Without Feedback......Page 692
J.21 Concentrated Absorber in an Otherwise Homogeneous Lining......Page 695
J.22 Wide Splitter-Type Silencer with Locally Reacting Splitters......Page 700
J.23 Splitter-Type Silencer with Locally Reacting Splitters in a Hard Duct......Page 703
J.24 Splitter Type Silencer with Simple Porous Layers as Bulk Reacting Splitters......Page 708
J.25 Splitter-Type Silencer with Splitters of Porous Layers Covered with a Foil......Page 712
J.26 Lined Duct Corners and Junctions......Page 713
J.27 Sound Radiation from a Lined Duct Orifice......Page 717
J.28 Conical Duct Transitions; Special Case: Hard Walls......Page 722
J.29 Lined Conical Duct Transition, Evaluated with Stepping Duct Sections......Page 725
J.30 Lined Conical Duct Transition, Evaluated with Stepping Admittance Sections......Page 732
J.31 Mode Mixtures......Page 735
J.32 Mode Excitation Coefficients......Page 738
J.33 Cremer’s Admittance......Page 740
J.34 Cremer’s Admittance with Parallel Resonators......Page 745
J.35 Influence of Flow on Attenuation......Page 751
J.36 Influence of Temperature on Attenuation......Page 760
J.37 Stationary Flow Resistance of Splitter Silencers......Page 761
J.38 Non-linearities by Amplitude and/or Flow......Page 762
J.39 Flow-Induced Non-linearity of Perforated Sheets......Page 768
J.41 Mode Sets in Flat Ducts with Unsymmetrical, Locally Reacting Lining......Page 770
J.42 Mode Sets in Annular Ducts with Unsymmetrical, Locally Reacting Lining......Page 774
J.44 Bent, Flat Ducts with Locally Reacting Lining......Page 782
J.45 Lined Bow Duct Between Lined Straight Ducts......Page 795
J.46 Zero-Order and First-Order Transmission Loss of Turning-Vane Splitter Silencers......Page 801
J.47 Bent and Straight Ducts with Unsymmetrical Linings......Page 805
J.48 Silencer with Rectangular Turning-Vane Splitters......Page 807
References......Page 810
K.1 Acoustic Power in a Flow Duct......Page 813
K.2 Radiation from the Open End of a Flow Duct......Page 815
K.4 Muffler Performance Parameters......Page 816
K.5 Uniform Tube with Flow and Viscous Losses......Page 818
K.6 Sudden Area Changes......Page 819
K.7 Extended Inlet/Outlet......Page 821
K.8 Conical Tube......Page 823
K.10 Hose......Page 824
K.11 Two-Duct Perforated Elements......Page 826
K.12 Three-Duct Perforated Elements......Page 834
K.13 Three-Duct Perforated Elements with Extended Perforations......Page 840
K.14 Three-Pass (or Four-Duct) Perforated Elements......Page 845
K.15 Catalytic Converter Elements......Page 848
K.16 Helmholtz Resonator......Page 850
K.18 Bellows......Page 851
K.19 Pod Silencer......Page 852
K.20 Quincke Tube......Page 853
K.21 Annular Airgap Lined Duct......Page 854
K.22 Micro-Perforated Helmholtz Panel Parallel Baffle Muffler......Page 856
K.23 Acoustically Lined Circular Duct......Page 857
K.24 Parallel Baffle Muffler (Multipass Lined Duct)......Page 859
References......Page 860
L.1 The Energetic Approximation for the Efficiency of Capsules......Page 863
L.2 Absorbent Sound Source in a Capsule......Page 867
L.3 Semicylindrical Source and Capsule......Page 873
L.4 Hemispherical Source and Capsule......Page 877
L.5 Cabins, Semicylindrical Model......Page 881
L.6 Cabin with Plane Walls......Page 885
L.7 Cabin with Rectangular Cross Section......Page 889
References......Page 892
M.1 Eigenfunctions in Parallelepipeds......Page 893
M.2 Density of Eigenfrequencies in Rooms......Page 896
M.3 Geometrical Room Acoustics in Parallelepipeds......Page 897
M.4 Statistical Room Acoustics......Page 899
M.5.1 Foundation of Mirror Source Approximation......Page 902
M.5.2 General Criteria for Mirror Sources......Page 903
M.5.3 Field Angle of a Mirror Source......Page 904
M.5.4 Multiple Covering of MS Positions......Page 905
M.5.5 Convex Corners......Page 906
M.5.6 Interrupt Criteria in the MS Method......Page 907
M.5.8 Inside Checks......Page 908
M.5.9 What Is Needed in the Traditional MS Method?......Page 909
M.5.10 The Object......Page 910
M.5.11 A Concave Model Room, as an Example......Page 911
M.5.12 The MS Method in Rooms with Convex Corners......Page 916
M.5.13 A Model Room with Convex Corners......Page 919
M.5.14 Other Grouping of Mirror Sources......Page 923
M.5.15 Combination of Corner Fields to Obtain the Room Field......Page 926
M.5.16 Collection of the MSs of a Wall Couple in a Corner Source......Page 927
M.5.18 Limit Case of Parallel Walls......Page 930
M.5.19 The Second Principle of Superposition (PSP)......Page 933
M.5.20 The PSP for Unsymmetrical Absorption......Page 940
M.5.21 A Global Application of the PSP......Page 941
M.5.22 Reverberation Time with Results of the MS Method......Page 942
M.5.23 A Room with Concave Edges as an Example......Page 944
Appendix 1: Geometrical Subtasks......Page 946
Appendix 2: Algorithm of Mirror Source Scouting in Concave Rooms......Page 950
M.6 Ray-Tracing Models......Page 955
M.7 Room Impulse Responses, Decay Curves and Reverberation Times......Page 959
M.8 Other Room Acoustical Parameters......Page 960
References......Page 963
N.1.2 Properties of Fluids......Page 965
N.1.3 Models of Fluid Flows......Page 966
N.2.1 Averaging......Page 969
N.2.2 Decomposition (in General)......Page 970
N.2.3 Decomposition of the Physical Quantities in the Basic Equations......Page 971
N.2.5 Scales......Page 973
N.3.1 Continuity Equation, Momentum Equation, Energy Equation......Page 974
N.3.2 Thermodynamic Relationships......Page 975
N.3.3 Non-linear Perturbation Equations, non-linear Euler Equations......Page 976
N.3.4 Formulation of Euler Equations to Use in Computational Aeroacoustics (CAA)......Page 978
N.4 The Equations of Linear Acoustics......Page 980
N.5.1 Lighthill’s Inhomogeneous Wave Equation......Page 983
N.5.2 Solutions of Inhomogeneous Wave Equation......Page 985
N.6.1 Lighthill’s Representation of the Source Term with Use of Pressure......Page 987
N.6.2 Pressure-Source theory (Ribner)......Page 988
N.6.3 Pressure-Source Theory (Meecham)......Page 989
N.7.1 Phillips’s Convective Inhomogeneous Wave Equation......Page 990
N.7.2 Lilley’s Convective Inhomogeneous Wave Equation......Page 991
N.7.4 Convected Wave Equation for the Dilatation (Legendre)......Page 992
N.7.6 Goldstein-Howes Inhomogeneous Wave Equation......Page 993
N.7.7 Ribner’s Recent Reformulation of Lighthill’s Source Term......Page 994
N.7.8 Inhomogeneous Wave Equation Including Stream Function (Albring/Detsch)......Page 995
N.8.1 Powell’s Theory of Vortex Sound......Page 996
N.8.2 Howe’s Formulation of Acoustic Analogy Equation for Total Enthalpy......Page 997
N.8.4 Convected Wave Operators for Total Enthalpy in Comparison......Page 1000
N.8.5 Doak’s Theory of Aerodynamic Sound Including the Fluctuating Total Enthalpy as a Basic Generalised Acoustic Field for a Fluid......Page 1001
N.9.1 Ffowcs Williams–Hawkings (FW-H) Inhomogeneous Wave Equation, FW-H Equation in Differential and Integral Form......Page 1004
N.10.1 Acoustic Analogy in Terms of Entropy, Sound Generation by Fluctuating Heat Sources (Dowling, Howe)......Page 1008
N.10.3 Sound Power Radiated by a Turbulent Flame......Page 1011
N.10.4 Sound Generation by Turbulent Two-Phase Flow......Page 1012
N.11 Acoustics of Moving Sources......Page 1013
N.11.1 Sound Field of Moving Point Sources......Page 1014
N.11.2 Formulation of Equation of Sound Sources in Motion Based on Ffowcs Williams–Hawkings Equation......Page 1017
N.11.3 Moving Kirchhoff Surfaces......Page 1018
N.12.1 Jet Noise......Page 1020
N.12.2 Rotor Noise......Page 1027
N.13 Power Law of the Aerodynamic Sound Sources......Page 1032
References......Page 1035
O.1 Computational Optimisation of Sound Absorbers......Page 1039
O.2 Computing with Mixed Numeric-Symbolic Expressions, Illustrated with Silencer Cascades......Page 1048
O.3.1 The Radiation Problem......Page 1054
O.3.2 The Scattering Problem......Page 1056
O.3.4 The Coupled Fluid–Elastic Structure Interaction Problem......Page 1057
O.3.5 The Transmission Problem......Page 1059
O.4 The Source Simulation Technique (SST)......Page 1060
O.4.1 General Description of the Source Simulation Technique......Page 1061
O.4.2 Spherical Wave Functions and Symmetry Relations......Page 1062
O.4.3 Variants of the SST with Spherical Wave Functions......Page 1064
O.4.3.1 Null-Field-Like Equations......Page 1065
O.4.3.2 The Full-Field Equations......Page 1066
O.4.3.3 The Least Squares Minimization Technique......Page 1067
O.4.3.4 Summary: Weighting Functions and Corresponding Methods......Page 1068
O.4.3.5 Extension of the SST by Using Equivalent Sources with Complex Source Points......Page 1069
O.4.3.6 Extension of the SST to Bodies of Arbitrary Geometry......Page 1071
O.4.4 Position of Sources and Their Optimal Choice......Page 1073
O.4.5.1 Numerical Implementation......Page 1074
O.4.5.3 Calculation of Field Quantities and Sound Power......Page 1075
O.4.6 A Numerical Example: Sound Scattering from a Non-Convex Cat’s-Eye Structure......Page 1076
O.4.7 Concluding Remarks......Page 1077
O.5.1 Boundary Integral Equations......Page 1079
O.5.2 Discretization of the Boundary Integral Equation......Page 1083
O.5.3 Solution of the Linear System of Equations......Page 1084
O.5.4.1 Combined Integral Equation Formulation (CHIEF)......Page 1086
O.5.4.2 Combination with the Null-Field Equation......Page 1087
O.5.4.3 Combination with the Differentiated Integral Equation......Page 1088
O.5.4.4 Modified Green’s Functions......Page 1089
O.5.5 The Interior Problem: Sound Fields in Rooms and Half-Spaces......Page 1090
O.5.6 The Scattering and the Transmission Problem......Page 1092
O.6.1 Introduction......Page 1094
O.6.2 The Sound Field in Irregular Shaped Cavities with Rigid Walls......Page 1095
O.6.3 Supplementary Aspects and Fluid–Structure Coupling......Page 1098
O.7 The Cat’s Eye Model......Page 1101
O.7.1 Cat’s Eye Model and General Fundamental Solutions......Page 1102
O.7.2 Mode Orthogonality......Page 1105
O.7.3 Remaining Boundary Conditions......Page 1106
O.7.4 Mode Coupling Integrals......Page 1108
O.7.5 Reduction of the System of Equations......Page 1111
O.8.1 Elementary Solutions and Field Formulations......Page 1114
O.8.2 Orthogonality of Modes......Page 1115
O.8.3 Field Matching......Page 1116
O.8.5 Reduction of the Systems of Equations......Page 1118
O.8.6 Numerical Examples......Page 1119
Section O.4:......Page 1122
Section O.5:......Page 1124
Section O.6:......Page 1126
Sections O.7 & O.8:......Page 1127
Introduction......Page 1129
P.1 Eigenfrequencies of a Rigid-Walled Cavity and Modal Cut-on Frequencies of a Uniform Flat-Oval Duct with Zero Mean Fluid Flow......Page 1130
P.2 Sound Propagation in a Uniform Narrow Tube of Arbitrary Cross-Section with Zero Mean Fluid Flow......Page 1132
P.3 Sound Propagation in a Uniform, Rigid-Walled, Duct of Arbitrary Cross-Section with a Bulk-Reacting Lining and no Mean Fluid Flow: Low Frequency Approximation......Page 1137
P.4 Sound Propagation in a Uniform, Rigid-Walled, Rectangular Flow Duct Containing an Anisotropic Bulk-Reacting Wall Lining or Baffles......Page 1138
P.5 Sound Propagation in a Uniform, Rigid-Walled, Flow Duct of Arbitrary Cross-Section, with an Inhomogeneous, Anisotropic Bulk Lining......Page 1140
P.6 Sound Propagation in a Uniform Duct of Arbitrary Cross-Section with one or more Plane Flexible Walls, an Isotropic Bulk Lining and a Uniform Mean Gas Flow......Page 1144
P.7 Sound Propagation in a Rectangular Section Duct with four Flexible Walls, an Anisotropic Bulk Lining and no Mean Gas Flow......Page 1147
References......Page 1150
Q.1 Fundamental Equations of Motion......Page 1153
Q.2 Anisotropy and Isotropy......Page 1155
Q.3 Interface Conditions, Reflection and Refraction of Plane Waves......Page 1159
Q.4 Material Damping......Page 1160
Q.5.2 Surface Intensity......Page 1163
Q.5.4 Rayleigh’s Principle......Page 1164
Q.6 Random Media......Page 1165
Q.7 Periodic Media......Page 1166
Q.8.1 Bounds on Effective Moduli......Page 1168
Q.8.2 Effective Moduli for Particular Structures......Page 1169
Q.9.1 Anisotropic Media......Page 1171
Q.9.2 Isotropic Media......Page 1173
Q.10.1 Plate Waves......Page 1174
Q.10.2 Rayleigh Waves......Page 1179
Q.10.3 Waves in Thin Plates......Page 1180
Q.10.4 Waves in Thin Beams......Page 1183
Q.11 Moduli of Isotropic Materials and Related Quantities......Page 1185
Q.12 Modes of Rectangular Plates......Page 1190
Q.13 Partition Impedance of Plates......Page 1194
Q.14 Partition Impedance of Shells......Page 1196
Q.15 Density of Eigenfrequencies in Plates, Bars, Strings, Membranes......Page 1198
Q.16 Foot Point Impedances of Forces......Page 1199
Q.17 Transmission Loss at Steps, Joints, Corners......Page 1204
Q.18 Cylindrical Shell......Page 1206
Q.19 Similarity Relations for Spherical Shells......Page 1210
Q.20 Sound Radiation From Plates......Page 1211
References......Page 1214
R Ultrasound Absorption in Solids......Page 1217
R.1 Generation of Ultrasound......Page 1218
R.2 Ultrasonic attenuation......Page 1219
R.3 Absorption and Dispersion in Solids Due to Dislocations......Page 1224
R.4 Absorption Due to the Thermoelastic Effects, Phonon Scattering and Related Effects......Page 1226
R.5 Interaction of Ultrasound with Electrons in Metals......Page 1228
R.7 Absorption in Amorphous Solids and Glasses......Page 1230
R.10 Kramers-Kroning Relation......Page 1231
References......Page 1232
B. General Linear Fluid Acoustics......Page 1235
C. Equivalent Networks......Page 1237
D. Reflection of Sound......Page 1238
E. Scattering of Sound......Page 1240
F. Radiation of Sound......Page 1241
G. Porous Absorbers......Page 1243
H. Compound Absorbers......Page 1245
I. Sound Transmission......Page 1247
J. Duct Acoustics......Page 1249
K. Muffler Acoustics......Page 1253
L. Capsules and Cabins......Page 1255
M. Room Acoustics......Page 1256
N. Flow Acoustics......Page 1258
O. Analytical and Numerical Methods in Acoustics......Page 1261
P. Variational Principles in Acoustics......Page 1264
Q. Elasto-Acoustics......Page 1265
R. Ultrasound Absorption in Solids......Page 1268
General Index......Page 1271