Exploring the Dynamic Properties of Tropical and Temperate Wood Species for Musical Instruments

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The results of this study are applicable both for musical instrument manufacturers to choose new species integrated into the resonator body, as well as for researchers in the forestry industry regarding the physical, elastic, and acoustic properties of the studied species.

Abstract

This paper explores the dynamic behavior of different wood species in the form of violin boards, based on experimental modal analysis using a single-input, multiple-output configuration. Thus, two groups of species were studied: the first group for the violin top plates, being analyzed Picea abies (spruce), Taiwania cryptomerioides Hayata (Taiwania), and Cryptomeria japonica (Japanese cedar), and the second group, with species for the back plates, such as Acer pseudoplatanus (maple), Populus nigra (poplar), Salix alba (willow), and Firmiana simplex (Chinese parasol). The results highlighted the frequency spectrum and the dominant resonance frequency, as well as the frequency damping, the signal processing analysis being based on Fast Fourier Transform and Wigner–Ville distribution of signals. The results highlighted that the lowest values of acoustic radiation are recorded for maple wood (7.8 m⁴ kg⁻¹ s⁻¹) and Taiwania (10.08 m⁴ kg⁻¹ s⁻¹), and the highest values for spruce (14.7 m⁴ kg⁻¹ s⁻¹) and Chinese parasol (15.58 m⁴ kg⁻¹ s⁻¹). Regarding the resonance frequency, the Taiwania and Japanese cedar plates present the dominant frequency around 600–635 Hz in comparison with Norway spruce having 920 Hz. The ratios between dominant frequencies of the Chinese parasol, poplar, maple, and willow are 1:1.42:2.62:2.98. It can be concluded that spruce and maple wood present the best dynamic properties, but when using other species, Japanese cedar wood for the top plate and Chinese parasol wood for the back plate represent species with potential in the construction of stringed musical instruments. Either a mechano-thermal treatment or an appropriate finish can enhance the acoustic qualities of these wood species, research that can be undertaken in the future.

1. Introduction

In the construction of violins, spruce and maple wood are used by luthiers both for their acoustic and aesthetic properties, as well as for preserving the tradition inherited from the great violin-making schools. Stringed musical instruments such as the violin are traditionally made of spruce and maple wood, carefully selected in terms of anatomical quality (regularity of annual rings, width of annual rings, proportion of latewood/earlywood, lack of defects in spruce wood, waviness of the fiber, and esthetic appearance in maple wood). In terms of physical and elastic properties, these species present certain particularities, such as low density, high modulus of elasticity (in spruce wood), and high propagation speed in longitudinal and radial directions [1,2,3,4].

In the conditions of the restriction of the wood resource because of the exploitation of forests without a rigorous selection of logs with resonant wood, musical instrument builders are exploring the possibility of using alternative species, either species from the temperate zone or tropical species (for those who have easier access to such species). However, there are studies on the use of other wood species for violin backs, both from temperate and tropical areas, or composite materials, 3D-printed materials, and metamaterials as favorable alternatives, as were highlighted by [5,6]. Regarding the alternative wooden species from the temperate region, ref. [7] found that hornbeam and willow wood, closely followed by ash wood, have a good potential to be successfully used in the manufacture of violin backboards, while poplar wood does not show favorable properties. Walnut wood and bird’s-eye maple showed a wide variability regarding the modal and acoustic characteristics, due to the inhomogeneous structure. Refs. [2,8,9,10,11] mention a series of elastic and acoustic characteristics that are necessary for wood to be used in the construction of violins, among which can be mentioned density, Young’s modulus in the longitudinal and radial directions, sound propagation speed, impedance, sound radiation coefficient, the quality factor, and the logarithmic decrement.

