African Journal of
Plant Science

  • Abbreviation: Afr. J. Plant Sci.
  • Language: English
  • ISSN: 1996-0824
  • DOI: 10.5897/AJPS
  • Start Year: 2007
  • Published Articles: 807

Full Length Research Paper

Physical, mechanical and acoustic properties of Terminalia superba, Cleistopholis patens and Holarrhena floribunda woods used in sculpture and instrument making in Benin

Montcho Crépin Hounlonon
  • Montcho Crépin Hounlonon
  • Laboratoire de Physique du Rayonnement (LPR), Faculté des Sciences et Techniques, Université d’Abomey-Calavi, BP 526 Cotonou, Republic of Benin.
  • Google Scholar
Comlan Aristide Houngan
  • Comlan Aristide Houngan
  • Laboratoire de Caractérisation Thermophysique des Matériaux et Appropriation Energétique (Labo-CTMAE), ED-SDI, EPAC-UAC, BP 526 Cotonou, Republic of Benin.
  • Google Scholar
Clément Adéyèmi Kouchadé
  • Clément Adéyèmi Kouchadé
  • Laboratoire de Physique du Rayonnement (LPR), Faculté des Sciences et Techniques, Université d’Abomey-Calavi, BP 526 Cotonou, Republic of Benin.
  • Google Scholar
Alexis Enagnon Medehouenou1 and Basile Bruno Kounouhéwa
  • Alexis Enagnon Medehouenou1 and Basile Bruno Kounouhéwa
  • Laboratoire de Physique du Rayonnement (LPR), Faculté des Sciences et Techniques, Université d’Abomey-Calavi, BP 526 Cotonou, Republic of Benin.
  • Google Scholar


  •  Received: 19 April 2022
  •  Accepted: 27 June 2022
  •  Published: 31 October 2022

 ABSTRACT

Wood is important in several fields including sculpture and instrument making. In the last two fields, Terminalia superba, Cleistopholis patens, and Holarrhena floribunda are three of Benin’s most used wood species. In this work, we have, on prismatic samples (500 mm × 20 mm × 20 mm) of the wood of these species, used the acoustic method Beam Identification by Non-destructive Grading (BING) of CIRAD-Forêt to determine the density ρ, Young's modulus E, shear modulus G and internal friction tan ? that allowed the evaluation of the specific stiffness modulus E/ρ and the other acoustic parameters. These tests showed that T. superba, C. patens and H. floribunda wood species have specific moduli of elasticity of 18 ± 3, 17 ± 2 and 15 ± 1 GPa, respectively; internal friction of the order of 10-2  and sound velocities of the order of 4000 m s-1. All these three species have an average acoustic strength above 1.40 MPa s m-1 with acoustic radiation above 7 m4 kg-1 s-1 for a high ACE above 1000 m4 kg-1 s-1 for T. superba and C. patens and low around 674 m4 kg-1 s-1 for H. floribunda. All these species have a medium stability in service and a low propensity to deformation due to their shrinkage anisotropy. In view of these results, the wood of these species can be used in both structural and acoustic works specifically in sound insulation, art sculpture and instrument making.

 

Key words: Specific modulus, internal friction, sound velocity, acoustic radiation, acoustic impedance, acoustic conversion efficiency, insulation, musical instrument.


 INTRODUCTION

Wood is a material of choice that is found in almost all sectors of socio-economic development. The appreciation of its quality is then defined according to its adequacy to the envisaged uses. Each characteristic of wood can thus answer a given quality provided that it is associated with an application. The notion of wood quality covers all the properties that condition the technological aptitudes. The mechanical, physical, chemical and acoustic properties as well as the aesthetic aspect still make wood a preferred material in instrument making, the manufacture of art objects, interior constructions (concert halls), sound insulation, the construction of structures entirely of wood (Bucur, 2006; Wegst, 2006; FPL, 2010; Brémaud, 2012). In the special cases of miscellaneous carving and artisanal and semi-industrial manufacture of musical instruments and art objects, not all wood species are eligible (Wegst, 2006). The case of the royal treasures of Abomey returned to Benin in November 2021 and which did not suffer any visible deformation despite the constraints and rigors of the climate is a typical example of the professionalism of the makers and the efficient use of the material wood. In Benin and Africa in general, these trades are threatened because of the progressive disappearance of the holders of endogenous knowledge in the field but also because of the non-availability of appropriate wood species for the realization of these objects and the absence of documentation and reliable scientific information on the species. 

 

Deforestation, climate change, overexploitation, agriculture, demographic pressure, livestock, vegetation fires, etc. are the factors that contribute to the disappearance of these woody species. From 1990 to 1995, a total loss of 298 thousand hectares of Beninese forest cover was recorded (FAO, 2010). For the World Bank Group, citing national statistics, there appears to be a loss of 5.9 to 7.6 million hectares of forest, a decrease in area of 14% and a deforestation rate of 1.4% per year between 2005 and 2015 (World Bank Group, 2020). This decrease in vegetation cover has led to threats to many plant species, some of which are increasingly disappearing from their natural ecosystems. Among these endangered forest species in Africa are those whose wood is used as a basic material for carving, instrument making and other crafts. In studying the importance of biodiversity and tropical forests in South Benin, Adjovi et al. (2017) stratified the different uses of wood in our forests and noted, without being exhaustive, that for South Benin, about 13 species of wood are used in carving, 09 species for furniture making, 04 species of wood in light carpentry, 02 in formwork, 05 for boat building, two for mortar making and three for drumming. This study revealed that among the objects carved or manufactured are: tam-tams, masks, statuettes, mortars, decorative objects, handles, etc. The actors involved in this socio-economic activity include carvers, tradition keepers, dealers, art museum curators, etc. Among the species cited in carving and instrument making in Benin and other African countries (Schmelzer, 2006; Kimpouni, 2009; Lemmens, 2012), are the woods of Terminalia  superba, Cleistopholis patens and Holarrhena floribunda for which this work determined physical, mechanical and acoustic properties. The main properties determined are density, modulus of elasticity, shear modulus, modulus of specific rigidity, interna friction, speed of sound, acoustic radiation coefficient, acoustic conversion efficiency, and acoustic impedance. The knowledge of these parameters will make it possible to fill the documentary gap which characterizes the Beninese wood species and to better indicate the various uses of these wood species in instrument making.


 MATERIALS AND METHODS

Plant

 

In this study, trees of these species were identified and collected in the Pahou Forest and the Lama in Benin (Table 1). These are dense humid forests specifically of the Guinean-Congolese zone. This zone is the wettest in Benin and is located in its southern part in the Dahomey-Gap and extends from the coast to the latitude of the Commune of Djidja. The climate is sub-equatorial with a bimodal rainfall regime. There are four seasons, including two rainy seasons and two dry seasons. Annual rainfall varies from 900 mm in the west to 1,300 mm in the east. The dominant soil is ferralitic and deep. 

 

The study area covers the sites of occurrence of the materials and methods. After identification of the species of trees concerned in the field, on each marked and felled individual; a round of wood of 70 cm length was taken by species at man height (1 m 30). For the determination of physical, mechanical and acoustic properties, the sampled logs were cut into bars in the form of prismatic specimens 500 mm × 20 mm × 20 mm in the orthotopic directions of the wood (Photo 1).  Thus, we worked on 3 feet of C. patens, 2 feet of T. superba collected in Pahou and 5 feet of H. floribunda collected in Lama in Benin. From these plants we extracted 50 prismatic specimens without defects of H. floribunda, 80 specimens of T. superba and 85 of C. patens.

