Testing procedures showed the importance of good flatness and parallelism in sample in order to achieve accurate values for fundamental frequencies, as indicated by Lord and Morrel (2006); adequate polishing is also necessary to avoid production of undesired modes.
The high value of the said fundamental frequency (Fig. 3) is in agreement with Lord and Morrel (2006) which indicated fundamental longitudinal mode frequency 5-10 times greater than that of the fundamental flexural mode. Fundamental frequencies are also related to material that composes the sample and are used for elastic modulus evaluation. Amplitudes exhibited in graph are relative.
In Table 1, Ed, density and speed of sound data sets are presented. General average, standard deviation and coefficient of variation are also exposed. Figure 4 presents dot plot graphs of elastic modulus and density evaluated for all samples tested. For maçaranduba, Ed values were found in the range of 17.6-21.1 GPa, and density in the interval 1.07-1.11 g/cm3; for muiracatiara, these properties were maintained in the ranges 10.8-19.6 GPa and 0.87-0.95 g/cm3. Variability of Ed was more expressive than density to both wood species, and led to a similar variation of speed of sound; for this last property, averages were close (Table 1) despite the distinct variability patterns observed. Taking density into account, variation remained below 3%. Averages were found in agreement with the literature (Longui et al., 2010; Eleotério and Silva, 2012; Rosa et al., 2014; Alves et al., 2015). Level of variability in maçaranduba is similar to that presented by Longui et al. (2010) that obtained speed of sound propagation to evaluation of dynamic modulus. Results were compared with ebony (Table 1), which is traditionally used in fingerboards construction.
Sample code Maçaranduba Muiracatiara Ed (GPa) Density (g/cm3) Speed of sound (m/s) Ed (GPa) Density (g/cm3) Speed of sound (m/s) TP-01 18.4 1.10 4090 10.8 0.88 3510 TP-02 20.0 1.11 4245 14.1 0.87 4026 TP-03 18.6 1.09 4131 14.6 0.91 3992 TP-04 19.8 1.09 4262 19.6 0.91 4577 TP-05 18.3 1.08 4116 17.3 0.89 4409 TP-06 19.2 1.10 4178 10.9 0.88 3519 TP-07 17.6 1.07 4056 16.4 0.9 4269 TP-08 21.1 1.09 4389 19.6 0.95 4542 TP-09 - - - 13.3 0.87 3910 TP-10 - - - 12.1 0.91 3646 TP-11 - - - 17.0 0.90 4346 TP-12 - - - 17.1 0.89 4383 Mean 19.1 1.09 4183 15.1 0.9 4094 SD 1.03 0.01 103 2.88 0.02 369 CV 5% 1% 3% 19% 2% 9% Ebony* Mean 20.8 1.14 - - - - CV 15% 5% - - - - Note: Means and CV of Ed and density for Ebony (Sproßmann et al., 2017).
Table 1. Dynamic elastic modulus (Ed), density and speed of sound of maçaranduba and muiracatiara samples.
Equality of variances and means were investigated. Normality of data sets was verified via Shapiro-Wilk test for a significant level of 5%, allowing implementation of F-test (Table 2). Equality of variances was observed for density, and inequality for Ed and speed of sound for a significance level of 5%. Unequal variances t-test revealed statistical inequality of means for Ed and equality for speed of sound.
F-test (5% of significance) Unequal var. t-test (5% of significance) Muiracatiara (n = 12) Macaranduba (n = 8) Muiracatiara (n = 12) Macaranduba (n = 8) Density Var. 0.00049697 Var. 0.00015536 - - - - P = 0.13357 > 0.05 - Ed Var. 9.4588 Var. 1.2764 Mean 15.233 Mean 19.125 P = 0.01387 < 0.05 P = 0.00117 < 0.05 Speed of sound Var. 148380 Var. 12073.7 Mean 4094.08 Mean 4183.4 P = 0.002944 < 0.05 P = 0.4614 > 0.05
Table 2. Results of F-test and unequal variances t-test for 5% of significance level.
Relationship between Ed and density was examined by means regression analysis, revealing no satisfactorily correlations. Scattering graph is presented in Fig. 5. In spite of the limited number of samples, analysis of Fig. 5 allows to observe clearly relevant distinctions between both sets. The lesser scattering of maçaranduba is significant and, even though some Ed values are close (between muiracatiara and maçaranduba), no similarity is verified relatively to density.
In a visual exam of grain direction patterns of samples, it was possible to observe a large variation in inclination of fibers in muiracatiara, which exhibited pronounced variability in elastic modulus. On the other hand, maçaranduba, with low Ed variability, presented regular grain slope. This phenomenon seems to be in agreement with results provided by Carrasco et al. (2017). In view to determine Ed in function of fibers direction, authors applied acoustic tomography to some species, including Manilkara sp., and identified important correlations. Indeed, these conceptions are also in agreement with theories which investigate mechanical property variation of wood with grain slope, as that presented by Liu and Ross (1998).
In spite of findings achieved in this work, it is considered that relevance of differences must be examined in the light of numerical vibroacoustic analysis of the guitar. Numerical simulations involving all guitar elements can be conducted aiming to investigate possible alterations in tone derived from wood distinctions. In this context, Paté et al. (2013) studied alterations in sound and damping due to the conductance involved in string-structure coupling for two electric guitars having ebony and rosewood fingerboards, and it was verified that whatever the tuning is, it is likely the rosewood fingerboard grasps more energy of vibration from the string. Sproßmann et al. (2017) affirm that a high hardness value indicates good abrasion resistance on the fingerboard surface due to strings scratching while guitar playing. Taking into account proximity between maçaranduba and ebony relatively to properties like elastic modulus average, density, shrinkage, Janka hardness (Teles, 2005, Pereira et al., 2016, Sproßmann et al., 2017), grain straightness and fine texture, added to the least variability observed in the piece of maçaranduba examined here, it is possible to visualize this species as potentially capable to be applied in fingerboards providing quality results. In regard to inclination of fibers, straight-grained woods are appointed as the most desirable for musical instruments (Patten et al., 2010), which was not observed in muiracatiara. As previously mentioned, this wood exhibited high variability in Ed and large irregularity in fibers inclination. Such characteristics could lead to undesirable results relatively to the sound quality and can be an issue when tension applied by strings is regarded.