Thus, ref. [12] highlighted the acoustical properties of several Australian wood species using ultrasonic velocity methods: three softwood species (King William Pine (Athrotaxis selaginoides), Huon Pine (Dacrydium franklinii), and Celery-top Pine (Phyllocladus asplenifolius)) and three hardwood species (Southern Sassafras (Atherosperma moschatum), Blackwood (Acacia melanoxylon), and Tasmanian Beech, Myrtle (Nothofagus cunninghamii)). The authors draw attention to the fact that the quality of the studied species is unpredictable due to intra-species variations, and the collected data do not define or guarantee the acoustic quality of the musical instruments obtained from such assortments, additional studies being necessary. Ref. [11] studied the distribution of vibrational properties (specific dynamic modulus and damping coefficient) on 395 tropical species, observing, like ref. [13], that there are large variations in wood properties, the specific dynamic modulus varying between 16 and 35 GPa, and the coefficient of damping tan δ between 5 × 10⁻³ and 9.5 × 10⁻³. Also, acoustic and mechanical properties of tropical species such as Indian Rosewood (Dalbergia latifolia Roxb.), Ziricote (Cordia dodecandra DC), African Blackwood (Dalbergia melanoxylon Roxb.), and Ebony (Diospyros crassiflora Hiern.) were studied by ref. [14]. All researchers concluded that tropical species show a high variability of properties because of variations in wood microstructure and chemical components between species and within trees, as well as environmental factors [15,16]. However, tropical wood can be found in many old and current musical instruments. The purpose of the paper is to investigate the vibrational properties of tropical species from Taiwan and other European wood species with potential in the construction of stringed musical instruments, especially the violin. This concerns, on the one hand, the use of Taiwan’s wood resources, resulting from serious natural hazards, but also the superior exploitation of species such as Taiwania cryptomerioides Hayata (Taiwania), Cryptomeria japonica (Japanese cedar), and Firmiana simplex (Chinese umbrella), as well as the possibility of using European species instead of the traditional ones—spruce and maple wood. The novelty of the study consists of the analysis of the physical, acoustic, and vibrational characteristics of violin boards made of tropical and temperate wood species compared to the traditional ones (spruce and maple).

2. Materials and Methods

2.1. Materials

In the present study, three tropical wood species from Taiwan, such as Taiwania cryptomerioides Hayata (Taiwania), Cryptomeria japonica (Japanese cedar), and Firmiana simplex (Chinese umbrella), and four temperate wood species from Romania (Picea abies (Norway spruce), Acer pseudoplatanus (maple), Populus nigra (poplar), Salix alba (willow), and Firmiana simplex (Chinese parasol known as Phoenix tree)) were analyzed. The spruce wood samples were obtained from wood logs harvested from the Moldovița Forest District (Suceava-Bucovina), Romania, known for its stands of resonant Norway spruce. The maple wood samples with curly fiber come from trees harvested from the Gurghiu Mountains, Romania, and the poplar and willow wood come from the Mures River Plain, Romania [17,18]. The tropical wood—Taiwania cryptomerioides Hayata (Taiwania), Cryptomeria japonica (Japanese cedar), and Firmiana simplex (Chinese umbrella)—comes from Taiwan. The Taiwania and Japanese cedar wood comes from trees felled by typhoons, their harvesting being quite difficult due to the high altitudes [19,20,21,22]. Also, identifying the use of wood from trees felled by typhoons to produce different components for violins and guitars is an objective of sustainable wood utilization [23,24,25]. The two Taiwanese wood species used in this study—Taiwania, or Taiwan cedar, and Chinese parasol—were obtained from thinning wood approximately 40 years old and 20 years old, respectively. Their density and annual ring spacing differ significantly from traditional spruce and maple, which may be a major factor influencing their acoustic properties. The plates were grouped into two categories: group 1 containing the coniferous samples—spruce, Japanese cedar, and Taiwania—and group 2 containing the deciduous species—maple, poplar, willow, and Chinese parasol. Figure 1 shows the types of samples tested, and Table 1 presents the physical characteristics of the samples. The experimental violin plates were prepared following the standard templates used for traditional spruce and maple violin plates. Therefore, the results from this study can provide valuable reference data for future processing or adaptation of these alternative wood species, offering more informed guidance to instrument makers.

