Modal-acoustic radiation measurements on 17 “bad-to-excellent” quality-rated violins—including three-dimensional modal analyses of Titian and Willemotte Stradivari and Plowden Guarneri del Gesu violins to investigate extensional as well as flexural motions—were examined for quality-related trends, generally by contrasting the properties of “excellent” and “bad” violins. All violins tested showed the same five “signature” modes below 600Hz, with no obvious quality trends for mode frequencies or total damping. Bad–excellent comparisons of band-/modal-averaged damping (total, radiation and internal), mobility, radiativity, directivity, fraction-of-vibrational-energy radiated, effective critical frequency, and radiativity profiles up to 4kHz generally showed no significant difference; the only “robust” quality differentiator was the ∼280Hz, Helmholtz-type A0 cavity mode radiativity where excellent violins were significantly higher. Radiation and total damping of two old Italian violins appeared slightly highe...

Structural acoustics of good and bad violins.

This paper presents a three-dimensional time-domain numerical model of the vibration and acoustic radiation from a guitar. The model involves the transverse displacement of the string excited by a force pulse, the flexural motion of the soundboard, and the sound radiation. A specific spectral method is used for solving the Kirchhoff-Love's dynamic top plate model for a damped, heterogeneous orthotropic material. The air-plate interaction is solved with a fictitious domain method, and a conservative scheme is used for the time discretization. Frequency analysis is performed on the simulated sound pressure and plate velocity waveforms in order to evaluate quantitatively the transfer of energy through the various components of the coupled system: from the string to the soundboard and from the soundboard to the air. The effects of some structural changes in soundboard thickness and cavity volume on the produced sounds are presented and discussed. Simulations of the same guitar in three different cases are also performed: "in vacuo," in air with a perfectly rigid top plate, and in air with an elastic top plate. This allows comparisons between structural, acoustic, and structural-acoustic modes of the instrument. Finally, attention is paid to the evolution with time of the spatial pressure field. This shows, in particular, the complex evolution of the directivity pattern in the near field of the instrument, especially during the attack.

http://eaton.math.rpi.edu/CSUMS/Papers/Instruments/Time%20domain%20simulation%20of%20a%20guitar%20model%20and%20method.pdf

Time-domain simulation of a guitar: Model and method

An electronic speckle interferometer, arranged for out-of-plane
sensitivity and with an off-axis reference beam to produce spatial
phase bias, is used for three-dimensional deformation field
measurements. The complex amplitude of the object wave is
calculated by application of a Fourier-transform method to a single
interferogram. The change in phase after object deformation yields
the out-of-plane component of the displacement field. The two
in-plane components are obtained by cross correlation of subimages of
the reconstructed object wave’s intensity, a method that is also
referred to as digital speckle photography. The Fourier-transform
algorithm is extended and modified, leading to random measurement
errors that are below widely accepted theoretical limits and also to an
extended measuring range. These properties and the mutually
combined information improve the accuracy of both methods compared with
their usual single implementation. The performance is evaluated in
experiments with pure out-of-plane, pure in-plane, and combined
deformations and compared with theoretical values. An example of a
practical application is given.

Speckle interferometry: three-dimensional deformation field measurement with a single interferogram.

Vibrations of the resonance box of the guitar have been studied by means of the modal analysis technique and the finite-element method. An expert craftsman constructed the guitar box with all the structures, internal and external, characteristic of a real instrument for the experimental measurements. The boundary conditions were chosen in order to clarify the soundboard-back interaction only via the internal air coupling. The numerical model allows one to study the influence of each component on the whole box, and the contribution of the modes of the components (wooden box and its parts, and air), to the coupled modes by calculating their participation factors. The coupled modes of the guitar box are discussed taking into account both the finite-element and modal analysis results.

Coupled modes of the resonance box of the guitar.

A scanning laser Doppler vibrometer is used to record two-dimensional ultrasound fields in air. The laser light of the vibrometer traverses the sound field to and from a rigid reflector and determines the velocity field, a quantity proportional to the sound pressure rate, in each scanned point relative to the sound source. The object sound is the scattered field from objects outside the recording area. Digital reconstruction by use of phase conjugation (time reversal) of the object sound field is then performed, and the original object field intensity and phase is reconstructed.

Reconstructing two-dimensional acoustic object fields by use of digital phase conjugation of scanning laser vibrometry recordings.

The compensation of large in-plane motions in digital speckle-pattern interferometry (DSPI) with the use of digital speckle photography (DSP) is demonstrated. Ordinary recordings of DSPI are recombined and analyzed with DSP. The DSP result is used to compensate for the bulk speckle motion prior to calculation of the phase map. This results in a high fringe contrast even for deformations of several speckle diameters. In addition, for the case of an in-plane deformation, it is shown that the absolute phase change in each pixel may be unwrapped by use of the DSP result as an initial guess. The principles of this method and experiments showing the in-plane rotation of a plate and the encounter of two rounded plates are presented.

Digital speckle-pattern interferometry: fringe retrieval for large in-plane deformations with digital speckle photography

Standing Waves in a Rectangular Sound Box Recorded by TV Holography

Earlier investigations have assumed only “out-of-plane” vibrations of the plates of the violin. The violin body can, however, be described as a thin-walled, double-arched shell structure and as such it may very well elongate in one direction as it contracts in another. Therefore, at least two orthogonal vibration components have to be included to describe the vibrations. The operating deflection shapes (ODSs) of a good, professionally made and carefully selected violin were therefore measured in several directions by TV holography to determine both “in-plane” and out-of-plane vibration components of the ODSs. The observations were limited to the frequency range 400–600 Hz, as this interval includes two most-prominent resonance peaks of bridge mobility and sound radiation as well as a third poorly radiating resonance. These three peaks clearly showed orthogonal vibration components in the ODSs. The vibration behavior of the violin body, sectioned in the bridge plane, was interpreted as the vibrations of an...

On operating deflection shapes of the violin body including in-plane motions.

Phase modulated TV holography is used to measure sound pressure variations of standing waves of the air inside cavities of transparent models of a violin and a guitar. The accompanying motions, the ...

Operating deflection shapes of the plates and standing aerial waves in a violin and a guitar model

Amplitude and phase distribution of air cavity modes in a rectangular box, in a guitar, and in a violin are measured using TV holography. The box and the top and back plates of the guitar and the violin are made transparent using 5‐mm‐thick and flat PMMA plates. Standing waves in the enclosed cavities are generated by a loudspeaker. Object laser light is sent through the cavities to a rigid white‐painted steel block and reflected back again through the cavities to the optical unit of the TV holography interferometer. Laser light traveling through a sound pressure field will experience a phase delay, since an increased air pressure is accompanied by a higher air density as well as a higher index of refraction which in turn gives a slower speed of the laser light, which generates a phase delay compared to undisturbed air. This often small phase change is made visible by the highly sensitive phase‐modulated TV holography technique. The optical system will be described and air cavity modes in a simple rectangular box, in a guitar, and in a violin will illustrate the presentation.

Anna Runnemalm

Papers

Digital speckle-pattern interferometry: fringe retrieval for large in-plane deformations with digital speckle photography

Standing Waves in a Rectangular Sound Box Recorded by TV Holography

On operating deflection shapes of the violin body including in-plane motions.

Operating deflection shapes of the plates and standing aerial waves in a violin and a guitar model

Air cavity modes in sound boxes recorded by TV holography