Acoustics of musical instruments:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
ASA Press ; Springer
[2016]
|
| Ausgabe: | 1st ed. 2016 |
| Schriftenreihe: | Modern acoustics and signal processing
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | First English-language translation of Acoustique des instruments de musique, second edition |
| ISBN: | 9781493936779 |
Internformat
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| 100 | 1 | |a Chaigne, Antoine |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Acoustique des instruments de musique |
| 245 | 1 | 0 | |a Acoustics of musical instruments |c Antoine Chaigne ; Jean Kergomard |
| 250 | |a 1st ed. 2016 | ||
| 264 | 1 | |a New York |b ASA Press ; Springer |c [2016] | |
| 264 | 4 | |c © 2016 | |
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| 490 | 0 | |a Modern acoustics and signal processing | |
| 500 | |a First English-language translation of Acoustique des instruments de musique, second edition | ||
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Datensatz im Suchindex
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| adam_text | Contents
Part I Basic Equations and Oscillators
1 Continuous Models.................................................... 3
Antoine Chaigne and Jean Kergomard
1.1 Strings, Membranes, Bars, Plates, and Shells ..................... 3
1.1.1 Introduction............................................... 3
1.1.2 Membranes and Strings...................................... 5
1.1.3 Stress and Strain.......................................... 9
1.1.4 Constitutive Equations of Materials: Linear Elasticity ... 12
1.1.5 Bars and Plates........................................... 16
1.1.6 Equation of Shells.................................... 26
1.2 3D Acoustic Waves............................................ 32
1.2.1 State Equation of a Gas................................... 33
1.2.2 Momentum Conservation .................................... 34
1.2.3 Conservation of Mass ..................................... 37
1.2.4 Acoustic Wave Equation.................................... 37
1.2.5 Simple Solutions: Traveling and Standing Waves ........... 38
1.3 Energy, Intensity, and Power..................................... 41
1.3.1 Example of the Vibrating String........................... 41
1.3.2 Example of Linear Acoustic Waves ....................... 43
1.3.3 Power and Impedance....................................... 43
1.4 Sources in Musical Acoustics: Excitation Mechanisms............. 45
1.4.1 Generalities About Sources and Types of Oscillations ... 46
1.4.2 Acoustic Sources.......................................... 47
1.4.3 Transient Mechanical Excitation........................... 60
1.5 Lumped Elements; Helmholtz Resonator........................... 60
1.6 Vibrating Strings-Sound Pipes Analogies...................... 63
1.6.1 Note on the Definition of Impedances
for Forced Oscillations.................................. 66
XV
XVI
Contents
1.7 Numerical Methods........................................... 67
1.7.1 Finite Difference Methods........................... 67
1.7.2 Finite Element Method............................... 70
References............................................................ 73
2 Single-Degree-of-Freedom Oscillator .................................. 77
Antoine Chaigne and Jean Kergomard
2.1 Introduction................................................ 77
2.2 Solution With and Without a Source: Green’s Function........ 79
2.2.1 Solution Without a Source; Eigenfrequency ............. 79
2.2.2 Solution with an Elementary Source: Green’s Function .. 81
2.2.3 General Solution with a Source Term................. 82
2.3 Examples of Free and Forced Oscillations....................... 84
2.3.1 Displacement of a System from Equilibrium.............. 84
2.3.2 Excitation (Forced) by a Steady Sinusoidal Force.... 84
2.3.3 Excitation by a Sinusoidal Force Starting at t = 0..... 85
2.3.4 Excitation by a Sinusoidal Force Stopping at t = 0..... 86
2.4 Forced Oscillations: Frequency Response..................... 87
2.4.1 Remarks on the Determination of the
Resonance Frequency................................. 90
2.5 Energy, Power, and Efficiency.................................. 92
2.5.1 Energy and Power....................................... 92
2.5.2 Mechanical Air Loaded Oscillator....................... 95
Part II Waves and Modes
3 Modes................................................................ 101
Antoine Chaigne and Jean Kergomard
3.1 Introduction.................................................. 101
3.2 Time Scale: Transition from Wave to Mode...................... 103
3.3 Definitions and Basic Properties of the Eigenmodes............ 104
3.3.1 Discrete System....................................... 104
3.3.2 Extension to Continuous Systems....................... 108