Figure 1. The shapes of the wooden samples studied: (a) the rectangular shape of the samples for determining the acoustic parameters (L—length; B—width; h—thickness); (b) the violin plate shape for experimental modal analysis.

Table 1. Physical features of samples (mean values and standard deviation).

The Main Groups of Samples	Wood Species	Moisture Content MC (%)	Density (g/cm3)
Group 1 Coniferous species	Norway spruce	7.0	0.430
	(Picea abies)	(0.90)	(0.045)
	Taiwania	6.2	0.357
	(Taiwania cryptomerioides Hayata)	(0.8)	(0.030)
	Japanese cedar	6.5	0.392
	(Cryptomeria japonica)	(0.7)	(0.020)
Group 2 Deciduous species	Maple	7.5	0.640
	(Acer pseudoplatanus)	(0.90)	(0.043)
	Poplar	7.6	0.420
	(Populus nigra)	(0.7)	(0.027)
	Willow	7.3	0.450
	(Salix alba)	(1.05)	(0.044)
	Chinese parasol	6.8	0.279
	(Firmiana simplex L.)	(0.7)	(0.020)

Two types of samples were prepared in terms of geometric shape: rectangular prisms from each species to determine the density, sound propagation velocity in the longitudinal direction of the wood, elastic modulus, and acoustic impedance, and samples with violin board geometry (one from each species) to determine the resonance frequency spectrum, quality factor, and logarithmic decrement.

2.2. Methods

2.2.1. Determination of Acoustic Properties

• Sound velocity in wood (SV)

The sound velocity in wood was determined based on the ultrasound (US) method [26,27]. This method consists of the application of elastic physical waves on the tested sample, knowing the distance between transducers. The principle of the test method presented in Figure 2 consisted of fixing the wooden sample (1) between the two transducers (2, 3) of the ultrasound device (5), which transmits the ultrasound flow through the investigated material. The signal was captured by the receiver (3), which is connected to the microcontroller through the connector (4). Both the input and output signals are analyzed and compared against time by means of the microcontroller built into the measuring device (5) [28,29].

Figure 2. The experimental setup for the determination of sound velocity. (Legend: 1—sample; 2—US transmitter; 3—receiver; 4—connectors; 5—microcontroller device).

• Dynamic Modulus of Elasticity (DMOE)

Knowing the wood density $\rho$ of each sample based on the ratio between the mass and the volume of the samples, the dynamic modulus of elasticity in the longitudinal direction (denoted DMOE_L) was calculated as a function of the speed of ultrasound propagation ($V_{LL}$) according to Equation (1).

$${DMOE}_L=V_{LL}^2\ast \rho ,$$

(1)

• The acoustic impedance, $z$, is calculated according to relation Equation (2):

$$z=V_{LL}\ast \rho ,$$

(2)

• The sound radiation coefficient, $R$, is determined by Equation (3):

$$R={\displaystyle \frac{V_{LL}}{\rho },}$$

(3)

2.2.2. Experimental Modal Analysis (EMA)

The modal behavior of the violin plates was investigated using the technique of experimental modal analysis (EMA). Theoretical approaches mainly included the evaluation of the stabilization diagram and the modal fitting procedure based on 36 modes. Thus, it obtained spectral frequencies and damping ratios, respectively [30]. Considering the spectral damping ratio easily results in the spectral quality factors and the resonance response time. Supplementary to the joint time-frequency advanced analyses were considered, supposing the Short-Time-Fast-Fourier-Transform (STFFT) and Wigner–Ville Distribution (WVD) to investigate and compare, respectively, the spectral remanences for each dominant frequency within the spectrum. The experimental setup for the EMA procedure was developed supposing the single-input-multiple-outputs technique application. Thus, the wooden plates (1) were suspended through an elastic support (2), the data being collected under free-free conditions [30]. A vibration test was performed, exciting the violin board at 35 different points with an impact hammer (3) (Figure 3). For modal identification, a set of three uniaxial accelerometers (4) was used, placed in three different positions on the violin plate (denoted A, B, and C), according to the scheme in Figure 3. The signals acquired by accelerometers were transmitted through a conditioning device to a Dynamic Signal Acquisition System (DAQ) (5)—NI USB-9233 by National Instruments (Austin, TX, USA), connected to a laptop (6). The signal was acquired by means of a special application developed by the authors in NI-LabVIEW© (National Instruments, Austin, TX, USA), and the data was processed and analyzed by means of a group of applications (7) developed in MatLab© (MathWorks, Torrance, CA, USA). Figure 4 presents the types of violin reeds studied and how they were grouped for the comparative analysis of the dynamic response. It was considered the effective application of each type of tone wood for the violin body components (in terms of front or back plate type).