 

Vibration measurement

 

Measurements of physical and mechanical parameters were made by the vibratory method developed by CIRAD-forest and whose operation was described in the work of Brancheriau (2002, 2006), Brancheriau and Baillères (2002), Brémaud (2006, 2008), Traoré et al. (2010), Brémaud et al. (2012), Roohnia (2016), Hounlonon et al. (2017, 2021), Sproßmann et al. (2017), Saadtnia et al. (2018a, b) and Ahmed and Adamopoulos (2018). It is based on the spectral analysis of beam vibration natural frequencies and fast Fourier Transforms (FFTs) programmed under the Beam Identification by Non-destructive Grading (BING) software version 9. The test setup is the one presented in the work of Hounlonon et al. (2021), the principle of which is as shown in Figure 1 (Saadtnia et al., 2018a, b).

 

 

The basic physical, mechanical and acoustic characteristics determined are density, modulus of elasticity and shear, and the internal  friction  coefficient. The  most  important  physical property determined is the density which indirectly gives the density of the sample.

 

In the range of mechanical properties, we have the modulus of elasticity and shear according to Timoshenko's theory and the modulus of elasticity according to Bernoulli. While it is proven that the most elaborate method is Timoshenko's, the modulus of elasticity according to Timoshenko and the modulus of elasticity according to Bernoulli of 1st order (mode 1) are not very different and are of the same order of magnitude (Brancheriau, 2002; Brémaud, 2006), we focused in terms of mechanical properties on the modulus of elasticity according to Bernoulli mode 1 to extract the acoustic properties (Ahmed and Adamopoulos, 2018). At the end of the vibratory or acoustic properties, the properties of primary interest in structural mechanics such as the speed of sound and internal friction have been determined. 

 

If the acoustic properties of wood, such as the sound level, quality and color of xylophone bars and soundboards, are determined by the mechanical properties of the material from which they are made, this is justified by the fact that sound is produced by the material's own vibration. According to Wegst (2006), the properties on which the acoustic performance depends are mainly the density, the Young's modulus and the damping coefficient. They determine the speed of sound in the material, the natural frequencies and the intensity of acoustic radiation. The most important acoustic properties for the selection of materials with applications in acoustics such as musical instruments and building interiors are the velocity V of sound in the material, the acoustic impedance z, the acoustic radiation coefficient K and the loss coefficient tanδ and the acoustic conversion coefficient ACE (Wegst, 2006; Brémaud, 2012; Ahmed and Adamopoulos, 2018).

 

The speed of sound in a structural material depends on the modulus of elasticity and density. In wood, the speed of sound also varies with the direction of the grain because the transverse modulus of elasticity is at least twenty times lower than the longitudinal value. Across the grain, the speed of sound is about one fifth to one third of the longitudinal value (FPL, 2010). It is given, according to the work of Ahmed and Adamopoulos (2018), Saadtnia et al. (2018a, b), Roohnia (2016), Brémaud (2006), Wegst (2006), Holz (1996a), and James (1961), by relation (Equation 1).

 

 

where V (m s-1) is the speed of sound; E (Pa) is the modulus of elasticity, ρ is the density (kgm-3), l (m) is the length of the specimen, and f (Hz) is the resonant frequency.

E is the modulus of elasticity of the first mode of vibration according to Bernoulli's model (Brancheriau, 2002; Brémaud, 2006). According to this theory, the specific Young's modulus of the nth mode is given by relation (Equation 2).

 

 

The independence of E to the frequency increase (in the audible range) requires taking into account the influence of shear and rotational inertia in model of Timoshenko (Hearmon, 1958; Bordonné, 1989) which is a more elaborate model (Brancheriau, 2002; Brémaud, 2006).

 

The  acoustic  impedance  or  mechanical  impedance  z  (Wegst, 2006; Roohnia, 2016) of the material is given by the product of the velocity V (m s-1) of sound in the material by its density ρ (kg m-3). It can also be expressed as a function of density and Young's modulus. The impedance z is expressed in MPa s m-1 by the relation (Equation 3).

 

 

The acoustic radiation coefficient K (m4 kg-1 s-1) reflects the acoustic radiation damping (Wegst, 2006). This parameter is conceptually different from internal frictional damping (Roohnia, 2016). Noted K, it depends on the elastic modulus (Pa) and density (kgm-3), the influence of which is higher than in the case of specific modulus (Wegst, 2006; Roohnia, 2016). It is expressed by relation (Equation 4).

 

 

The inverse of this coefficient is called the anti-vibration parameter according to Yoshikawa (2007).

 

The Acoustic Conversion Efficiency ACE defines the efficiency with which vibrational energy is transformed into sonic energy and has been accepted as an overall estimate of acoustic properties (Aizawa et al., 1998; Rujinirun et al., 2005; Roohnia et al., 2011). It is the ratio of the radiation ratio to the damping coefficient or internal friction (Brémaud, 2008; Aizawa et al., 1998; Yano et al., 1992; Obataya et al., 2000; Roohnia, 2016) and the acoustic conversion efficiency, expressed in m4 kg-1 s-1, is formulated by relation (Equation 5).

 

 

High radiation damping combined with low internal friction damping means that less sound energy is consumed in the internal friction and more is emitted as sound radiation to the environment - exactly what is expected from musical instrument soundboards.

The transmission parameter or relative acoustic conversion efficiency was also defined which according to Yoshikawa (2007) is given by expression (Equation 6).

 

 

Internal friction is the term used to refer to the mechanism that causes the dissipation of vibrational energy from a body (FPL, 2010; Roohnia 2016), that is, internal dissipation of acoustic waves (Roohnia, 2016). When a solid is stretched, some of the mechanical energy is dissipated as heat (FPL, 2010). As a result, the damping capacity often referred to by the mechanism that causes it as 'internal friction' is also referred to as 'damping due to internal friction' or 'loss coefficient' (Roohnia et al., 2015; Wegst, 2006; Roohnia, 2016).  Internal friction is the property of solid materials that reflects the transformation of mechanical energy into heat under cyclic stress (Brancheriau et al., 2010). The loss coefficient measures the degree to which vibrational energy is dissipated by internal friction in a material. It  is  given  by  tan? = ?/?  where  ?  is the logarithmic decrement (Newland, 1989; Bodig and Jayne, 1993; Wegst, 2006; Roohnia, 2016). During this study, the internal friction is collected, following the development of the work of Brancheriau (2002) and Brancheriau and Baillères, 2002; Brancheriau et al., 2010, 2011) along with the physical-mechanical and vibrational properties in a raw text file.

 

The data collected or calculated were tabulated and processed in Excel to give the results of descriptive statistics represented by the mean and standard deviation of each parameter and presented subsequently.


