| Uniform title | Physik der Geige. English |
| Contents |
Introduction. Status and goal of research on string instruments ; Organization of the material -- The bowing of the string. Self-sustained oscillation by dry friction. The simplest possible representation, in one degree of freedom ; Nearly free oscillation and switching oscillation ; Comparison to other self-sustained systems -- The plucked string. The wave equation ; D'Alembert's solution ; The requirement of pure fifths ; Input force on the bridge ; Taking damping into consideration ; Bernoulli's solution ; Range of validity of the linear wave equation for a string under tension -- The bowed string considered as a free oscillation. Helmholtz's experimental observations ; Helmholtz's theoretical inferences ; Representations of Helmholtz motion ; Transverse force on the bridge ; Superposition of several Helmholtz motions ; Superposition of static displacement resulting from constant friction -- The bowed string as a forced oscillation. Incorporating distributed viscous friction ; Temporal and spatial Fourier analysis of the excitation ; Calculation of the force spectrum from the velocity spectrum ; Extending the model to include other losses ; Raman's model ; Necessity of minimum bowing pressure -- Extension of Helmholtz motion using corrective waves. Review of previous chapters ; Rounded corners and their relationship to bowing pressure ; Method of the round trip of the rounded corner ; Introducing a simple frequency-dependent bridge impedance into the model ; Influence of bowing pressure in the chosen example ; Influence of oscillations of the string perpendicular to the bow ; The flattening effect ; Upper limit of bowing pressure -- Accounting for the torsion of the string. Generation of torsional waves by bow-friction forces ; Analysis of the problem with impulse excitation ; Longitudinal compliance of the bow hairs ; Transformation of transverse waves into torsional waves by reflection from the bow in the regime of sticking friction ; Measurement of the reflection and transmission factors of the bow in the regime of sticking friction ; Reflection, transmission, and transformation in the regime of sliding friction ; Fate of the secondary waves -- Accounting for the bending stiffness of the string. A general look at the properties of a string with bending stiffness ; Reflection from the bow at the outside of a string of finite thickness, taking bending stiffness into account ; Point impedance of a string with bending stiffness -- Toward complete solutions. Modeling the string as a lumped-constant transmission line ; Use of a computer as a restricted analog system ; Accounting for torsion in the restricted analog system ; Theory of pulse synthesis ; Periodic pulse synthesis ; Accounting for torsion in pulse synthesis ; Integral equation of the bowed string ; Transients of the bowed string ; Periodic integral equation ; Possible fluctuations in the length of the period -- The body of the instrument. The bridge. Function and form of the bridge ; Measurement of the input impedance and the force transfer factor of a rigidly supported bridge ; Holography applied to the study of the oscillatory modes of the bridge ; Model of the cello bridge as a system of two kinematic degrees of freedom ; A corresponding model of the violin bridge ; The bridge of the instrument ; The effect of the mute -- The body of the instrument as a system of few degrees of freedom. Choice of the number of partial masses of the model ; Motions of the body as a unit ; Helmholtz resonance and f-hole resonance ; Coupled oscillations of the top and back plates ; Comparison of the model and measurements on an instrument ; The wolf tone -- The body of the instrument as a system of oscillating continua. The three continua ; General laws for plates with bending stiffness ; Influence of the arching of the top and back plates ; Natural modes of the cavity of the violin ; Coupling between two infinite plates separated by an air cushion ; Coupling between the lowest natural plate vibrations and a finite cavity -- Observing the natural modes and conclusion. Making the natural modes visible ; Holographic photographs taken during various phases of construction ; Holographic photographs of assembled violins ; Possibility of statistical analysis ; Laws of similarity -- The radiated sound. Source small in comparison to the wavelength. The spherical wave field ; The point radiator (monopole) ; The dipole ; Tesseral and axial quadrupoles ; Application to the behavior of string instruments ; Synthesis of the sound field of any vibrating rigid body by means of spherical fields -- Wavelength comparable to the source dimensions. Two point sources at larger distances ; Shadowing by the body of the instrument ; Synthesis using directional Green's functions ; Shadowing by the player ; Efforts to enlarge the radiating area -- Wavelength small in comparison to the source dimensions. The critical frequency ; Experimental observations and conclusions -- The influence of the room. Room dimensions comparable to the wavelength ; Statistical treatment of rooms of moderate size ; Reverberation ; The room impulse response ; Additional geometric considerations in large rooms. |
| Abstract |
This major work covers almost all that has been learned about the acoustics of stringed instruments from Helmholtz's 19th-century theoretical elaborations to recent electroacoustic and holographic measurements. Many of the results presented here were uncovered by the author himself (and by his associates and students) over a 20-year period of research on the physics of instruments in the violin family. Lothar Cremer is one of the world's most respected authorities on architectural acoustics and, not incidentally, an avid avocational violinist and violist. The book?which was published in German in 1981?first of all meets the rigorous technical standards of specialists in musical acoustics. But it also serves the needs and interests of two broader groups: makers and players of stringed instruments are expressly addressed, since the implications of the mathematical formulations are fully outlined and explained; and acousticians in general will find that the work represents a textbook illustration of the application of fundamental principles and up-to-date techniques to a specific problem. The first?and longest?of the book's three parts investigates the oscillatory responses of bowed (and plucked) strings. The natural nonlinearities that derive from considerations of string torsion and bending stiffness are deftly handled and concisely modeled. The second part deals with the body of the instrument. Special attention is given to the bridge, which transmits the oscillations of the strings to the wooden body and its air cavity. In this case, linear modeling proves serviceable for the most part?a simplification that would not be possible with lute?like instruments such as the guitar. The radiation of sound from the body into the listener's space, which is treated as an extension of the instrument itself, is the subject of the book's final part. |
| General note | Translation of: Physik der Geige. |
| Bibliography note | Includes bibliographies and index. |
| LCCN | 84003920 |
| ISBN | 0262031027 |
