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Tables of Contents for The Physics of the Violin
Chapter/Section Title
Page #
Page Count
Preface to the American Edition
xi
Preface to the German Edition
xiii
Glossary of Symbols
xvii
Introduction
1
1
Status and goal of research on string instruments
1
1
Organization of the material
2
3
I THE BOWING OF THE STRING
5
196
Self-Sustained Oscillation by Dry Friction
7
10
The simplest possible representation, in one degree of freedom
7
5
Nearly free oscillation and switching oscillation
12
3
Comparison to other self-sustained systems
15
2
The Plucked String
17
18
The wave equation
17
1
D'Alembert's solution
18
3
The requirement of pure fifths
21
1
Input force on the bridge
22
4
Taking damping into consideration
26
1
Bernoulli's solution
27
4
Range of validity of the linear wave equation for a string under tension
31
4
The Bowed String Considered as a Free Oscillation
35
26
Helmholtz's experimental observations
35
4
Helmholtz's theoretical inferences
39
4
Representations of Helmholtz motion
43
2
Transverse force on the bridge
45
8
Superposition of several Helmholtz motions
53
2
Superposition of static displacement resulting from constant friction
55
6
The Bowed String as a Forced Oscillation
61
16
Incorporating distributed viscous friction
61
2
Temporal and spatial Fourier analysis of the excitation
63
1
Calculation of the force spectrum from the velocity spectrum
64
2
Extending the model to include other losses
66
1
Raman's model
67
4
Necessity of a minimum bowing pressure
71
6
Extension of Helmholtz Motion Using Corrective Waves
77
35
Review of previous chapters
77
2
Rounded corners and their relationship to bowing pressure
79
5
Method of the round trip of the rounded corner
84
5
Introducing a simple frequency-dependent bridge impedance into the model
89
4
Influence of bowing pressure in the chosen example
93
6
Influence of oscillations of the string perpendicular to the bow
99
7
The flattening effect
106
2
Upper limit of bowing pressure
108
4
Accounting for the Torsion of the String
112
24
Generation of torsional waves by bow-friction forces
112
4
Analysis of the problem with impulse excitation
116
3
Longitudinal compliance of the bow hairs
119
4
Transformation of transverse waves into torsional waves by reflection from the bow in the regime of sticking friction
123
3
Measurement of the reflection and transmission factors of the bow in the regime of sticking friction
126
3
Reflection, transmission, and transformation in the regime of sliding friction
129
2
Fate of the secondary waves
131
5
Accounting for the Bending Stiffness of the String
136
17
A general look at the properties of a string with bending stiffness
136
6
Reflection from the bow at the outside of a string of finite thickness, taking bending stiffness into account
142
4
Point impedance of a string with bending stiffness
146
7
Toward Complete Solutions
153
48
Modeling the string as a lumped-constant transmission line
153
5
Use of a computer as a restricted analog system
158
8
Accounting for torsion in the restricted analog system
166
4
Theory of pulse synthesis
170
5
Periodic pulse synthesis
175
4
Accounting for torsion in pulse synthesis
179
2
Integral equation of the bowed string
181
3
Transients of the bowed string
184
7
Periodic integral equation
191
7
Possible fluctuations in the length of the period
198
3
II THE BODY OF THE INSTRUMENT
201
156
The Bridge
203
41
Function and form of the bridge
203
5
Measurement of the input impedance and the force transfer factor of a rigidly supported bridge
208
5
Holography applied to the study of the oscillatory modes of the bridge
213
8
Model of the cello bridge as a system of two kinematic degrees of freedom
221
6
A corresponding model of the violin bridge
227
6
The bridge on the instrument
233
7
The effect of the mute
240
4
The Body of the Instrument as a System of Few Degrees of Freedom
244
39
Choice of the number of partial masses of the model
244
4
Motions of the body as a unit
248
5
Helmholtz resonance and f-hole resonance
253
10
Coupled oscillations of the top and back plates
263
9
Comparison of the model and measurements on an instrument
272
2
The wolf tone
274
9
The Body of the Instrument as a System of Oscillating Continua
283
47
The three continua
283
1
General laws for plates with bending stiffness
284
8
Influence of the arching of the top and back plates
292
13
Natural modes of the cavity of the violin
305
6
Coupling between two infinite plates separated by an air cushion
311
7
Coupling between the lowest natural plate vibrations and a finite cavity
318
12
Observing the Natural Modes and Conclusions
330
27
Making the natural modes visible
330
3
Holographic photographs taken during various phases of construction
333
8
Holographic photographs of assembled violins
341
5
Possibility of statistical analysis
346
4
Laws of similarity
350
7
III THE RADIATED SOUND
357
88
Source Small in Comparison to the Wavelength
359
25
The spherical wave field
359
6
The point radiator (monopole)
365
3
The dipole
368
5
Tesseral and axial quadrupoles
373
3
Application to the behavior of string instruments
376
6
Synthesis of the sound field of any vibrating rigid body by means of spherical fields
382
2
Wavelength Comparable to the Source Dimensions
384
30
Two point sources at larger distances
384
5
Shadowing by the body of the instrument
389
6
Synthesis using directional Green's functions
395
5
Shadowing by the player
400
5
Efforts to enlarge the radiating area
405
9
Wavelength Small in Comparison to the Source Dimensions
414
11
The critical frequency
414
5
Experimental observations and conclusions
419
6
The Influence of the Room
425
20
Room dimensions comparable to the wavelength
425
1
Statistical treatment of rooms of moderate size
426
5
Reverberation
431
5
The room impulse response
436
3
Additional geometric considerations in large rooms
439
6
Index
445