 RESULTS AND DISCUSSION

Preliminary investigations among some carvers in the lake regions of Benin, in the communes of Cotonou and surroundings, in Pobè, Kétou, Dassa, Parakou, Djougou and Natitingou have revealed that in carving, the woods most used are among others: Ricinodendron heudelotii, Tectona grandis, H. floribunda, T. superba, C. patens, Triplochiton scleroxylon, Milicia excelsa, Anogeissus leiocarpa, Khaya senegalensis, Terminalia catapa, Gmelina arborea, etc.

 

This finding reflects the work of Adjovi et al. (2017) who found in their work in South Benin that the top 13 most used wood species in carving are G. arborea, Pterocarpus erinaceus, T. grandis, Diospyros mespiliformis, K. senegalensis, M. excelsa, Eucalyptus species, Daniellia oliveri, Khaya grandifoliola, Afzelia africana, Azadirachta indica, Vitellaria paradoxa and Triplochiton scleroxylon. Of these thirteen species, the most used for the manufacture of dugouts is T. scleroxylon, Erythrophleum africanum, Cola spp., M. excelsa, Anarcadium occidentale.

 

Dendrometric parameters of C. patens, T. superba, and H. floribunda

 

The bark thickness and diameters of the three C. patens woods are summarized in Table 2. The two T. superba trees used show good stiffness with straight shafts, white wood. The heartwood and sapwood are not differentiated. The bark thickness of these trees is 0.2 cm with a diameter between 21.5 and 22.8 cm for one and 22.9 and 23.2 cm for the other. For the five feet of H. floribunda wood, the bark thickness varies between 0.1 and 0.2 cm shown in Table 3. 

 

Physical, mechanical and acoustic properties of the wood species studied

 

The physical-mechanical properties of the materials used in instrument making determine the acoustic properties of the instruments. With wood being a multifunctional material, certain physical-mechanical properties determine the acoustic performance. Among these parameters is density, Young's modulus, and the loss or damping coefficient or internal friction (Wegst, 2006). By combining the basic physical-mechanical properties (Table 4) with the acoustic models, we have determined the acoustic properties shown in Table 5.

 

 

Table 4 shows a similarity of Timoshenko and Bernoulli mode 1 moduli of elasticity confirming the observations of Brancheriau (2002) and Brémaud (2006). Compared to Ricinodendron heudelotii, all three species have higher densities, moduli of elasticity and shear. R. heudelotii is a light wood with a density of 130 to 300 kg m-3, soft and brittle with a modulus of elasticity of 3700 to 4800 MPa and a shear of 2.2 to 3.2 MPa (Tchoundjeu and Atangana, 2007). This species is highly prized in the sculpture of Guèlèdè masks, various statuettes and other art objects such as canes and tom-toms (Akpovo and Fandohan, 2021).

 

The comparison of Bernoulli mode 1 specific moduli and Timoshenko specific dynamic modulus, for all our samples of slenderness L/h of the order of 25, presents in the case of our three species good correlations (Figure 2) confirming the observations of Brémaud et al. (2012), Brémaud (2006) and Brancheriau (2002). 

 

The results of the internal friction obtained (Table 5) for these three species are in the range of the values obtained by Brancheriau  et al. (2006) for species of good acoustic quality whose internal friction is located between 0.82 and 1.26 × 10-2. From Table 5, it appears that, C. patens has the highest value of ACE and K, T. superba has the highest specific stiffness and the highest speed of sound while H. floribunda has the highest values of internal friction and acoustic impedance.

 

 

 

Density and modulus of elasticity

 

The modulus of elasticity and density are important acoustic parameters (Brémaud, 2012; Wegst, 2006; Roohnia, 2016; Ahmed and Adamopoulos, 2018) especially since they are determinant in the specific modulus of stiffness. The modulus of elasticity increases globally with density as already found in the work of Sproßmann et al. (2017). While the species T. superba correlates well with both parameters, C. patens and H. floribunda correlate less well as shown in Figure 3.

 

The density of wood used in instrument making covers a wide range from 300 to 1400 kg m-3 (Wegst, 2006). For example, the mass of the back and sides of a body or part of the body of an instrument is a function of the density of the wood used and can be controlled by acting on the thickness of the panels. A guitar body with high panel mass reduces the resonant frequency and increases the radiating area in phase, acoustically improving the midrange and extending the duration of the sound (Gore, 2011).

 

Our three species tested here have a density of 467 ± 41 kg m-3 for T. superba, 360 ± 44 kg m-3 for C. patens, 536 ± 36 kg m-3 for H. floribunda. Values that remain, for example, in the realm of soundboard resonance woods whose density varies 300 to 500 kg m-3 (Wegst, 2006; Ahmed and Adamopoulos, 2018). It is true that according to the same authors the woods of the bottoms and sides of violin and piano action have densities of 600 to 900 kg m-3; woods of high density for wind instruments, xylophone bars and violin hump; woods of high density of the order of 750 kg m-3 are used as electric guitar neck (Wegst, 2006; Ahmed and Adamopoulos, 2018). The back and sides of guitars, for example, are traditionally made of wood of the same species of wood for aesthetic reasons regardless of the stiffness and density of the material (Gore, 2011). According to Gore (2011), cited by Ncube and Masilinga (2017), wood species on  the  sides should be heat flexible with a density of 550 to 800 kg m-3; the density of 550 kg m-3, is more favorable for the back and sides of guitars. The properties for example required for guitar neck woods are strength, stiffness and dimensional stability over time against moisture gradient (Sproßmann et al., 2017). In view of these authors, H. floribunda and T. superba in their range of variation would offer usable samples in guitar making.

 

Indeed, depending on the age and level of harvesting, the density of the wood, as well as other wood parameters, of each of these species can vary widely. The values of the densities found remain within the range of the data of the Tropix 7 database which obtained 540 ± 70 kg m-3 ; of PROTA quoting Kimpouni (2009), 370 to 730 kg m-3 for T. superbaC. patens also has its average density close to that of PROTA citing Lemmens (2012) who found a density ranging from 290 to 500 kg m-3.

 

Of the three species studied, H. floribunda has the best density. However, the results of the literature remain almost empty on its physical-mechanical characteristics. Indeed, the work done so far remains in the field of life and earth sciences (Schmelzer, 2006; Bayala et al., 2006; Orwa et al., 2009). However, it is also used in kitchen framing (Leciak and Bah, 2008). According to Schmelzer (2006) quoted by PROTA, this wood species is used in Benin to build granaries, beds or children's cribs; its wood is resistant to attack by Prostephanus truncatus. For carving, stools and other carved seats, H. floribunda is considered the best wood (Schmelzer, 2006; Orwa et al., 2009). Recent work in Ghana by Antwi et al. (2022) showed that branch and trunk wood have similar densities close to those in our work. This study found a density of 467.53 ± 70.87 kg m-3 for branch wood and 457.40 ± 70.46 kg.m-3 for H. floribunda trunk wood.

 

The average Bernoulli dynamic modulus of each of these species as presented in Table 4 shows that they have moduli in the range of instrument making that runs from 6000 to 40000 MPa (Wegst, 2006; Ahmed and Adamopoulos, 2018).

 

 

Indeed, T. superba has a mean modulus of 8305 ± 1716 MPa; C. patens (6126 ± 1014 MPa) and H. floribunda (7957 ± 929 MPa).

 

If it is true that the acoustic properties are decisive in the choice of a type of wood in acoustics, it will be taken into account the dimensional stability of the species studied, T. superba has the highest modulus of elasticity and shear. 