Figure 3. Experimental setup for EMA. (Legend: 1—the violin plate; 2—elastic supports; 3—impact hammer applied in marked points (1—35); 4—accelerometers (A, B, C); 5—Dynamic Signal Acquisition System; 6—computer; 7—processing data program; The red, yellow, blue arrows represent the connections from the accelerometers to the acquisition board).

Figure 4. Violin plates grouped for dynamic analysis (Legend: a—Taiwania; b—Japanese cedar; c—Chinese parasol).

2.2.3. Processing Signals

Pre-processing of acquired signals was directly performed within the NI-LabVIEW application, which mainly covers and manages the acquisition procedural stage. Post-processing, analysis, and management of raw data were performed using a set of conformal applications (developed by the authors in the Matlab platform, R2025a version). Modal analysis in terms of stabilization diagram and modal fitting has supposed the whole ensemble of acquired data for a plate (105 raw acquired signals). Considering that one of the main aims of this study is the comparative analysis between different plate responses in terms of dominant frequencies, it was considered the normalized spectral magnitude by its maximum value [29,30]. In addition, the average spectral response was used to facilitate the evaluation of spectral differences. Dominant frequencies and spectral damping ratios, respectively, were computed based on a modal fitting technique with 36 imposed modes (the same value was also used within stabilization diagram evaluation). Modal fitting was performed using the least-squares complex exponential (LSCE) method, which computes the impulse response corresponding to each frequency-response function (provided as input) and fits to the response a set of complex damped sinusoids with respect to Prony’s method. The spectral remanence (or spectral components persistence) was investigated supposing both STFFT and WVD diagrams, considering that STFFT provides a global view of spectrum changes during analysis time, while the WVD algorithm could dignify especially the dominant frequencies with respect to the time-frequency domain. The quality factor and the resonance response time were computed according to the damping ratio evaluated for maximum dominant frequency within each average magnitude spectrum, using an advanced procedure implying the half-power method and interpolation techniques.

3. Results

3.1. Acoustic and Elastic Parameters

An important characteristic of wood for musical instruments is the speed of sound propagation, a property that has been studied by numerous researchers [31,32,33,34]. Thus, in Figure 5a, one can observe the stratification of the species studied according to the speed of sound propagation, highlighting the distribution of data through quartiles, showing the minimum, first quartile, median, third quartile, and maximum values. It can be noticed that there is a normal distribution of values for Taiwania and maple samples, a positive skew for Japanese cedar, poplar, and spruce, respectively, and a negative skew for Chinese parasol and willow.

Figure 5. The distribution of (a) sound velocity and (b) DMOE in the longitudinal direction of wood samples.