3.4 Application to Vibrating Strings.............................. 109
3.4.1 Heterogeneous String.................................. 110
3.4.2 Ideal String Fixed at Both Ends....................... 115
3.4.3 Initial Conditions and Starting Transients............ 116
3.4.4 Plucked String........................................ 116
3.4.5 String with a Moving End.............................. 121
3.4.6 Influence of Spatial Width and Duration of the Excitation 129
3.4.7 Struck String......................................... 132
3.4.8 Driving-Point and Transfer Admittance................. 132
3.4.9 Strings of Bowed Instruments.......................... 139
3.5 Application to Percussion Instruments......................... 143
3.5.1 Vibration of Beams.................................... 143
3.5.2 Vibrations of Membranes In Vacuo...................... 152
Contents xvii
3.5.3 Transverse Vibrations of Thin Plates.................. 156
3.5.4 Vibrations of Shells................................. 165
References.......................................................... 170
4 Waves ............................................................... 173
Antoine Chaigne and Jean Kergomard
4.1 Introduction.................................................. 173
4.2 Solutions Without Source, First Reflection.................... 174
4.3 Successive Reflections of Waves Produced by a Pulse Source... 176
4.3.1 General Expression.................................... 176
4.3.2 Reflections and Modes Periodicity..................... 178
4.3.3 Remark on the Reflection Function (4.3)............... 179
4.4 One-Dimensional Green’s Function.............................. 180
4.4.1 Expression of the Green’s Function ................... 180
4.4.2 Approximated “Practical” Realization.................. 180
4.5 Solutions Without Source in the Frequency Domain;
Transmission Lines............................................ 183
4.6 Green’s Function in Sinusoidal Regime: the Particular
Case of the Input Impedance................................... 186
4.6.1 Closed-Form Solution of the Green’s Function.......... 186
4.6.2 Modal Expansion....................................... 190
4.6.3 The Particular Case of a Source at the Input:
Input Impedance...................................... 193
4.6.4 Closed-Form Expression: Back to the Time Domain...... 194
References.......................................................... 197
5 Dissipation and Damping.............................................. 199
Antoine Chaigne and Jean Kergomard
5.1 Introduction: Dissipative Phenomena in Musical Acoustics..... 199
5.2 Generalizing the Concept of Mode.............................. 200
5.2.1 Dissipative Discrete System........................... 201
5.2.2 Continuous Systems.................................... 207
5.2.3 Continuous Complex Modes.............................. 214
5.3 Damping Mechanisms in Solid Materials......................... 218
5.3.1 Introduction.......................................... 218
5.3.2 String Damping Due to Air Viscosity................... 219
5.3.3 Thermoelasticity in Orthotropic Plates................ 220
5.3.4 Viscoelasticity....................................... 224
5.3.5 Hysteretic Damping.................................... 228
5.4 Damping Mechanisms in Cylindrical Pipes....................... 229
5.4.1 Introduction.......................................... 229
5.4.2 Viscous Effects ...................................... 231
5.4.3 Thermal Conduction Effects............................ 234
5.4.4 Radiation Dissipation at the Open End of the Pipe.... 238
5.5 Transmission Line Equations................................... 239
5.5.1 General Equations and Solutions....................... 239
XV111
Contents
5.5.2 Numerical Values of Main Constants in Air.......... 241
5.5.3 “Wide” Pipes....................................... 241
5.5.4 “Narrow” Pipes..................................... 248
5.6 Modes of a (Reed) Cylindrical Instrument................... 249
5.6.1 Presentation....................................... 249
5.6.2 Modes Orthogonality Method (Without Radiation)..... 250
5.6.3 Residue Calculus (Taking Radiation into Account)... 252
References....................................................... 255
6 Coupled Systems.................................................. 259
Antoine Chaigne and Jean Kergomard
6.1 Introduction............................................... 259
6.2 Structure-Cavity Interaction............................... 260
6.2.1 Mechanical Oscillator Coupled to a Pipe............ 260
6.2.2 Soundboard-Cavity Coupling in Stringed
Instruments at Low Frequencies..................... 264
6.3 Coupling of Piano Strings ................................. 272
6.3.1 General Equations of the Problem................... 273
6.3.2 Formulation of the Problem in Terms of Forces...... 277
