Results from the first three resonances were obtained by Richardson and Walker [ 21 ] using holographic interferometry. That is, the bridge lies on an antinodal area since this is the location where the strings transfer vibration to the soundboard.
Therefore, if the soundboard can be made as thin as possible, then total sound radiation would increase. This is an important consideration for the classical guitar if the sound level from this instrument is to be increased. This is an attempt to quantify quality of the classical guitar. Global properties could be measured in terms of the -value of resonances. The -values could also be a parameter associated with quality of the instrument according to Richardson et al.
A 4-degree-of-freedom model by Popp [ 10 ] was used to gauge the relative importance of low-order modes in relation to midfrequency response. The stiffness of the soundboard and back plate were measured directly and their effective areas and masses were used to calculate the resonances and phases.
Vibrations of the neck were shown to significantly affect the frequency response in some guitars. The calculated and measured resonances agree reasonably well as shown in Figure 4 and the relative phases between the air piston, back plate, and top plate are as shown in Figure 5. This model was used to investigate the effects of brace positioning on the acoustics of the classical guitar in terms of loudness of tones based on the first resonant peak.
This first resonant peak is a result of the coupling between the soundboard and the back plate via the air mass inside the guitar box. It was found that brace positioning had an effect on the peak amplitudes of the frequency response function. This model consists of a combination of mass, spring, damper, and a massless membrane as proposed by Sali and Hindryckx [ 11 ] and Sali [ 12 ].
This model was used to investigate the importance of the first mode on the tonal quality of the instrument. A comparison between good and bad quality guitars indicated that good quality guitars have lower frequency of the first mode and correspondingly higher amplitude in the frequency response function and lower or equal damping.
This first mode corresponds to the first peak in the frequency response function of the instrument. It was found that the intensity or amplitude of the first mode was inversely proportional to the damping of the soundboard. The objective of this model was to optimize the placing of bracing for a better-quality instrument. Sumi and Ono [ 24 ] conducted experiments with three different quality guitars and modal analysis using ANSYS showed that the best quality guitar had a thickness of 3. However, this is only an experimental work and no analytical model was available.
Dumond and Baddour [ 25 , 26 ] studied the effects of scalloped braces on mode shapes. A simple analytical model based on Kirchhoff plate theory was used to study the vibration of a rectangular board with and without braces.
The effects of rectangular braces on the resonant frequencies were compared with those from scalloped braces. Mathematically, it was shown that the shape of a scalloped brace can be modelled as a 2nd order piecewise polynomial function with peaks at positions and of the brace length.
It was concluded that reducing the thickness of the brace reduced the lowest resonant frequency as this reduces the stiffness of the plate. It was also concluded that, by using scalloped braces, it was possible to control the 1st and the 4th natural frequencies of the brace-plate system simultaneously but control of two natural frequencies simultaneously is not possible using rectangular braces. Thus, scalloped braces will further assist the luthiers in controlling the type of soundboards they prefer their instruments to have.
This simple model of the soundboard was modelled as a rectangular plate. Though this model is far from reality as the shape of the soundboard is more complex, consisting of a series of curves, it nevertheless suffices to explain the effects of plate thickness on modal frequencies.
Davies [ 27 ] has shown that the boundary of the guitar soundboard could be successfully modelled using Chebyshev polynomials. Attempts were also made to model the boundary using Fourier and polynomial series but these resulted in large errors in their derivatives at the extremes of the fitted domain. The use of Chebyshev series minimized these errors. This mathematical concept could be used to modify the results of the rectangular plate in future research.
Besnainou et al. The soundboard was split longitudinally along its axis of symmetry. Accelerometers were placed in front of the 2nd and 5th strings.
Caldersmith [ 15 ] discovered that the displacements of the back plate of an acoustic guitar are only a very small proportion of that of the top plate at the fundamental resonance.
This observation was obtained from measurements with piezoelectric transducers attached to both the top and bottom plates. Based on this study and that of Richardson et al. Instead of wood, carbon fibre reinforced polymer CFRP was used as a material for the soundboard.
These were compared to empirical results obtained from the soundboard of an acoustic guitar. It was found that there was a striking similarity in the mode shapes though the frequencies showed some variations as the shape of an actual guitar soundboard is different from that of a rectangular plate. Davies [ 27 ] had also arrived at a similar conclusion with regard to the similarity of mode shapes. Wegst [ 30 , 31 ] has shown that wood is still the material of choice for soundboards of musical instruments due to its mechanical and acoustical properties.
A finite element model is a discretization of a continuum into a large but finite number of nonoverlapping elements connected at their nodes. The response of the continuum is then approximated by the response of the finite element model. The finite element method is an appropriate approach for analysing the vibration of a continuum such as the soundboard over a wide range of frequencies.
This range of frequencies is found in the work of Czajkowska [ 17 ], who attempted to differentiate higher quality instruments from lower quality ones. Modal analysis of soundboards made from a composite of polyurethane foam reinforced with carbon fibre was analysed by Okuda and Ono [ 32 ] using the finite element method.
Results showed that the relationship between frequency and mode number could be freely controlled by adjusting the physical properties of this material. This is an attempt to introduce soundboards with consistent tones as those from wooden materials tend to be affected by humidity and moisture content of the surrounding air as shown by Borland [ 2 ].
Research into the potential use of an industrially moulded plastic component such as the guitar soundboard is given by Pedgley et al. Stanciu et al. Plates without bracing, with 3 bracings, and with 5 bracings were studied. Their influence on the resonant frequencies was obtained for the first 10 modes. It was concluded that, for a given design, plates with higher density have lower resonant frequencies and that lower frequencies resulted in greater acoustic power.
