Mathematical Modelling and Acoustical Analysis of Classical Guitars and Their Soundboards

Research has shown that the soundboard plays an increasingly important role compared to the sound hole, back plate, and the bridge at high frequencies. The frequency spectrum of investigation can be extended to 5 kHz. Design of bracings and their placements on the soundboard increase its structural stiffness as well as redistributing its deflection to nonbraced regions and affecting its loudness as well as its response at low and high frequencies. This paper attempts to present a review of the current state of the art in guitar research and to propose viable alternatives that will ultimately result in a louder and better sounding instrument. Current research is an attempt to increase the sound level with bracing designs and their placements, control of natural frequencies using scalloped braces, as well as improve the acoustic radiation of this instrument at higher frequencies by deliberately inducing asymmetric modes in the soundboard using the concept of “splitting board.” Various mathematical methods are available for analysing the soundboard based on the theory of thin plates. Discrete models of the instrument up to 4 degrees of freedom are also presented. Results from finite element analysis can be utilized for the evaluation of acoustic radiation.