6.3.3 Eigenvalues of the Strings-Bridge Coupled System... 278
6.3.4 Bridge Motion...................................... 280
6.4 String-Soundboard Coupling................................. 282
6.4.1 Determination of Mass and Stiffness Matrices....... 283
6.4.2 Mode Crossing...................................... 285
6.4.3 Musical Consequences of the Coupling............... 289
6.5 Soundboard-Bridge Coupling in Violins...................... 290
References....................................................... 294
7 Wind Instruments: Variable Cross Section and Toneholes........... 295
Jean Kergomard
7.1 Introduction............................................... 295
7.2 Pipes with Variable Cross Section: General Equations ...... 296
7.2.1 Horn Equation...................................... 296
7.2.2 Orthogonality of Modes............................. 298
7.2.3 Horn Equation with Boundary Layer Effects ......... 299
7.2.4 Lumped Elements of Horns........................... 299
7.2.5 Modal Expansion of the Input Impedance............. 300
7.3 Pipes with Cross Section Discontinuities:
First Approximation........................................ 301
7.3.1 Elementary Model: Example of the
Eigenfrequencies Equation: the Helmholtz Resonance... 301
7.3.2 Waves: Successive Reflections...................... 304
7.3.3 Modes of a Chimney Pipe: The Case
of a Reed Instrument............................... 307
7.3.4 Brass Instrument Mouthpiece........................ 312
7.3.5 Cylindrical Instrument with Flute Mouthpiece....... 317
Contents
xix
7.4 Conical Instruments........................................... 322
7.4.1 Equations and Solutions for a Lossless
Conical Resonator................................ .... 322
7.4.2 Validity of the Horn Equation for a Truncated Cone... 324
7.4.3 Transfer Matrix of a Truncated Cone................... 325
7.4.4 Eigenfrequencies: Elementary Approximations........... 325
7.4.5 Equations with “Averaged” Losses, Transfer Matrices ... 328
7.4.6 Modal Expansion for a Conical Reed Instrument........ 329
7.4.7 Changes in Conicity................................... 334
7.5 Tubes with Variable Cross Section............................. 336
7.5.1 Bells of Brass Instruments: Analytical Solution....... 336
7.5.2 Numerical Solution of the Horn Equation for
Woodwinds and Brass Instruments..................... 341
7.6 Duct Modes and Simple Discontinuities......................... 347
7.6.1 Cavity Modes and Duct Modes: Cartesian Geometry .... 347
7.6.2 Cylindrical Duct Modes................................ 351
7.6.3 Cross Section Discontinuities and Diaphragms.......... 353
7.7 Generalized Junction of Waveguides: Application to Tonehoies.. 364
7.7.1 Overview.............................................. 364
7.7.2 Two Waveguides Converging Into a Third................ 366
7.7.3 Right-Angle Bends..................................... 367
7.7.4 Bends in Cylindrical Thbes............................ 369
7.7.5 Tonehoies and Derivations............................. 370
7.8 Lattice of Tonehoies.......................................... 377
7.8.1 Generalities About the Waves in a Periodic Medium.... 378
7.8.2 Periodic Lattice of Open Holes........................ 380
References........................................................... 389
Part HI Nonlinearities and Self-Oscillations
8 Nonlinearities........................................................ 395
Antoine Chaigne, Joel Gilbert, Jean-Pierre Dalmont, and
Cyril Touz6
8.1 An Example of Asymmetry: The Interrupted Pendulum............ 396
8.1.1 Equation of Motion.................................... 397
8.1.2 Solution by a Perturbation Method..................... 397
8.2 Duffing Equation.............................................. 400
8.2.1 Example............................................... 401
8.2.2 Solutions for the Forced Duffing Oscillator........... 402
8.2.3 Generation of Subharmonics............................ 406
8.3 Nonlinear Vibrations of Strings............................... 407
8.3.1 Simplified Equations of Motion ....................... 408
8.3.2 Forced Vibrations..................................... 410
8.3.3 Transverse-Longitudinal Coupling: Simplified Approach 411
XX
Contents
8.3.4 Exact Geometrical Model of Piano Strings
with Intrinsic Stiffness ............................ 414
8.4 Nonlinearities in Wind Instruments Resonators................ 419
8.4.1 Nonlinear Propagation................................ 419
8.4.2 Nonlinear Distortion and Shock Waves,
Method of Characteristics............................ 423
8.4.3 Competition Between Nonlinear Effects and Dissipation 424
8.4.4 Shock Waves and Brassy Sounds........................ 425
8.4.5 Localized Nonlinear Dissipation...................... 427
8.5 Geometric Nonlinearities in Gongs and Cymbals................ 429
8.5.1 Sinusoidal Forced Excitation......................... 431