 

Regarding modulus of elasticity T. superba has lower moduli than Tropix 7 (11750 ± 2480 MPa) but in the range of PROTA (Kimpouni, 2009) which varies from 3625 to 16660 MPa.  C. patens has, according to PROTA citing Lemmens (2012), a modulus of elasticity in the range of 6080 to 8230 MPa which is not much different from our values for the same species. H. floribunda, according to the work of Antwi et al. (2022), has a static modulus of elasticity of 8213.83 ± 116.23 MPa for the branches and 8654.96 ± 108.30 for the trunk. These values show that the mechanical stiffness of H. floribunda wood from Benin is similar to that from Ghana.

 

Treated woods, as well as, pure species can be suitable for the manufacture of soundboards for moduli of about 6000 to 19000 MPa; violin backs and sides for a modulus of about 8000 to 19000 MPa, wind instruments for about 7000 to 18000 MPa), piano mechanics for about 14000 to 19000 MPa) and for xylophone bars from 12000 to 20000 MPa (Wegst, 2006; Ahmed and Adamopoulos, 2018). Therefore, all our woods can be used in soundboard making; T. superba and H. floribunda for violin backs and sides and wind instruments.

 

Also, coupling density and stiffness modulus, T. superba and H. floribunda can be used as back and side woods for guitars following the classification of Sproßmann et al. (2017) which categorized woods from 700 to 1100 kg m-3 and 9000 to 18000 MPa as back and side woods, and woods from 1000 to 13000 kg m-3 and 14000 to 26000 MPa as guitar fret woods.

 

Yoshikawa (2007), in Japan, working on the wood species traditionally used for making stringed instruments (Picea abies, Picea sitchensis, Paulownia tomentosa, Morus alba, Acer platanoides, Acer sp., Pterocarpus indicus and Dalbergia nigra) and substitute species used in the same manufacture (Pinus albicaulis, Tsuga species, Sequoia sempervirens, Thuja plicata, Cinnamomum camphora, Zelkova serrata, Cupressus sempervirens, Pyrus communis, Prunus serotina, Juglans nigra, Ptercarpus dalbergioides, and Ochroma pyramidale) density, modulus of elasticity, and velocity values for the two groups of 260 to 873 kg m-3; 6300 to 20000 MPa; 3130 to 5300 m s-1 and 380 to 710 kg m-3; 2800 to 22000 MPa; 3500 to 5400 m s-1. These values crossed with our average values recorded in the two previous tables predispose our wood species to certain potentialities in instrument making of stringed instruments whereas in the light of the work of Traoré et al. (2010) on veneer (Pterocarpus erinaceus Poir.) the density and the modulus of elasticity of these studied species remain weak and unsuitable for the manufacture of xylophone bars.

 

Speed of sound

 

The speed of sound is directly related to density and modulus of elasticity. The speed of sound in wood and any hygroscopic material decreases with increasing temperature or humidity and is proportionally influenced by density and modulus of elasticity (Tsoumis, 1991). The velocity of sound, in wood, reflects the speed of transmission of the energy received thus woods with high velocity and low damping coefficient better facilitate the transmission of vibration energy (Ahmed and Adamopoulos, 2018). Materials with high sound propagation velocities, that is, low densities for high relative stiffness or low internal friction are the best facilitators of energy transfer (Bourgeois, 1994; Gore, 2011).

 

For the wood samples we tested, T. Superba has a velocity (4188 ± 322 m s-1); C. patens (4141 ± 279 m s-1); H. floribunda (3868 ± 178 m s-1). In the literature, it is reported that, the highest velocities of sound propagation, are obtained in the longitudinal direction followed significantly by a lower velocity in the radial direction and by a lower velocity in the tangential direction (Kúdela and Kunštár, 2011). Several acoustic parameters are necessary for wood selection in instrument making. In the case of velocity, the range of desired values for the woods used varies from 3000 to 6500 m s-1. Often woods of high celerity are used as resonance woods (Wegst, 2006). Woods for piano action, violin bows, xylophone bars, violin backs and sides, and wind instruments have low velocities (Ahmed and Adamopoulos, 2018).  Thus, all three species studied have velocities that are in the range of velocities (Wegst, 2006) thus showing suitability for making different musical instruments. The speed of sound, of P. kesiya and Pterocarpus angolensis, used in guitar making in Zambia, is 4481 and 3799 m s-1, respectively, while that of Picea abies is 4894 m s-1 (Ncube and Masilinga, 2017). Hilde et al. (2014) found a velocity of 5600 m s-1 (with variation from 5200 to 6300 m s-1) for spicea and 3500 m s-1 for pine. The high modulus of rigidity of P. sitchensis and its relatively low density prevail of a high sound velocity (Bourgeois 1994). It is expected that resonance woods have a high sound velocity around 3000 m s-1 although velocities of 4000 to 6500 m s-1 are preferred for soundboards (Wegst 2008). In this range, all our three wood species have good resonance potential. For instruments with impulsive excitation, the parameters of sound decay are particularly important (Hase, 1987; Holz, 1996b; Brancheriau et al., 2006; Aramaki et al., 2007; Chaigne and Doutaut, 1997; Wegst, 2006). Spruce, often used as a high quality wood in instrument making, has a low density of 450 kg m-3 and a very high specific modulus of elasticity of 26 to 36 GPa, arguing for a sound speed above 6000 m s-1 (Haines, 2000; Bucur, 2006; Yano et al., 1990, 1992). Combining speed with density and, referring to Figure 4 (Wegst, 2006) of sound speed versus density, T. superba and C. patens can be used in the manufacture of soundboards while H. floribunda would be a candidate for the manufacture of violin backs and sides or wind instruments. The case of C. patens is illustrated by its uses which, according to Lemmens (2012) reported by PROTA, vary from use in carpentry (roofing, doors, beams, dugouts, furniture, veneers, plywood, floats...) to carving musical instruments such as making drums. 

 

 

Sound radiation coefficient K and acoustic impedance z

 

Figure 5 shows the variations of K and z as a function of the speed of sound. In general, the acoustic radiation coefficient K and the acoustic impedance z increase when the speed of sound increases. It also shows a good correlation between these different parameters for T. superba, C. patens and H. floribunda.

 

The sound radiation coefficient is a measure of the vibration in wood when damped by sound radiation. High values of the sound radiation coefficient K are desired for materials used to produce loud sound, and as such, it is very important for its resonance quality (Ahmed and Adamopoulos, 2018). A high radiation coefficient means that there is less energy dissipation due to the inertia of the vibrating body. For resonators, it is desired to resonate the sound by using a lightweight resonator body or top plate with a higher modulus of elasticity. This parameter for wood in soundboards can range from 7 to 16 m4 kg-1 s-1 but slightly lower acoustic coefficients can be accepted for other parts of musical instruments (Roohnia, 2016).

