A literature review:
The acoustics of the violin
Lei Fu April, 2015 Instructor: Prof. Gary P. Scavone
Final project of Seminar MUMT 618 Schulich School of Music, McGill University
3.2 The low modes of a violin body
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3.2.1 Measurement methods
The earlier measurements were not really of mode shapes but of what would now be called operating deflection shapes (ODSs): the spatial pattern of forced vibration in response to sinusoidal force input.
The great attraction of holographic interferometry methods is that it gives a full-field visualization of the body vibration, or at least of as much of it as the experimenter’s ingenuity allows to be illuminated simultaneously: tricks can be done with mirrors to combine different views in one image.
Signal processing techniques have been developed, and estimate the modal parameter values from a measured transfer function.
Some examples of a few of the lower-frequency modes of a guitar are shown in figure 15, visualized by time-average holographic interferometry.
3.2.2 Modal results
Early measurements of the low- frequency ‘signature modes’ of a violin body were based on point measurements or holographic interferometry. The results were often plotted as nodal line patterns, such as the examples shown in figure 16. The patterns revealed are not easy to describe or to visualize, and they seem much less intuitive than those of the guitar.
The most striking examples of Bissinger’s measurements appear in the ‘Strad 3D’ project , a collaboration with violin maker Sam Zygmuntowicz to assemble a wide range of technical and constructional information about three classic Italian violins into a single DVD. Bissinger also measured the radiated sound field on a spherical array of microphones.
3.2.3 The origin of the signature modes
Until recently, no very persuasive description had been given of why the low modes of a violin body should take these particular forms, or how an instrument maker might be able to influence the details (and in particular the sound radiation from them). However, an extensive series of explorations by Gough using finite element (FE) analysis is now giving answers to these questions. Gough has done something more fundamental: he has explored a series of models starting from very simple assumptions, then gradually adding in the complications of violin design one at a time so that the progressive evolution and emergence of the signature modes can be charted, and the relative influence of various contributory factors assessed. Typical examples of the first few such modes are illustrated in figure 17. They do not yet look very much like the modes of the final violin, but they make a useful set of ‘component modes’ or basis functions, which can be used in linear combinations to describe the evolving make-up of actual mode shapes when the two symmetries are successively broken as the model is made progressively more realistic.
The next step towards a normal violin is to add the f-holes, and allow the top and back plates to be more realistically different in details (but still with no soundpost, bass bar or neck). Examples of the modes, compared to experimental measurements on a normal violin at this stage of construction, are shown in figure 18.