8.5.2 Internal Resonances .................................. 434
8.5.3 Weakly Nonlinear Regime.............................. 435
8.5.4 Energy Transfer Through Combination of Resonances... 436
8.5.5 Nonlinear Mechanical Model........................... 443
8.6 Chaotic Regime .............................................. 449
8.6.1 Degrees of Freedom................................... 450
8.6.2 Characterization of Chaos: Lyapunov Exponents........ 454
8.7 Nonlinear Normal Modes....................................... 456
8.7.1 Introduction......................................... 456
8.7.2 First Approach of Nonlinear Normal Modes............. 457
8.7.3 Invariant Manifolds.................................. 458
8.7.4 Calculation of Nonlinear Normal Modes................ 461
8.7.5 Conclusion........................................... 463
References......................................................... 464
9 Reed Instruments.................................................... 469
Jean Kergomard
9.1 Background on Self-Sustained Oscillations.................... 470
9.2 Reed Instruments Models...................................... 472
9.2.1 Introduction......................................... 472
9.2.2 Mechanical Response of a Reed: Experimental Data..... 473
9.2.3 Dynamic of the Fluid Passing the Reed ............... 478
9.2.4 Reed Opening Area and Flow Rate...................... 482
9.2.5 Basic Model (Clarinet-Like Reed)..................... 484
9.2.6 Basic Model (Lip Reed)............................... 488
9.3 Behavior of the Two-Equation Model (Regimes,
Existence and Stability, Transients) Without Reed Dynamics... 489
9.3.1 Introduction......................................... 489
9.3.2 Static Regime and “Ab Initio” Method................. 490
9.3.3 Lossless Approximation for a Cylinder:
Helmholtz Motion..................................... 493
9.3.4 One-Mode Approximation............................... 501
9.4 Away from the Reed Resonance (Two-Equation
Model): Steady-State Regimes ................................ 505
Contents xxi
9.4.1 Principle of the Harmonic Balance Method:
First Harmonic Approximation........................... 505
9.4.2 Characteristic Equation and Instability
Threshold of the Static Regime...................... 508
9.4.3 The Harmonic Balance Method: An Overview.............. 509
9.4.4 The Variable Truncation Method, and Its
Application to Clarinet-Like Instruments............... 510
9.4.5 Variation of the Playing Frequency
with the Excitation Level.............................. 517
9.4.6 Beating Reed and Sound Extinction...................... 519
9.4.7 Miscellaneous Considerations About
Clarinet-Like Instruments.............................. 523
9.4.8 Conical Reed Instruments............................... 524
9.5 Behavior of the 3-Equation Model with Reed
Dynamics (Non-beating Reed).................................... 536
9.5.1 Introduction........................................... 536
9.5.2 Oscillation Threshold for an Inward-Striking Reed..... 537
9.5.3 Oscillation Threshold for an Outward-Striking Reed.... 547
9.5.4 Modal Approach of the Dynamical System................. 549
9.5.5 Discussion of the Results......................... 550
References....................................................... 552
10 Flute-Like Instruments................................................ 559
Benoit Fabre
10.1 Introduction and General Description........................... 559
10.1.1 The Air Jet, Driving the Oscillation in Flutes......... 560
10.1.2 The Sounds of Flutes................................... 564
10.2 A Global Model for the Instrument............................. 566
10.2.1 General Description.................................... 566
10.2.2 Important Parameters................................. 567
10.2.3 Localized or Distributed Interaction?.................. 569
10.3 A Modeling for the Jet Oscillation.............................. 571
10.3.1 Jet Formation.......................................... 571
10.3.2 Jet Instability........................................ 575
10.3.3 Turbulent Jet.......................................... 585
10.4 Aeroacoustic Sound Sources.................................... 586
10.4.1 The Jet-Drive Model.................................... 587
10.4.2 A Discrete Vortex Model................................ 589
10.4.3 Aeroacoustic Formulation............................... 591
10.5 A Lumped Model of the Oscillation in a Flute.................. 597
10.5.1 Nonlinear Losses at the Blowing Window................. 597
10.5.2 Jet Velocities Fluctuations............................ 598
10.5.3 Direct Hydrodynamic Feedback......................... 601
10.5.4 The Minimal Oscillator................................. 601
10.6 Discussion About the Model................................... 603
References..........................................................
xxii Contents
11 Bowed String Instruments........................................... 607
Xavier Boutilion
11.1 Introduction................................................. 607
11.2 Bow-String Interaction ...................................... 609
11.2.1 Quasi-Static Models of Friction...................... 609
11.2.2 Tribology of Rosin................................... 611
11.3 Bow Models................................................... 613
11.4 Dynamical Regimes of the Bowed String....................... 614
11.4.1 The Ideal Helmholtz Motion........................... 616
11.4.2 Real Helmholtz Motion................................ 622
11.4.3 Other Regimes........................................ 629
11.5 Recent Results............................................... 630
References......................................................... 630
Part IV Radiation and Sound-Structure Interaction
12 Elementary Sources and Multipoles.................................. 635
Antoine Chaigne and Jean Kergomard
12.1 Introduction: Acoustical Radiation of Musical Instruments... 635
12.1.1 General Problem of Radiation ....................... 637
12.2 Elementary Sources........................................... 638
12.3 Pulsating Sphere............................................. 639
12.3.1 Pressure and Velocity Fields......................... 639
12.3.2 Acoustic Intensity and Sound Power................... 641
12.3.3 Force Exerted by the Fluid on the Sphere:
Radiation Impedance.................................. 642
12.3.4 Concept of Point Source.............................. 643
12.3.5 Monopole Arrays...................................... 645
12.4 Oscillating Sphere........................................... 650
12.4.1 Pressure and Velocity Field.......................... 650
12.4.2 Acoustic Intensity and Radiated Pressure............. 651
12.4.3 Concept of Elementary Dipole......................... 653
12.4.4 Distribution of Dipoles: Example of the
Vibrating String..................................... 655
12.4.5 Quadruples........................................... 657
12.5 Radiation of a Source with Arbitrary Shape................... 661
12.5.1 Kirchhoff-Helmholtz Integral ........................ 661
12.5.2 Multipolar Decomposition........................... 666
12.5.3 Radiation of Sound in a Semi-Infinite Space.......... 672
12.6 Radiation of Sound Tubes .................................... 681
12.6.1 Radiation Impedances................................. 682
12.6.2 Field Radiated by a Tube: Directivity ............... 688
12.6.3 Radiation by Two Tubes or Two Orifices............... 689
References........................................................ 692
Contents xxiii
13 Radiation of Vibrating Structures..................................... 695
Antoine Chaigne
13.1 Introduction.................................................. 695
13.2 Basic Concepts in Structural Acoustics........................ 696
13.2.1 Vibrating Beam Coupled to an Infinite Fluid
Medium: Modal Approach.............................. 697
13.2.2 Forced Regime......................................... 702
13.2.3 Energy Approach....................................... 706
13.3 Radiation of an Infinite Thin Plate.......................... 709
13.3.1 Elastic Equation...................................... 709
13.3.2 Acoustic Equations.................................... 710
13.3.3 Dispersion Equations and Critical Frequency........... 710
13.3.4 Pressure, Velocity, and Acoustic Power................ 712