 

The acoustic radiation coefficients, of the species we studied, are: T. Superba (9.00 ± 0.69 m4 kg-1 s-1); C. patens (11.81 ± 1.79 m4 kg-1 s-1); H. floribunda (7.25 ± 0.67 m4 kg-1 s-1). These values are much higher than those of vène (Pterocarpus erinaceus) wood. Thus according to Roohnia (2016), these species can be used in soundboard manufacturing although Wegst (2006) advocates values of K > 8 m4 kg-1 s-1 would be ideal for soundboard manufacturing. The radiation coefficient K, for Sitka spruce and western cedar is about 12 m4 kg-1 s-1. These two species have a large sound radiation coefficient which is highly appreciated for producing loud sound (Wegst 2006) as does Cleistopholis patens with its sound radiation coefficient of about 12 m4 kg-1 s-1.

 

Wood in music will also need to have a high characteristic impedance to allow for the reflection of sound in the surrounding environment as maple does (Wegst 2006). Like the velocity and the acoustic radiation coefficient K, the acoustic impedance z is related to the modulus of elasticity and density. According to the graphs in Figures 6 to 8, the impedance is related to the density by a linear law while the radiation coefficient is related to the density by a power law with strong correlation in both cases.

 

 

 

Impedance is important when the transmission of vibration is from one medium to another as in the case of musical instruments. For strings, it is a very important quantity and low impedances are highly valued (Wegst, 2006; Hilde et al., 2014) as in the case of sound transmission in air. Values of z between 1.2 and 3.4 MPa. s. m-1 are required for stringed instruments and high values required for percussion instruments such as xylophones such that resonance will be over a large time period (Hilde et al., 2014). For the three species that are the subject of our study, the average characteristic impedances are for T. Superba (1.96 ± 0.29 MPa s m-1); C. patens (1.47 ± 0.18 MPa s m-1); H. floribunda (2.07 ± 0.14 MPa s m-1). Thus according to Hilde et al. (2014), these species can be used in the manufacture of ropes. Kollmann and Coté (1968) found sound wave resistance values ranging from 2 to 3.7 MPa s m–1 for wood while they found values of 39.5 MPa s m–1 for steel and 25.8 MPa s m-1 for iron (Roohnia, 2016). Excellent sound radiators such as T. plicata and P. sitchensis, has a low acoustic impedance, 1.683 and 2.165 MPa s m-1. The acoustic impedance of P. angolensis, 2.298 MPa s m-1 is similar to that of Picea spp. Acer saccharum has a sufficiently high impedance of 2.982 MPa s m-1 that allows the wood to act as a reflector and contribute to sound radiation (Wegst, 2006). In contrast, P. kesiya for the soundboard impedance 2.733 MPa s m-1, the slightly lower impedance of P. angolensis for the back and sides reduces sound deflection according to Ncube and Masilinga's (2017) guitar study in Zambia. These values prove in a general way therefore the low mechanical impedance of wood compared to materials like some metal alloys and the strong potentiality of our wood species to be used both in instrument making and sound insulation.

 

The impedance of the soundboard is proportional to the acoustic impedance of the material it is made of and also to the square of its thickness. Soundboards of considerable thickness, such as those of pianos for example, have an impedance clearly higher than that of the strings. The achievement of a high sound quality is therefore dependent on a meticulous monitoring of the impedances of the strings and the soundboards (Wegst, 2006). Experimental tests with the dimensioning of different instruments are desirable to further refine the specific observations.

 

Internal friction tanδ, acoustic conversion efficiency (ACE), and specific stiffness modulus E/ρ

 

The internal friction or damping coefficient is a parameter that reflects the energy dissipation in the wood.  If the characteristic impedance z indicates the transmission of vibration from one medium to another, the acoustic radiation coefficient K describes the amplitude or loudness while the acoustic conversion efficiency represents the maximum response (Barlow, 1997; Wegst, 2006).  ACE is  the  efficiency  of  converting  vibrational energy into sound energy and for some musical instruments, better wood rhymes with high ACE (Yano and Minato, 1993). A low tanδ is often required as one of the necessary conditions for a wood to be used as soundboards of piano, guitar and other musical instruments (Matsunaga et al., 1999).

 

For our three species, the internal friction tanδ and the acoustic conversion efficiency ACE are respectively for: T. superba (1.05 ± 0.50).10-2 and (1039 ± 454) m4 kg-1 s-1; C. patens (1.10 ± 0.43) 10-2 and (1242 ± 506) m4 kg-1 s-1; H. floribunda (1.23 ± 0.46) 10-2 and (674 ± 267) m4 kg-1 s-1. The specific modulus of stiffness of these three species is as follows: T. superba (18 ± 3 GPa); C. patens (17 ± 2 GPa); H. floribunda (15 ± 1 GPa). 

 

The tanδ values of the species studied are slightly higher than those of Traoré et al. (2010) for veneer used in Mali for xylophone manufacture. Compared to this same species, the ACEs found here are significantly higher. T. superba has a higher specific stiffness than vène wood (Traoré et al., 2010), while the other two species have specific stiffnesses of the same order. Xylophone woods have a very low damping coefficient tanδ and a high value of the peak sound radiation ACE, but not of the average sound radiation coefficient K, and harmonic table woods have higher values for ACE and K. (Wegst, 2006). Thus, T. superba and C. patens, on this basis, are recommendable for soundboards. Working on tropical woods, Brémaud (2012) measured ACE values of 700 to 800 m4 kg-1 s-1 generally higher than those of H.  floribunda but lower than the other two species. Baar et al. (2016), working on the tropical hardwood species Afzelia, Intsia, Astronium and Millettia species, meeting the criteria for idiophones such as xylophone bars, found a low internal friction of 0.006 to 0.008 and an ACE of about 700 to 800 m4 kg-1 s-1 for a specific stiffness around 16.6 to 21.0 GPa. For Afzelia spp. the internal friction of value 0.0075 found is just like for the other species is lower than the values of our species; its specific rigidity of 16.6 GPa is in the range of that of our species while its ACE of 649 m4 kg-1 s-1 is in the range of that of H.  floribunda but very low compared to those of the two other species here studied.

 

The internal friction tanδ of these three species is not in the range of poor acoustic quality woods with a damping coefficient between 1.52 × 10-2 and 2.21 × 10-2 but rather in the range of good acoustic quality woods with tanδ between 0.82 × 10-2 and 1.26 × 10-2 (Brancheriau et al., 2006). The best perceived acoustic material 'quality' was that of very low internal friction even though the variability of the damping coefficient for wood was restricted to its lowest range between 0.25 × 10-2 and 0.55 ×10-2 (Hase, 1987; Brémaud, 2012).

 

Wegst (2006) argues that resonator woods should have a high ACE unlike other parts of musical instruments. Coupling the ACE with the internal friction, and reading the graph in Figure 9a (Wegst, 2006), the average values of our species  indicate  that  C.  patens can be used in making soundboards and H. floribunda for violin backs and sides.

 

 

According to Wegst (2006), modulus of elasticity can be related to internal friction as shown in Figure 9b. Based on this graph and our average values, the three species studied here would all be candidates for the manufacture of violin backs and sides. Based on the following Figure 9a from Wegst (2006), Roohnia (2016) concluded that light tone woods for resonator soundboards can exhibit ACE beyond 2000 m4 kg-1 s-1.

 

In wood acoustics, these species under certain conditions can be used for the manufacture of musical instruments such as woodwinds, percussion instruments, strings and brass bands (Bucur, 2006). Indeed, by combining the acoustic and mechanical properties of wood, we group wood species under the generic term of resonance wood. Woods of high specific modulus (frequency descriptor) find wide application in the manufacture of resonators for musical instruments requiring minimum weight; that is, the utility of specific stiffness is to find wood parts with minimum weight for bending vibration of the body of a sound producing instrument whose primary design constraint is physical deflection or deformation, rather than loading at a point of failure. There are no better materials or materials similar to wood to be combined with or to substitute for wood in these very important acoustical properties to achieve structural wood quality (Bucur, 2006).

 

The sound produced by a string is barely audible because a single string is capable of moving a small volume of air. So to produce a sound of satisfactory volume for our ears, the  string  must  be  coupled  with  a resonator that will transmit the vibration energy of the string and radiate the sound.  Generally, high ACE woods are known to be excellent soundboards (Brémaud, 2012). Wegst (2006) finds that xylophone bar woods have fairly high values of peak response (maximum response) ACE but not average loudness K. Both their ACE and K are lower than spruce for string soundboards, which corresponds to less radiation damping, and their higher z-impedance would result in less energy loss through the mounts. Numerical simulation showed that the decay time of xylophone bars was governed primarily by internal friction, but very little by losses through the supports (Chaigne and Doutaut, 1997). A high specific modulus may allow radiation at low frequencies (Yano et al., 1994). Fairly light, spruce, with a specific modulus of about 31 GPa, has a moderate characteristic impedance of 2.683 MPa s m-1 (Bucur, 2006), which can promote the transmission of sound in air (Wegst, 2006).

 

Figures 10 to 12 show for each species, the variation of ACE as a function of tanδ and then the variation of internal friction tanδ as a function of specific modulus. Overall, ACE follows a power law of internal friction with strong correlation coefficients. The strong dispersion of the specific modulus as a function of internal friction did not allow us to have the exact power law tanδ = 10-A×(E/ρ)-B of Ono and Morimoto (1983), which is the reference. Instead, we have a power law of the form tanδ = (E/ρ)-B given the high dispersion of our species, which are tropical wood species.

 

In general, woods with high specific stiffness E/ρ combined with low damping coefficient tanδ are accepted for  piano,  guitar,  and violin soundboards (Matsunaga et al., 1996).

The relationship between internal friction tanδ and specific stiffness E/ρ is determined by the orientation of the wood elements and can be modeled by considering the microfibril angle or grain angle (Obataya et al., 2000; Brémaud et al., 2011b). Thus the difference observed from the standard form of Ono and Morimoto (1983) can be explained by the fact that our species are tropical species either by the chemical composition or presence of extractives or by the water content of the wood or the presence of compression wood or the structure of the wood (Obataya et al., 2000; Brémaud et al., 2010a, 2011a; Obataya et al., 1998; Sasaki   et  al., 1988)  which influences the internal friction tanδ more than the stiffness modulus E/ρ (Brémaud et al., 2013). Extractables can be without effect as they can decrease, or at times, grow, the internal friction tanδ by a coefficient that can reach at most 2 with very little influence on the stiffness modulus E/ρ (Brémaud et al., 2012).

 

Since the modulus of elasticity generally increases with density, a higher mechanical impedance is recommended for panels of musical instrument body frames or others (Pollens, 1984; Yoshikawa, 2001). Also, high values of the specific modulus of elasticity E/ρ are highly recommended for excellent soundboards (Bucur, 2006; Ono,  1996;  Ono  and  Morimoto, 1984). Because of this, the performance of soundboards and cases cannot be predicted solely from the modulus of elasticity and velocity (Yoshikawa, 2007), internal friction, and others. For Western instruments (marimbas and xylophones), the required wood qualities have been defined as high density, modulus of elasticity, and good moisture-related dimensional stability (Holz, 1996b). 

 

Shrinkability

 

Shrinkability is a parameter influencing the dimensional stability of wood in both structural and instrumental applications. The physical properties of shrinkage and infradensity of the studied species were researched in the literature. Values of volume shrinkage and radial and tangential shrinkage given the R/T ratio indicate that these species are dimensionally stable in the face of moisture gradient. Indeed, according to Tropix 7, T. superba has a tangential shrinkage RT of 6.1%; a radial shrinkage RR of 4.3% for RT/RR ratio of 1.4 for a volume shrinkage coefficient of 0.42% and is required to be medium stable in service. PROTA reporting Lemmens (2012) found that C. patens has a radial shrinkage RR of 5.0%, a tangential shrinkage RT of 9.6% for a shrinkage anisotropy RT/RR of 1.9; it is a moderately stable wood in service. The literature is silent on the physical, mechanical and acoustic properties of H. floribunda, which remains in the domain of natural sciences (Bayala et al., 2006). However, recent work by Antwi et al. (2022) shows that the branch wood of this species has similar properties to the trunk wood. Antwi et al. (2022) found that branch  wood  has  a  tangential  shrinkage  of  (3.8 ± 0.7%), a radial shrinkage of (2.0 ± 0.5%) and a shrinkage anisotropy of 1.9 ± 0.2 similar to trunk wood, which has a tangential shrinkage of 3.6 ± 0.6% and a radial shrinkage of 1.9 ± 0.2% with a shrinkage anisotropy of 1.9 ± 0.4. R. heudelotii heartwood dries rapidly with little or no degradation. Its tangential shrinkage RT ranges from 4.7 to 5.4% and its radial shrinkage RR ranges from 1.9 to 2.4%. Its shrinkage anisotropy ranges from 2.0 to 2.8. The wood is easy to saw and work, and nails without splitting, but turning and planing are difficult (Tchoundjeu and Atangana, 2007). Thus, the wood of the species studied has, overall, a lower propensity to deformation than the wood of R. heudelotii, which nevertheless has the best dimensional stability. These species have good potential for sculptural works requiring low dimensional variation in the face of humidity variations.

 


 CONCLUSION

At the end of this work, it appears that Benin has many species of wood that can be used in sculpture such as C. patens, T. scleroxylon, M. excelsa, A. leiocarpa, D. mespiliformis, H. floribunda, and T. superba. Thus to better value some of them, we determined the most important physical, mechanical and acoustic properties of T. superba, C. patens and H. floribunda. Taking into account their velocity of about 4000 m s-1 and basic properties, such as density and modulus of elasticity, these three species offer great potential for instrument making. Based on the densities found, T. superba and H. floribunda are good candidates for guitar case panels. Because of their modulus of  elasticity,  all  three  species can be used for the manufacture of soundboards; T. superba and H. floribunda for the back and sides of violins and wind instruments. By combining the speed of sound and the coefficient of acoustic radiation of these three species of wood, it is concluded that the woods of these species are potential resonance woods for the manufacture of soundboards. The specific stiffness of each of these three species is greater than 15 GPa and reinforces their nature as resonance woods.  Their acoustic impedance suggests their use in strings. With their internal friction, the three species studied are in the range of wood species with good acoustic quality. T. superba and C. patens have peak ACE responses above 1000 m4 kg-1s-1 while all three wood species have a radiation coefficient above 7 m4 kg-1 s-1. Compared to the properties Afzelia spp. H. floribunda can be a good substitute in the manufacture of musical instruments especially xylophone bars. Their shrinkage and shrinkage anisotropy predestine them to good use in art sculpture.


 CONFLICT OF INTERESTS

The authors have not declared any conflict of interests.


 ACKNOWLEDGEMENTS

This work was supported financially from the Fonds d'Aide à la Recherche Forestière of the Office National du Bois du Bénin. The authors thank the Direction Générale des Eaux, Forêts et Chasse (DGEFC) of Benin and the Cellules Techniques d'Aménagement Forestiers (CTAF) of Lama and Pahou.



 REFERENCES

Adjovi EC, Amadji TA, Olodo E (2017). Importance and Role of Biodiversity and Tropical Forests in the Cultural, Socio-Economic and Religious Life of African Black People: Case of Benin. Journal of Environmental Science and Engineering B 6:312-322.
Crossref

 

Ahmed SA, Adamopoulos S (2018). Acoustic properties of modified wood under different humid conditions and their relevance for musical instruments. Applied Acoustics 140:92-99.
Crossref

 

Aizawa H, Obataya E, Ono T, Norimoto M (1998). Acoustic converting efficiency and anisotropic nature of wood. Wood Research: Bulletin of the Wood Research Institute Kyoto University 85:81-83.

 

Akpovo AH, Fandohan AB (2021). Usages, distribution des connaissances traditionnelles et valeur économique de Ricinodendron heudelotii au Bénin. Revue Marocaine des Sciences Agronomiques et Vétérinaires 9(2):276-287.

 

Antwi K, Cremer T, Frimpong-Mensah K (2022). Physical and mechanical properties of Holarrhena floribunda and Nesogordonia papaverifera branch wood in Ghana. African Journal of Plant Science 16(3):29-33.
Crossref

 

Aramaki M, Bailleres H, Brancheriau L, Kronland M, Ystad S (2007). Sound quality assessment of wood for xylophone bars. Journal of the Acoustical Society of America 121(4):2407-2420.
Crossref

 

Baar J, Tippner J, Gryc V (2016). Wood anatomy and acoustic properties of selected tropical hardwoods. IAWA Journal 37(1):69-83.
Crossref

 

Barlow CY (1997). Materials selection for musical instruments. Proceedings-Institute of Acoustics 19:69-78.

 

Bayala B, Tamboura HH, Pellicer MTR, Zongo D, Traoré A, Ouédraogo L, Malpaux B, Sawadogo L (2006). Effets œstrogéniques du macéré aqueux des feuilles de Holarrhena ?oribunda (G. Don) Dur & Schinz chez la rate ovariectomisée. Biotechnology, Agronomy, Society and Environment 10(3):173-180.

 

Bodig J, Jayne BA (1993). Mechanics of Wood Composites. Reprinted edition.

 

Bordonné PA (1989). Module dynamique et frottement intérieur dans le bois. Mesures sur poutres flottantes en vibrations naturelles. PhD, Institut National Polytechnique de Lorraine, Nancy, France.

 

Bourgeois D (1994). How the selection of species helps define the sound of your guitar. Acoustic Guitar Magazine, March/April 1994.

 

Brancheriau L (2002). Expertise mécanique des sciages par analyses des vibrations dans le domaine acoustique. Thèse de l'Université de la Méditerranée - Aix Marseille II, Ecole Supérieure de Mécanique de Marseille 267p.

 

Brancheriau L (2011). Corrections for Poisson effect in longitudinal vibrations and shearing deformations in transverse vibrations applied to a prismatic orthotropic body. In "Mechanical Vibrations: Types, Testing and Analysis", Nova Science Publishers, pp. 205-223.

 

Brancheriau L, Baillères H (2002). Natural vibration analysis of clearwooden beams: a theoretical review. Wood Science and Technology 36:347-365.
Crossref

 

Brancheriau L, Baillères H, Détienne P, Kronland R, Gril J (2006). Key signal and wood anatomy parameters related to the acoustic quality of wood for xylophone-type percussion instruments. Journal of Wood Science 52(3):270-273.
Crossref

 

Brancheriau L, Kouchade C, Brémaud I (2010). Internal friction measurement of tropical species by various acoustic methods. Journal of Wood Science 56(5):371-379.
Crossref

 

Brémaud I (2006). Diversité des bois utilisés ou utilisables en facture d'instruments de musique. Doctorat, Université Montpellier II, France.

 

Brémaud I (2008). Caractérisation mécanique des bois et facture: Origines et recensement de la variabilité. Actes de la Journée d'Etude le bois: Instrument du Patrimoine Musical - Cite de la Musique 29:24-46.

 

Brémaud I (2012). Acoustical properties of wood in string instruments soundboards and tuned idiophones: biological and cultural diversity. Journal of the Acoustical Society of America 131(1):807-818.
Crossref

 

Brémaud I, Amusant N, Minato K, Gril J, Thibaut B (2011a). Effect of extractives on vibrational properties of African Padauk (Pterocarpus soyauxii Taub.). Wood Science and Technology 45:461-472.
Crossref

 

Brémaud I, Cabrolier P, Gril J, Clair B, Gérard J, Minato K, Thibaut B (2010) Identification of anisotropic vibrational properties of Padauk wood with interlocked grain. Wood Science and Technology 44:355-367.
Crossref

 

Brémaud I, Gril J, Thibaut B (2011b). Anisotropy of wood vibrational properties: dependence on grain angle and review of literature data. Wood Science and Technology 45:735-754.
Crossref

 

Bucur V (2006). Acoustics of Wood, 2nd ed. Springer-Verlag (Ed.), Berlin, Germany.
Crossref

 

Chaigne A, Doutaut V (1997). Numerical simulations of xylophones. I. Time-domain modeling of the vibrating bars. Journal of the Acoustical Society of America 101:539-557.
Crossref

 

Food and Agriculture Organisation (FAO) (2010). Evaluation des Ressources Forestières Mondiales 2010, Rapport National: Benin. Rome: FAO. Available at:

View

 

Forest Products Laboratory (FPL) (2010). Wood handbook - wood as an engineering material. General Technical Report, FPL-GTR-190. Madison, WI: U.S. Department of Agriculture, Forest Service.

 

Gore T (2011). Wood for guitars in: session 3aMU: musical acoustics. Proceedings of 161st Meeting on Acoustics 23-27 May 2011, Seattle-Washington.
Crossref

 

Haines DW (2000). The essential mechanical properties of wood prepared for musical instruments. Catgut Acoustical Society Journal 4:20-32.

 

Hase N (1987). A comparison between acoustic physical factors of Honduras rosewood for marimbas and xylophones and a sensory evaluation of these instruments (in Japanese). Mokuzai Gakkaishi 33:762-768.

 

Hearmon RFS (1958). The influence of shear and rotatory inertia on the free flexural vibration of wooden beams. British Journal of Applied Physics 9:381-388.
Crossref

 

Hilde C, Woodward R, Avramidis S, Hartley ID (2014). The acoustic properties of water submerged lodgepole pine (Pinus contorta) and Spruce (Picea spp.) wood and their suitability for use as musical instruments. Materials 7(8):5688-5699.
Crossref

 

Holz D (1996a). Tropical hardwoods used in musical instruments -can we substitute them by temperate zone species? Holzforschung 50:121-129.
Crossref

 

Holz D (1996b). Acoustically important properties of xylophone-bar materials: Can tropical woods be replaced by European species?. Acta Acustica United with Acustica 82(6):878-884.

 

Hounlonon MC, Kouchadé AC, Kounouhéwa BB (2017). Physical and mechanical properties of teak wood of Tanzanian and local provenance in Benin. Bois et Forêts des Tropiques 331:45-53.
Crossref

 

Hounlonon MC, Kouchadé AC, Kounouhéwa BB (2021). Physical and mechanical properties of Acacia auriculiformis A. Cunningham Ex Benth used as timber in Benin. Journal of Materials Science and Surface Engineering 8(1):992-1000.
Crossref

 

James WL (1961). Effect of temperature and moisture content on internal friction and speed of sound in Douglas fir. Forest Products Journal 9(9):383-390.

 

Kimpouni V (2009). Terminalia superba Engl. & Diels. Prota.

 

Kollmann FP, Cote JrA (1968). Principles of Wood Science and Technology Springer-Verlag, New York, USA, pp. 301-302.
Crossref

 

Kúdela J, Kunštár M (2011). Physical-acoustical characteristics of maple wood with wavy structure. Annals of Warsaw University of Life Sciences-SGGW. Forestry and Wood Technology 75:12-18.

 

Leciak E, Bah O (2008). Les végétaux du quotidien : usages des ligneux dans les terroirs de Guinée maritime. Bois et Forêts des Tropiques 298(4):77-88.

 

Lemmens RHMJ (2012). Cleistopholis patens (Benth.) Engl. & Diels. Lemmens RHMJ, Louppe D, Oteng-Amoako AA (eds.), PROTA (Plant Resources of Tropical Africa / Ressources végétales de l'Afrique tropicale), Wageningen.

 

Matsunaga M, Minato K, Nakatsubo F (1999). Vibrational property changes of spruce wood by impregnation with watersoluble extractives of pernambuco (Guilandina echinate Spreng.). Journal of Wood Science 45(6):470-474.
Crossref

 

Matsunaga M, Sugiyama M, Minato K, Norimoto M (1996). Physical and mechanical properties required for violin bow materials. Holzforschung 50(6):511-517.
Crossref

 

Ncube E, Masilinga P (2017). Prospective Zambian tonewoods for dreadnought acoustic guitar. International Wood Products Journal 8(4):216-226.
Crossref

 

Newland DE (1989). Mechanical vibration analysis and computation, Longman, Harlow, UK.

 

Obataya E, Norimoto M, Gril J (1998). The effects of adsorbed water on dynamic mechanical properties of wood. Polymer 39:3059-3064.
Crossref

 

Obataya E, Ono T, Norimoto M (2000). Vibrational properties of wood along the grain. Journal of Material Science 35:2993-3001.
Crossref

 

Ono T (1996). Frequency responses of wood for musical instruments in relation to the vibrational properties. Journal of the Acoustical Society of Japan 17:183-193.
Crossref

 

Ono T, Norimoto M (1983). Study on Young's modulus and internal friction of wood in relation to the evaluation of wood for musical instruments. Japanese Journal of Applied Physics 22:611-614.
Crossref

 

Ono T, Norimoto M (1984). On physical criteria for the selection of wood for soundboards of musical instruments. Rheologica Acta 23:652-656
Crossref

 

Orwa C, Mutua A, Kindt R, Jamnadass R, Anthony S (2009). Agroforestree Database: a tree reference and selection guide version 4.0. Available at:

View

 

Pollens S (1984). The pianos of Bartolomeo Cristofori. Journal of American Musical Instruments Society 10:32-68.

 

Roohnia M (2016). Wood: Acoustic properties, book chapter. Reference Module in Materials Science and Materials Engineering. Elsevier Incorporated.

 

Roohnia M, Hossein MA, Alavi-tabar SE, Tajdini A, Jahan-Latibari A, Manouchehri N (2011). Acoustic properties in Arizona Cypress logs: a tool to select wood for sounding board. BioResources 6:386-399.
Crossref

 

Roohnia M, Kohantorabi M, Tajdini A (2015). Maple wood extraction for a better acoustical performance. European Journal of Wood and Wood Products 73(1):139-142.
Crossref

 

Rujinirun C, Phinyocheep P, Prachyabrued W, Laemsak N (2005). Chemical treatment of wood for musical instruments. Part I: acoustically important properties of wood for the Ranad. Wood Science and Technology 39:77-85.
Crossref

 

Saadtnia MA, Sattari N, Roohnia M, Bahmani M (2018a). Acoustically quality evaluation of date palm samples from the pith to the bark. Iranian Journal of Wood and Paper Industries 9(1):65-74.

 

Saadtnia MA, Sattari N, Roohnia M, Bahmani M (2018b). Comparison of stiffness parameters of two types of date palmwood using nondestructive test. Iranian Journal of Wood and Paper Science Research 33(1):133-141.

 

Sasaki T, Norimoto M, Yamada T, Rowell RM (1988). Effect of moisture on the acoustical properties of wood (in Japanese). Mokuzai Gakkaishi 34:794-803.

 

Schmelzer GH (2006). Holarrhena floribunda (G. Don) T. Durand & Schinz. PROTA (Plant Resources of Tropical Africa/Ressources végétales de l'Afrique tropicale), Wageningen, Netherlands.

 

Sproßmann R, Zauer M, Wagenführ A (2017). Characterization of acoustic and mechanical properties of common tropical woods used in classical guitars. Results in Physics 7:1737-1742.
Crossref

 

Tchoundjeu Z, Atangana AR (2007). Ricinodendron heudelotii (Baill.) pierre ex Heckel. Record from Protabase.

 

Traoré B, Brancheriau L, Perré P, Stevanovic T, Diouf P (2010). Acoustic quality of vène wood (Pterocarpus erinaceus Poir.) for xylophone instrument manufacture in Mali. Annals of Forest Science 67:815.
Crossref

 

Tsoumis G (1991). Science and technology of wood: structure, properties and utilization. New York: Van Nostrand Reinhold.

 

Wegst UG (2008). Bamboo and wood in musical instruments. Annual Reviews of Materials Research 38:323-349.
Crossref

 

Wegst UGK (2006). Wood for sound. American Journal of Botany 93(10):1439-1448.
Crossref

 

World Bank Group (2020). Note sur les forêts du Bénin. Report No: AUS0001346.

 

Yano H, Kajita H, Minato K (1994). Chemical treatment of wood for musical instruments. The Journal of the Acoustical Society of America 96(6):3380-3391.
Crossref

 

Yano H, Matsuoka I, Mukudai J (1992). Acoustic properties of wood for violins. Mokuzai Gakkaishi 38:122-127 (in Japanese).

 

Yano H, Minato K (1993). Controlling the timbre of wooden musical instruments by chemical modification. Wood Science and Technology 27(4):287-293.
Crossref

 

Yano H, Oonishi K, Mukudai J (1990). Acoustic Properties of Wood for the Top Plate of Guitar. Journal of the Society of Materials Science, Japan 39:1207-1212 (in Japanese).
Crossref

 

Yoshikawa S (2001). From the cembalo to the piano: Progress in early keyboard instruments. Journal of the Acoustical Society of Japan 57:704-711 (in Japanese).

 

Yoshikawa S (2007). Acoustical classification of woods for string instruments, Journal of the Acoustical Society of America 122(1):568-573.
Crossref

 




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