The extreme values are given by Taiwanese cedar wood, which records the lowest values of the propagation speed (3300 m/s), and at the opposite pole is Norway spruce wood, with the average value of 5854 m/s. Unlike [34], who determined the propagation speed on Taiwania cryptomerioides Hayata specimens with large lengths and on different quality classes at the equilibrium humidity with the environment, obtaining values between 4154 and 4558 m/s, in the presented study, the values obtained were determined on samples conditioned at a humidity of 7–8%. Japanese cedar wood reaches maximum values of the propagation speed of 5081 m/s, but since there is a large dispersion of the values depending on the anatomical characteristics of the samples, the choice of this species for the manufacture of musical instruments must be made rigorously. The analyzed hardwood species (maple, poplar, willow, and Firmiana simplex) record values of the propagation speed ranging from 4300 to 4800 m/s, as can be seen in Figure 5a. Based on the relationship (2), the value of the dynamic modulus of elasticity was determined, whose variation according to the species is presented in Figure 5b. According to [34], the longitudinal dynamic modulus of elasticity (DMOE) of Taiwania samples at equilibrium humidity (15–18%) varies between 5700 and 7500 MPa, and the modulus of rupture varies between 30 and 42 MPa. In the current study, the DMOE values of Taiwania samples at 7–8% humidity varies between 4100 and 5500 MPa, being the species with the lowest values of the modulus of elasticity. The Chinese parasol samples are characterized by a higher value of DMOE compared to the Taiwanese cedar, reaching values ranging between 4600 and 6200 MPa, and those of Japanese cedar vary between 9000 and 11,000 MPa. Due to intraspecific diversity in tropical species, the authors reserve the right to present the values obtained on the tested samples. In temperate species, the DMOE shows the following values: poplar (9200–11,000 MPa), willow (7700–13,000 MPa), maple (10,900–15,000 MPa), and spruce (8000–16,000 MPa). Comparing the values of tropical species with temperate ones, respectively, in the two groups (conifers and deciduous trees), it results that the tropical samples present lower values of the dynamic modulus of longitudinal elasticity, of approximately 1.5 (Japanese cedar)–3.0 (Tawiania) compared to Norway spruce wood, and 2.5 (Firmiana simplex L.) and 1.3 (willow and poplar) compared to maple wood [35]. In the case of spruce and maple samples, it is observed in Figure 5 that there are some outliers (points represented individually beyond the whiskers), which are distributed approximately uniformly on both sides of the graph, resulting from the samples tested for different quality classes.

The variation in acoustic impedance depending on the tested wood species is presented in Figure 6a, and in Figure 6b, the variation in acoustic radiation. The variation in acoustic impedance according to the tested wood species is presented in Figure 6a, and in Figure 6b, the variation in acoustic radiation. Acoustic impedance represents the resistance that wood opposes to the propagation of sound, being related to the difficulty of transmitting vibration from one medium to another [36], e.g., from the strings to the sound box, or, in other words, the agility of sound in wood [37]. According to ref. [2], the sound intensity tends to zero if the propagation media in contact have very different acoustic impedances. As can be seen in Figure 6a, the lowest values of acoustic impedance are recorded for wood species Chinese parasol and Taiwania (1.24–1.26) × 10⁶ N s m⁻³, while the highest values are for spruce (2.43 × 10⁶ N s m⁻³) and maple (3.0 × 10⁶ N s m⁻³). From the perspective of the musical quality of the instrument, acoustic impedance indicates agility and lightness. To maximize the strength of the sound, ref. [38] recommends that materials be selected in the construction of the musical instrument that ensures the highest radiation in relation to the loss of sound energy. Thus, the wood for the top plate should give strength to the sound, and the back should be from a species that dampens the sound—the optimal size ratio between their acoustic radiations being 2:1 [1]; as a result, the two components of the music box will be cut from different species, the back species having considerably heavier wood than the face species [1]. In Figure 6b, the stratification of acoustic radiation according to the tested species indicates that the lowest values of acoustic radiation are recorded for maple wood (7.8 m⁴ kg⁻¹ s⁻¹) and Taiwania (10.08 m⁴ kg⁻¹ s⁻¹), and the highest values for spruce (14.7 m⁴ kg⁻¹ s⁻¹) and Chinese parasol (15.58 m⁴ kg⁻¹ s⁻¹).

Figure 6. Stratification of the studied wood species according to (a) acoustic impedance and (b) acoustic radiation.

