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Chapter 2

CHAPTER 2

LITERATURE REVIEW

The need by the luthier to control the natural frequency of mode (0, 0) of the top plate and back plate of the guitar, and to control the modal effective weight of mode (0, 0) of the top plate has been implicitly and explicitly expressed in literature by researchers conducting work in the area of musical acoustics. Recent work performed by Elejabarrieta, Ezcurra, and Santamaria [2002] made use of the finite element method and modal analysis to model a classical guitar and report on coupling of the air modes with the top and back resonant modes. Richardson [2002], with help of colleagues at Cardiff University, made a case for and provided simple techniques for the luthier to control not only the natural frequencies of the top and back plates, but also the modal effective weight of the top plate. In a work directed at the everyday luthier, David C. Hurd [6] [2004] again accentuated the need to control the fundamental frequency of mode (0, 0) of the top and back plate with precision in order to improve sound quality.

Elejabarrieta, Ezcurra, and Santamaria [2] have authored numerous articles on vibrational behavior of the guitar including soundboard behavior along successive construction phases, guitar soundboard and air resonance behavior analyzed by finite element method, and coupled modes of the guitar resonance box. In Catgut Acoustical Society Journal [2002], the group outlined the aggregate of their work which included the creation of a finite element model of a classical guitar, including mesh of the surrounding air. Concurrently, a luthier working in conjunction with the researchers created the same actual guitar. The finite element model was correlated to the real guitar using modal analysis techniques and the modal coupling effects were reported. Research work did not delve into modal effective mass effects.

Bernard Richardson [7] [1985] performed work on classical guitars to establish the influence individual features had on the modal shapes and frequencies. No work was done on steel-string guitars or modal effective weight. Richardson [8] [2002] states that research performed by he and colleagues at Cardiff University has shown that, though mode frequencies play a part in the puzzle of sound quality of a guitar, there may be other parameters which they consider to be more critical and have a more important effect than the mode frequencies, 1 of them being the modal effective masses of the modes. Here Richardson makes a strong case for the modal effective mass as a having a “global” effect on the overall sound quality, while the mode frequencies have a “local” effect, along with influence over the balancing of “bass” and “treble” response of the instrument. Richardson outlines simple methods for frequency tuning and controlling acoustic merit of the fundamental mode, both based on a simple model of the top plate as a thin, circular and isotropic plate, and evaluating for both clamp and hinged edge boundary conditions.

David C. Hurd [6] [2004], while referencing research performed by Graham Caldersmith on guitars, stated that a desirable feature in a stringed instrument is to make “ . . . the first top plate resonant frequency an octave higher than the air resonance and a semitone above or below the back plate first resonance.” Hurd presents hand calculations to calculate the fundamental frequencies of the top and back plate, but because of the orthotropic nature of wood along with the complex shape of the structure and its components, hand calculations can only give approximations and guidelines to the builder.