Curtu et al. Vernet [ 36 ] also investigated the influence of bracing on the mode shapes and resonant frequencies of the soundboards of guitars using the finite element method but did not use scalloped braces. Results showed that there were significant variations of some of the mode shapes and modal frequencies due to differences in soundboard stiffness. The influence of the bridge on the response of the soundboard was investigated by Torres and Boullosa [ 38 ] using finite element method.
Gorrostieta-Hurtado et al. Its characteristics in various stages of development of the instrument were evaluated using modal analysis results from finite element method.
The vibroacoustic characteristics of the complete instrument can also be investigated by finite element method as shown by Paiva and Dos Santos [ 39 ]. The boundary element method belongs to the group of boundary type formulations. In this group, only the surface boundary of an acoustical fluid needs to be discretized. The number of degrees of freedom is considerably reduced as there is no need to discretize the entire volume of the fluid.
This is especially applicable to our system comprising the soundboard structure surrounded by air fluid as only the sound pressure and sound velocity need to be defined at the boundary.
Xu and Huang [ 40 ] showed that acoustic radiation of a three-dimensional structure could be computed using the finite element method as well with the boundary element method and that the latter method required less computation as only the surface needs to be meshed.
In the case of the finite element method the volume of the object needs to be meshed and the boundary conditions of the exterior need to be specified as well. The boundary element method is further enhanced with the advent of a fast multipole algorithm which further reduces solution time and uses less computer memory. Future research into soundboard acoustic radiation could proceed along this concept. A new approach to studying acoustic radiation of thin structures is to model them as surfaces without thickness and using the boundary element method as in Venkatesh et al.
It was shown that the errors in their numerical solutions were better than those obtained by treating them as thin plates. This is also a possible alternative to investigate acoustic radiation from soundboards.
Investigations into the vibroacoustic behaviour of thin structures such as the soundboard could also proceed by modelling the soundboard using finite elements and the surrounding air by boundary elements. This results in coupling of both subsystems. The solution leads to the structural behaviour of the soundboard structure under the influence of air fluid as well as the propagation of acoustic waves within the air.
Exact solutions for an irregular-shaped plate such as the soundboard of a guitar which is subjected to various boundary conditions are difficult to obtain. This challenge prompts further research using current mathematical methods such as Variational Iteration, Adomian Decomposition, Perturbation, Least Squares, Collocation, and Rayleigh-Ritz. These have been used to solve various engineering problems involving fourth-order parabolic partial differential equations with constant coefficients as well as with variable coefficients.
Current trend in research indicates a return from numerical methods to analytical methods in attempts to seek exact solution for vibrating plates. This is evident from research on free vibration of irregular-shaped plates as well as rectangular plates with variable thickness by Sakiyama and Huang [ 44 ], [ 45 ], respectively, and on rectangular plates with central circular holes by Torabi and Azadi [ 46 ].
Cho et al. The soundboard with bracings is considered as a stiffened plate. The concept of equivalent rectangular plates, Davies [ 27 ], could be used to study the vibration of irregular-shaped plates. Mass remnant ratio as proposed by Mali and Singru [ 49 ] could be used to study the effect of holes on the natural frequencies of plates.
Czajkowska [ 17 ] recommended that the bandwidth of investigations can be extended to 3 octaves above the E-note of the 1st string at the 12th fret.
This frequency is 5. This minimum is still valid based on revised ISO as shown in Figure 6. Investigation of the acoustics of soundboards is concerned with the maximum acoustic power that it can radiate. Wood for guitars needs to be treated to provide minimum acoustic absorption. Special attention must be paid to the method of treatment as a study by Mamtaz et al. Expressions for the numerical evaluation of radiation efficiencies and radiation power of simply supported baffled plates such as those proposed by Lemmen and Panuszka [ 53 ] could be used as postprocessing tools in finite element analysis to evaluate the performance of soundboards for various boundary conditions.
The boundary condition in the case of the guitar soundboard varies between simply supported and fixed support. An expression for the radiated power from forced vibration due to a harmonic point force of lightly damped simply supported plates is also available in [ 53 ]. Van Engelen [ 55 ] has also proposed expressions for evaluating radiation power and radiation efficiency from velocities and pressures obtained from finite element analysis. The radiation efficiency of the soundboard can also be computed as shown by Perry and Richardson [ 51 ].
Wenge, a dense, dark-colored African hardwood unrelated to the rosewoods, has tonal properties remarkably similar to those of Brazilian rosewood. Ebony, the traditional fingerboard material found on violins, classical guitars, and high-end steel strings, has the lowest velocity of sound of all the woods commonly used in lutherie and has definite damping characteristics. This may not be much of a problem for large-bodied guitars made of red spruce or Brazilian rosewood, but it may be something to consider when designing smaller guitars, particularly those using some of the less resonant woods for tops and backs.
Redwoods and cedar, for instance, are often used in soundboards by American guitar-makers to great effect. In some cases, two different kinds of wood are used together to give the guitar a distinctive appearance and tone. The following is a summary of woods commonly used in soundboards and the characteristics of each:.
In low-end instruments, laminated or plywood soundboards are often used. Although these materials often impart great strength and stability to the instrument, via layers of perpendicular grains, they do not vibrate the same way that natural wood does, generally producing an inferior tone with less amplification.
Instruments with laminated or plywood soundboards should be avoided if possible. Actively scan device characteristics for identification. Use precise geolocation data. Select personalised content. Create a personalised content profile. Measure ad performance. Select basic ads.
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