3.2. Experimental Modal Analysis

3.2.1. Spectrograms of Signals

The results obtained by modal analysis were grouped into two groups: group 1—boards from coniferous species, and group 2—from deciduous species. In Figure 7, the comparative analysis of the spectrograms highlights a fundamental characteristic of the categories of boards analyzed. Thus, tropical wood boards present harmony with a wide frequency spectrum but with low remanence. The exception is the dominant harmonic that is found over the entire analyzed time domain, being in the 500–600 Hz range, unlike temperate wood boards whose dominant frequency is in the 800–1500 Hz range. The remanence of harmonics for these types of plates is increased, even if the dominant frequency does not cover the entire analyzed time domain. The differences between the dynamic responses of boards made of different wood species are more pronounced, especially in the deciduous species (the second group) (Figure 7b). These observations are also underlined by the analysis based on the Wigner–Ville distribution presented in Figure 8. Also, the Wigner–Ville diagrams reveal spectral elements characteristic of the two categories of wood species: tropical and temperate. Thus, temperate wood plates show clear spectral transitions throughout the dynamic regime, while tropical wood boards have a constancy of spectral components (highlighting the spectral transitions of tropical wooden plates is also made difficult by the fact that their dynamic regime is much reduced compared to that of temperate wooden plates).

Figure 7. Spectrograms of signals: (a) violin plates from group 1; (b) violin plates from group 2.

Figure 8. Wigner–Ville distribution of signals: (a) violin plates from group 1; (b) violin plates from group 2.

3.2.2. Comparison of Frequency Spectrum

In the comparisons of the frequency spectra, the Norway spruce plate was considered as a reference for group 1 because this is the wood species established for violin top plates (Figure 9a), and the Chinese parasol wood plates were considered as a reference for the second group (Figure 9b). Within the analysis of each group, overlapping spectra (in the upper part of each figure) and spectral differences (in the lower part) can be distinguished. Regarding the first group of boards analyzed (spruce versus Taiwania and Japanese cedar), it can be stated that the comparative analysis of the frequency spectra clearly highlights the following aspects: the Taiwania plate presents a dominant frequency around 600 Hz, otherwise having an amplitude spectrum rich in harmonics (extending up to 3500 Hz), but with reduced weights in the spectral ensemble; the Japanese cedar plate offers a much richer spectrum, with representative harmonics up to 4000 Hz, with dominant harmonics below 1000 Hz and a representative peak around 1500 Hz. With all these apparently different characteristics, the spectral difference diagram clearly indicates that the tropical wooden plates offer a relevant spectrum in a range lower than the 800 Hz value, while the spruce board presents two dominant spectral components near the values of 900 Hz and 1800 Hz (Figure 9a). The second group of plates shows that plates from temperate wood species have representative spectral components in the range above 1000 Hz, while tropical wood plates do not exceed 950 Hz. The frequency spectrum of these boards are much richer in harmonics, but the comparative representativeness is clearly in favor of those from temperate wood for the medium-high frequency range and of tropical wood for the low frequencies (Figure 9b). Table 2 presents the values of the resonance frequencies extracted from the FFT analysis, and the dominant frequencies are highlighted in bold.

Figure 9. Comparison between frequency spectra: (a) violin plates from group 1; (b) violin plates from group 2.

Table 2. The resonance frequency of the studied wood species in the low and medium frequency domains.

Wood Species	Weight (g)	Resonance Frequency (Hz)
		1	2	3	4	5	6	7	8	9	10
Norway spruce	92	848	922 *	1062	1282	1349	1508	1660	1886	2045	2307
Taiwania	95	403	635 *	836	903	1270	1416	1593	2026	2588	3180
Japanese cedar	97	385	604 *	824	970	1459	1794	2289	2368	2765	3778
Maple	129	1105	1208	1245	1550 *	1685	1929	2368	2710	3406	3790
Poplar	125	604	739	842 *	1135	1453	1569	1898	2142	2368	2539
Willow	83	311	677	1019	1135	1392	1465	1624	1770 *	2112	2246
Chinese parasol	76	323	360	488	525	592 *	781	964	1477	1636	1929

(Legend: * Dominant Frequency).

3.2.3. