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Acoustics of Musical Instruments 1st ed. 2016 [Kõva köide]

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  • Formaat: Hardback, 844 pages, kõrgus x laius: 235x155 mm, kaal: 1871 g, 355 Illustrations, color; 2 Illustrations, black and white; XXV, 844 p. 357 illus., 355 illus. in color., 1 Hardback
  • Sari: Modern Acoustics and Signal Processing
  • Ilmumisaeg: 22-Apr-2016
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1493936778
  • ISBN-13: 9781493936779
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Acoustics of Musical Instruments 1st ed. 2016Suurem pilt
  • Formaat: Hardback, 844 pages, kõrgus x laius: 235x155 mm, kaal: 1871 g, 355 Illustrations, color; 2 Illustrations, black and white; XXV, 844 p. 357 illus., 355 illus. in color., 1 Hardback
  • Sari: Modern Acoustics and Signal Processing
  • Ilmumisaeg: 22-Apr-2016
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1493936778
  • ISBN-13: 9781493936779
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781493936779.html
Märksõnad:

This book, the first English-language translation of Acoustique des instruments de musique, Second Edition, presents the necessary foundations for understanding the complex physical phenomena involved in musical instruments. What is the function of the labium in a flute? Which features of an instrument allow us to make a clear audible distinction between a clarinet and a trumpet? With the help of numerous examples, these questions are addressed in detail. The authors focus in particular on the significant results obtained in the field during the last fifteen years. Their goal is to show that elementary physical models can be used with benefit for various applications in sound synthesis, instrument making, and sound recording. The book is primarily addressed to graduate students and researchers; however it could also be of interest for engineers, musicians, craftsmen, and music lovers who wish to learn about the basics of musical acoustics. 

Arvustused

This book is a great repository of state of the art knowledge. It is a handbook for looking-up concepts, derivations and mathematical methodologies currently developed and employed in the field of musical acoustics. This book is a handbook and a great reference for researchers and PhD level graduate students . This book will definitely become a classic like the one by Fletcher and Rossing . (Wilfried Kausel, Euracoustics.org, April, 2017)

Antoine Chaigne and Jean Kergomard have applied mathematical rigor with comprehensive scope, and the result is remarkable. The text and math are lucid throughout and should be easily understood by readers with a basic grasp of mechanics. The authors are justified in recommending the book to students at masters and doctorate levels [ and] researchers, engineers and other physicists with a strong interest in musiceach of those groups will find the information they need in Acoustics of Musical Instruments. (Barry Greenhut, Physics Today, April, 2017)

Each author has extensive research experience, a publication record of note, familiarity with the literature, and interaction with French and international colleagues. Acoustics of Musical Instruments provides a quantitative analysis of many instruments found in the classical repertoire. The text will be of use to players, including students and instructors, and those concerned with the physical production of sound from these instruments, including makers of real and simulated instruments. (William Strong, Journal of the Audio Engineering Society, Vol. 65 (1-2), January, 2017)

Part I Basic Equations and Oscillators
1 Continuous Models
3(74)
Antoine Chaigne
Jean Kergomard
1.1 Strings, Membranes, Bars, Plates, and Shells
3(29)
1.1.1 Introduction
3(2)
1.1.2 Membranes and Strings
5(4)
1.1.3 Stress and Strain
9(3)
1.1.4 Constitutive Equations of Materials: Linear Elasticity
12(4)
1.1.5 Bars and Plates
16(10)
1.1.6 Equation of Shells
26(6)
1.2 3D Acoustic Waves
32(9)
1.2.1 State Equation of a Gas
33(1)
1.2.2 Momentum Conservation
34(3)
1.2.3 Conservation of Mass
37(1)
1.2.4 Acoustic Wave Equation
37(1)
1.2.5 Simple Solutions: Traveling and Standing Waves
38(3)
1.3 Energy, Intensity, and Power
41(4)
1.3.1 Example of the Vibrating String
41(2)
1.3.2 Example of Linear Acoustic Waves
43(1)
1.3.3 Power and Impedance
43(2)
1.4 Sources in Musical Acoustics: Excitation Mechanisms
45(15)
1.4.1 Generalities About Sources and Types of Oscillations
46(1)
1.4.2 Acoustic Sources
47(3)
1.4.3 Transient Mechanical Excitation
50(10)
1.5 Lumped Elements; Helmholtz Resonator
60(3)
1.6 Vibrating Strings-Sound Pipes Analogies
63(4)
1.6.1 Note on the Definition of Impedances for Forced Oscillations
66(1)
1.7 Numerical Methods
67(10)
1.7.1 Finite Difference Methods
67(3)
1.7.2 Finite Element Method
70(3)
References
73(4)
2 Single-Degree-of-Freedom Oscillator
77(24)
Antoine Chaigne
Jean Kergomard
2.1 Introduction
77(2)
2.2 Solution With and Without a Source: Green's Function
79(5)
2.2.1 Solution Without a Source; Eigenfrequency
79(2)
2.2.2 Solution with an Elementary Source: Green's Function
81(1)
2.2.3 General Solution with a Source Term
82(2)
2.3 Examples of Free and Forced Oscillations
84(3)
2.3.1 Displacement of a System from Equilibrium
84(1)
2.3.2 Excitation (Forced) by a Steady Sinusoidal Force
84(1)
2.3.3 Excitation by a Sinusoidal Force Starting at t = 0
85(1)
2.3.4 Excitation by a Sinusoidal Force Stopping at t = 0
86(1)
2.4 Forced Oscillations: Frequency Response
87(5)
2.4.1 Remarks on the Determination of the Resonance Frequency
90(2)
2.5 Energy, Power, and Efficiency
92(9)
2.5.1 Energy and Power
92(3)
2.5.2 Mechanical Air Loaded Oscillator
95(6)
Part II Waves and Modes
3 Modes
101(72)
Antoine Chaigne
Jean Kergomard
3.1 Introduction
101(2)
3.2 Time Scale: Transition from Wave to Mode
103(1)
3.3 Definitions and Basic Properties of the Eigenmodes
104(5)
3.3.1 Discrete System
104(4)
3.3.2 Extension to Continuous Systems
108(1)
3.4 Application to Vibrating Strings
109(34)
3.4.1 Heterogeneous String
110(5)
3.4.2 Ideal String Fixed at Both Ends
115(1)
3.4.3 Initial Conditions and Starting Transients
116(1)
3.4.4 Plucked String
116(5)
3.4.5 String with a Moving End
121(8)
3.4.6 Influence of Spatial Width and Duration of the Excitation
129(3)
3.4.7 Struck String
132(1)
3.4.8 Driving-Point and Transfer Admittance
132(7)
3.4.9 Strings of Bowed Instruments
139(4)
3.5 Application to Percussion Instruments
143(30)
3.5.1 Vibration of Beams
143(9)
3.5.2 Vibrations of Membranes In Vacuo
152(4)
3.5.3 Transverse Vibrations of Thin Plates
156(9)
3.5.4 Vibrations of Shells
165(5)
References
170(3)
4 Waves
173(26)
Antoine Chaigne
Jean Kergomard
4.1 Introduction
173(1)
4.2 Solutions Without Source, First Reflection
174(2)
4.3 Successive Reflections of Waves Produced by a Pulse Source
176(4)
4.3.1 General Expression
176(2)
4.3.2 Reflections and Modes Periodicity
178(1)
4.3.3 Remark on the Reflection Function (4.3)
179(1)
4.4 One-Dimensional Green's Function
180(3)
4.4.1 Expression of the Green's Function
180(1)
4.4.2 Approximated "Practical" Realization
180(3)
4.5 Solutions Without Source in the Frequency Domain; Transmission Lines
183(3)
4.6 Green's Function in Sinusoidal Regime: the Particular Case of the Input Impedance
186(13)
4.6.1 Closed-Form Solution of the Green's Function
186(4)
4.6.2 Modal Expansion
190(3)
4.6.3 The Particular Case of a Source at the Input: Input Impedance
193(1)
4.6.4 Closed-Form Expression: Back to the Time Domain
194(3)
References
197(2)
5 Dissipation and Damping
199(60)
Antoine Chaigne
Jean Kergomard
5.1 Introduction: Dissipative Phenomena in Musical Acoustics
199(1)
5.2 Generalizing the Concept of Mode
200(18)
5.2.1 Dissipative Discrete System
201(6)
5.2.2 Continuous Systems
207(7)
5.2.3 Continuous Complex Modes
214(4)
5.3 Damping Mechanisms in Solid Materials
218(11)
5.3.1 Introduction
218(1)
5.3.2 String Damping Due to Air Viscosity
219(1)
5.3.3 Thermoelasticity in Orthotropic Plates
220(4)
5.3.4 Viscoelasticity
224(4)
5.3.5 Hysteretic Damping
228(1)
5.4 Damping Mechanisms in Cylindrical Pipes
229(10)
5.4.1 Introduction
229(2)
5.4.2 Viscous Effects
231(3)
5.4.3 Thermal Conduction Effects
234(4)
5.4.4 Radiation Dissipation at the Open End of the Pipe
238(1)
5.5 Transmission Line Equations
239(10)
5.5.1 General Equations and Solutions
239(2)
5.5.2 Numerical Values of Main Constants in Air
241(1)
5.5.3 "Wide" Pipes
241(7)
5.5.4 "Narrow" Pipes
248(1)
5.6 Modes of a (Reed) Cylindrical Instrument
249(10)
5.6.1 Presentation
249(1)
5.6.2 Modes Orthogonality Method (Without Radiation)
250(2)
5.6.3 Residue Calculus (Taking Radiation into Account)
252(3)
References
255(4)
6 Coupled Systems
259(36)
Antoine Chaigne
Jean Kergomard
6.1 Introduction
259(1)
6.2 Structure-Cavity Interaction
260(12)
6.2.1 Mechanical Oscillator Coupled to a Pipe
260(4)
6.2.2 Soundboard-Cavity Coupling in Stringed Instruments at Low Frequencies
264(8)
6.3 Coupling of Piano Strings
272(10)
6.3.1 General Equations of the Problem
273(4)
6.3.2 Formulation of the Problem in Terms of Forces
277(1)
6.3.3 Eigenvalues of the Strings-Bridge Coupled System
278(2)
6.3.4 Bridge Motion
280(2)
6.4 String-Soundboard Coupling
282(8)
6.4.1 Determination of Mass and Stiffness Matrices
283(2)
6.4.2 Mode Crossing
285(4)
6.4.3 Musical Consequences of the Coupling
289(1)
6.5 Soundboard-Bridge Coupling in Violins
290(5)
References
294(1)
7 Wind Instruments: Variable Cross Section and Toneholes
295(100)
Jean Kergomard
7.1 Introduction
295(1)
7.2 Pipes with Variable Cross Section: General Equations
296(5)
7.2.1 Horn Equation
296(2)
7.2.2 Orthogonality of Modes
298(1)
7.2.3 Horn Equation with Boundary Layer Effects
299(1)
7.2.4 Lumped Elements of Horns
299(1)
7.2.5 Modal Expansion of the Input Impedance
300(1)
7.3 Pipes with Cross Section Discontinuities: First Approximation
301(21)
7.3.1 Elementary Model: Example of the Eigenfrequencies Equation: the Helmholtz Resonance
301(3)
7.3.2 Waves: Successive Reflections
304(3)
7.3.3 Modes of a Chimney Pipe: The Case of a Reed Instrument
307(5)
7.3.4 Brass Instrument Mouthpiece
312(5)
7.3.5 Cylindrical Instrument with Flute Mouthpiece
317(5)
7.4 Conical Instruments
322(14)
7.4.1 Equations and Solutions for a Lossless Conical Resonator
322(2)
7.4.2 Validity of the Horn Equation for a Truncated Cone
324(1)
7.4.3 Transfer Matrix of a Truncated Cone
325(1)
7.4.4 Eigenfrequencies: Elementary Approximations
325(3)
7.4.5 Equations with "Averaged" Losses, Transfer Matrices
328(1)
7.4.6 Modal Expansion for a Conical Reed Instrument
329(5)
7.4.7 Changes in Conicity
334(2)
7.5 Tubes with Variable Cross Section
336(11)
7.5.1 Bells of Brass Instruments: Analytical Solution
336(5)
7.5.2 Numerical Solution of the Horn Equation for Woodwinds and Brass Instruments
341(6)
7.6 Duct Modes and Simple Discontinuities
347(17)
7.6.1 Cavity Modes and Duct Modes: Cartesian Geometry
347(4)
7.6.2 Cylindrical Duct Modes
351(2)
7.6.3 Cross Section Discontinuities and Diaphragms
353(11)
7.7 Generalized Junction of Waveguides: Application to Toneholes
364(13)
7.7.1 Overview
364(2)
7.7.2 Two Waveguides Converging Into a Third
366(1)
7.7.3 Right-Angle Bends
367(2)
7.7.4 Bends in Cylindrical Tubes
369(1)
7.7.5 Toneholes and Derivations
370(7)
7.8 Lattice of Toneholes
377(18)
7.8.1 Generalities About the Waves in a Periodic Medium
378(2)
7.8.2 Periodic Lattice of Open Holes
380(9)
References
389(6)
Part III Nonlinearities and Self-Oscillations
8 Nonlinearities
395(74)
Antoine Chaigne
Joel Gilbert
Jean-Pierre Dalmont
Cyril Touze
8.1 An Example of Asymmetry: The Interrupted Pendulum
396(4)
8.1.1 Equation of Motion
397(1)
8.1.2 Solution by a Perturbation Method
397(3)
8.2 Duffing Equation
400(7)
8.2.1 Example
401(1)
8.2.2 Solutions for the Forced Duffing Oscillator
402(4)
8.2.3 Generation of Subharmonics
406(1)
8.3 Nonlinear Vibrations of Strings
407(12)
8.3.1 Simplified Equations of Motion
408(2)
8.3.2 Forced Vibrations
410(1)
8.3.3 Transverse-Longitudinal Coupling: Simplified Approach
411(3)
8.3.4 Exact Geometrical Model of Piano Strings with Intrinsic Stiffness
414(5)
8.4 Nonlinearities in Wind Instruments Resonators
419(10)
8.4.1 Nonlinear Propagation
419(4)
8.4.2 Nonlinear Distortion and Shock Waves, Method of Characteristics
423(1)
8.4.3 Competition Between Nonlinear Effects and Dissipation
424(1)
8.4.4 Shock Waves and Brassy Sounds
425(2)
8.4.5 Localized Nonlinear Dissipation
427(2)
8.5 Geometric Nonlinearities in Gongs and Cymbals
429(20)
8.5.1 Sinusoidal Forced Excitation
431(3)
8.5.2 Internal Resonances
434(1)
8.5.3 Weakly Nonlinear Regime
435(1)
8.5.4 Energy Transfer Through Combination of Resonances
436(7)
8.5.5 Nonlinear Mechanical Model
443(6)
8.6 Chaotic Regime
449(7)
8.6.1 Degrees of Freedom
450(4)
8.6.2 Characterization of Chaos: Lyapunov Exponents
454(2)
8.7 Nonlinear Normal Modes
456(13)
8.7.1 Introduction
456(1)
8.7.2 First Approach of Nonlinear Normal Modes
457(1)
8.7.3 Invariant Manifolds
458(3)
8.7.4 Calculation of Nonlinear Normal Modes
461(2)
8.7.5 Conclusion
463(1)
References
464(5)
9 Reed Instruments
469(90)
Jean Kergomard
9.1 Background on Self-Sustained Oscillations
470(2)
9.2 Reed Instruments Models
472(17)
9.2.1 Introduction
472(1)
9.2.2 Mechanical Response of a Reed: Experimental Data
473(5)
9.2.3 Dynamic of the Fluid Passing the Reed
478(4)
9.2.4 Reed Opening Area and Flow Rate
482(2)
9.2.5 Basic Model (Clarinet-Like Reed)
484(4)
9.2.6 Basic Model (Lip Reed)
488(1)
9.3 Behavior of the Two-Equation Model (Regimes, Existence and Stability, Transients) Without Reed Dynamics
489(16)
9.3.1 Introduction
489(1)
9.3.2 Static Regime and "Ab Initio" Method
490(3)
9.3.3 Lossless Approximation for a Cylinder: Helmholtz Motion
493(8)
9.3.4 One-Mode Approximation
501(4)
9.4 Away from the Reed Resonance (Two-Equation Model): Steady-State Regimes
505(31)
9.4.1 Principle of the Harmonic Balance Method: First Harmonic Approximation
505(3)
9.4.2 Characteristic Equation and Instability Threshold of the Static Regime
508(1)
9.4.3 The Harmonic Balance Method: An Overview
509(1)
9.4.4 The Variable Truncation Method, and Its Application to Clarinet-Like Instruments
510(7)
9.4.5 Variation of the Playing Frequency with the Excitation Level
517(2)
9.4.6 Beating Reed and Sound Extinction
519(4)
9.4.7 Miscellaneous Considerations About Clarinet-Like Instruments
523(1)
9.4.8 Conical Reed Instruments
524(12)
9.5 Behavior of the 3-Equation Model with Reed Dynamics (Non-beating Reed)
536(23)
9.5.1 Introduction
536(1)
9.5.2 Oscillation Threshold for an Inward-Striking Reed
537(10)
9.5.3 Oscillation Threshold for an Outward-Striking Reed
547(2)
9.5.4 Modal Approach of the Dynamical System
549(1)
9.5.5 Discussion of the Results
550(2)
References
552(7)
10 Flute-Like Instruments
559(48)
Benoit Fabre
10.1 Introduction and General Description
559(7)
10.1.1 The Air Jet, Driving the Oscillation in Flutes
560(4)
10.1.2 The Sounds of Flutes
564(2)
10.2 A Global Model for the Instrument
566(5)
10.2.1 General Description
566(1)
10.2.2 Important Parameters
567(2)
10.2.3 Localized or Distributed Interaction?
569(2)
10.3 A Modeling for the Jet Oscillation
571(15)
10.3.1 Jet Formation
571(4)
10.3.2 Jet Instability
575(10)
10.3.3 Turbulent Jet
585(1)
10.4 Aeroacoustic Sound Sources
586(11)
10.4.1 The Jet-Drive Model
587(2)
10.4.2 A Discrete Vortex Model
589(2)
10.4.3 Aeroacoustic Formulation
591(6)
10.5 A Lumped Model of the Oscillation in a Flute
597(6)
10.5.1 Nonlinear Losses at the Blowing Window
597(1)
10.5.2 Jet Velocities Fluctuations
598(3)
10.5.3 Direct Hydrodynamic Feedback
601(1)
10.5.4 The Minimal Oscillator
601(2)
10.6 Discussion About the Model
603(4)
References
605(2)
11 Bowed String Instruments
607(28)
Xavier Boutillon
11.1 Introduction
607(2)
11.2 Bow-String Interaction
609(4)
11.2.1 Quasi-Static Models of Friction
609(2)
11.2.2 Tribology of Rosin
611(2)
11.3 Bow Models
613(1)
11.4 Dynamical Regimes of the Bowed String
614(16)
11.4.1 The Ideal Helmholtz Motion
616(6)
11.4.2 Real Helmholtz Motion
622(7)
11.4.3 Other Regimes
629(1)
11.5 Recent Results
630(5)
References
630(5)
Part IV Radiation and Sound-Structure Interaction
12 Elementary Sources and Multipoles
635(60)
Antoine Chaigne
Jean Kergomard
12.1 Introduction: Acoustical Radiation of Musical Instruments
635(3)
12.1.1 General Problem of Radiation
637(1)
12.2 Elementary Sources
638(1)
12.3 Pulsating Sphere
639(11)
12.3.1 Pressure and Velocity Fields
639(2)
12.3.2 Acoustic Intensity and Sound Power
641(1)
12.3.3 Force Exerted by the Fluid on the Sphere: Radiation Impedance
642(1)
12.3.4 Concept of Point Source
643(2)
12.3.5 Monopole Arrays
645(5)
12.4 Oscillating Sphere
650(11)
12.4.1 Pressure and Velocity Field
650(1)
12.4.2 Acoustic Intensity and Radiated Pressure
651(2)
12.4.3 Concept of Elementary Dipole
653(2)
12.4.4 Distribution of Dipoles: Example of the Vibrating String
655(2)
12.4.5 Quadrupoles
657(4)
12.5 Radiation of a Source with Arbitrary Shape
661(20)
12.5.1 Kirchhoff--Helmholtz Integral
661(5)
12.5.2 Multipolar Decomposition
666(6)
12.5.3 Radiation of Sound in a Semi-Infinite Space
672(9)
12.6 Radiation of Sound Tubes
681(14)
12.6.1 Radiation Impedances
682(6)
12.6.2 Field Radiated by a Tube: Directivity
688(1)
12.6.3 Radiation by Two Tubes or Two Orifices
689(3)
References
692(3)
13 Radiation of Vibrating Structures
695(70)
Antoine Chaigne
13.1 Introduction
695(1)
13.2 Basic Concepts in Structural Acoustics
696(13)
13.2.1 Vibrating Beam Coupled to an Infinite Fluid Medium: Modal Approach
697(5)
13.2.2 Forced Regime
702(4)
13.2.3 Energy Approach
706(3)
13.3 Radiation of an Infinite Thin Plate
709(18)
13.3.1 Elastic Equation
709(1)
13.3.2 Acoustic Equations
710(1)
13.3.3 Dispersion Equations and Critical Frequency
710(2)
13.3.4 Pressure, Velocity, and Acoustic Power
712(6)
13.3.5 Acoustic Loading of the Plate
718(1)
13.3.6 Dispersion Equation for the Acoustically Loaded Plate
719(1)
13.3.7 Radiation of a Point-Excited Plate
720(7)
13.4 Radiation from Finite Plates
727(20)
13.4.1 Spatial Fourier Transform
728(1)
13.4.2 Contribution of the Vibrating Modes to the Radiated Pressure
729(5)
13.4.3 Radiated Acoustic Power
734(10)
13.4.4 Radiation of Unbaffled Plates and Structural Volumes
744(3)
13.5 Radiation of an Axisymmetrical Nonplanar Source
747(7)
13.5.1 Dispersion Curves for Shells and Critical Frequency
748(1)
13.5.2 Radiated Pressure
749(3)
13.5.3 Influence of the Source Shape
752(2)
13.6 Application to Stringed Instruments
754(11)
13.6.1 Selection of Materials and Merit Index
755(2)
13.6.2 Example of the Piano Soundboard
757(3)
13.6.3 Compromise Between Loudness and Tone Duration
760(1)
References
761(4)
14 Radiation of Complex Systems
765(64)
Antoine Chaigne
Jean Kergomard
14.1 Example of the Vibraphone
766(7)
14.1.1 Introduction
766(3)
14.1.2 Radiation of the Beam
769(1)
14.1.3 Radiation of the Resonator
770(3)
14.2 Example of the Kettledrum
773(23)
14.2.1 Introduction
773(2)
14.2.2 Presentation of the Physical Model
775(4)
14.2.3 Eigenfrequencies, Damping Factors, and Tuning of the Instrument
779(6)
14.2.4 Acoustic and Vibratory Fields: Time-Domain Analysis
785(4)
14.2.5 Spatial Distribution of the Radiated Pressure. Radiation Efficiency
789(1)
14.2.6 Numerical Simulation of the Coupled Problem
790(6)
14.3 Example of the Guitar
796(10)
14.3.1 Introduction
796(1)
14.3.2 Physical Model
797(2)
14.3.3 Specificity of the Numerical Guitar Model
799(1)
14.3.4 Admittance at the Bridge
800(2)
14.3.5 Damping Factors
802(1)
14.3.6 Radiated Sound Field
803(1)
14.3.7 Acoustic Intensity and Power Balance
804(2)
14.4 Example of the Piano
806(9)
14.4.1 General Presentation of the Model
806(2)
14.4.2 Modal Analysis of the Soundboard
808(2)
14.4.3 Results of the Simulations
810(3)
14.4.4 Radiation and Directivity of the Piano
813(2)
14.5 Radiation of Wind Instruments with Several Orifices
815(14)
14.5.1 Open Flute at Low Frequencies
816(2)
14.5.2 Instruments with Toneholes
818(4)
14.5.3 Interaction of Two Tubes
822(3)
References
825(4)
Glossary 829(4)
Author Index 833(6)
Subject Index 839