13.3.5 Acoustic Loading of the Plate......................... 718
13.3.6 Dispersion Equation for the Acoustically
Loaded Plate.......................................... 719
13.3.7 Radiation of a Point-Excited Plate.................... 720
13.4 Radiation from Finite Plates.................................. 727
13.4.1 Spatial Fourier Transform............................. 728
13.4.2 Contribution of the Vibrating Modes to the
Radiated Pressure..................................... 729
13.4.3 Radiated Acoustic Power............................... 734
13.4.4 Radiation of Unbaffled Plates and Structural Volumes ... 744
13.5 Radiation of an Axisymmetrical Nonplanar Source............... 747
13.5.1 Dispersion Curves for Shells and Critical Frequency. 748
13.5.2 Radiated Pressure..................................... 749
13.5.3 Influence of the Source Shape......................... 752
13.6 Application to Stringed Instruments.........................* * 754
13.6.1 Selection of Materials and Merit Index................ 755
13.6.2 Example of the Piano Soundboard....................... 757
13.6.3 Compromise Between Loudness and Tone Duration....... 760
References.......................................................... 761
14 Radiation of Complex Systems.......................................... 765
Antoine Chaigne and Jean Kergomard
14.1 Example of the Vibraphone..................................... 766
14.1.1 Introduction.......................................... 766
14.1.2 Radiation of the Beam................................. 769
14.1.3 Radiation of the Resonator............................ 770
14.2 Example of the Kettledrum..................................... 773
14.2.1 Introduction.......................................... 773
14.2.2 Presentation of the Physical Model.................... 775
14.2.3 Eigenfrequencies, Damping Factors, and
Tuning of the Instrument.............................. 779
14.2.4 Acoustic and Vibratory Fields: Time-Domain Analysis .. 785
XXIV
Contents
14.2.5 Spatial Distribution of the Radiated Pressure.
Radiation Efficiency................................ 789
14.2.6 Numerical Simulation of the Coupled Problem........... 790
14.3 Example of the Guitar......................................... 796
14.3.1 Introduction......................................... 796
14.3.2 Physical Model ....................................... 797
14.3.3 Specificity of the Numerical Guitar Model............. 799
14.3.4 Admittance at the Bridge.............................. 800
14.3.5 Damping Factors....................................... 802
14.3.6 Radiated Sound Field.................................. 803
14.3.7 Acoustic Intensity and Power Balance ................. 804
14.4 Example of the Piano ......................................... 806
14.4.1 General Presentation of the Model..................... 806
14.4.2 Modal Analysis of the Soundboard.................... 808
14.4.3 Results of the Simulations ........................... 810
14.4.4 Radiation and Directivity of the Piano ............... 813
14.5 Radiation of Wind Instruments with Several Orifices........... 815
14.5.1 Open Flute at Low Frequencies......................... 816
14.5.2 Instruments with Toneholes............................ 818
14.5.3 Interaction of Two Tubes.............................. 822
References.......................................................... 825
Glossary................................................................. 829
Author Index............................................................. 833
Subject Index............................................................ 839
I
|
| any_adam_object | 1 |
| author | Chaigne, Antoine |
| author_facet | Chaigne, Antoine |
| author_role | aut |
| author_sort | Chaigne, Antoine |
| author_variant | a c ac |
| building | Verbundindex |
| bvnumber | BV043508701 |
| classification_rvk | LR 11125 |
| classification_tum | PHY 295f |
| ctrlnum | (OCoLC)951247700 (DE-599)BVBBV043508701 |
| discipline | Physik Musikwissenschaft |
| edition | 1st ed. 2016 |
| format | Book |
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| id | DE-604.BV043508701 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:27:35Z |
| institution | BVB |
| institution_GND | (DE-588)38830-0 |
| isbn | 9781493936779 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028924951 |
| oclc_num | 951247700 |
| open_access_boolean | |
| owner | DE-12 DE-20 DE-91G DE-BY-TUM |
| owner_facet | DE-12 DE-20 DE-91G DE-BY-TUM |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | ASA Press ; Springer |
| record_format | marc |
| series2 | Modern acoustics and signal processing |
| spelling | Chaigne, Antoine Verfasser aut Acoustique des instruments de musique Acoustics of musical instruments Antoine Chaigne ; Jean Kergomard 1st ed. 2016 New York ASA Press ; Springer [2016] © 2016 txt rdacontent n rdamedia nc rdacarrier Modern acoustics and signal processing First English-language translation of Acoustique des instruments de musique, second edition Akustik (DE-588)4000988-9 gnd rswk-swf Klang (DE-588)4030933-2 gnd rswk-swf Musikinstrumentenbau (DE-588)4040852-8 gnd rswk-swf Musikalische Akustik (DE-588)4123807-2 gnd rswk-swf Musikinstrument (DE-588)4040851-6 gnd rswk-swf Musikinstrument (DE-588)4040851-6 s Musikinstrumentenbau (DE-588)4040852-8 s Akustik (DE-588)4000988-9 s Klang (DE-588)4030933-2 s DE-604 Musikalische Akustik (DE-588)4123807-2 s b DE-604 Kergomard, Jean Sonstige oth Acoustical Society of America (DE-588)38830-0 isb Erscheint auch als Online-Ausgabe 978-1-4939-3679-3 Digitalisierung BSB Muenchen - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028924951&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chaigne, Antoine Acoustics of musical instruments Akustik (DE-588)4000988-9 gnd Klang (DE-588)4030933-2 gnd Musikinstrumentenbau (DE-588)4040852-8 gnd Musikalische Akustik (DE-588)4123807-2 gnd Musikinstrument (DE-588)4040851-6 gnd |
| subject_GND | (DE-588)4000988-9 (DE-588)4030933-2 (DE-588)4040852-8 (DE-588)4123807-2 (DE-588)4040851-6 |
| title | Acoustics of musical instruments |
| title_alt | Acoustique des instruments de musique |
| title_auth | Acoustics of musical instruments |
| title_exact_search | Acoustics of musical instruments |
| title_full | Acoustics of musical instruments Antoine Chaigne ; Jean Kergomard |
| title_fullStr | Acoustics of musical instruments Antoine Chaigne ; Jean Kergomard |
| title_full_unstemmed | Acoustics of musical instruments Antoine Chaigne ; Jean Kergomard |
| title_short | Acoustics of musical instruments |
| title_sort | acoustics of musical instruments |
| topic | Akustik (DE-588)4000988-9 gnd Klang (DE-588)4030933-2 gnd Musikinstrumentenbau (DE-588)4040852-8 gnd Musikalische Akustik (DE-588)4123807-2 gnd Musikinstrument (DE-588)4040851-6 gnd |
| topic_facet | Akustik Klang Musikinstrumentenbau Musikalische Akustik Musikinstrument |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028924951&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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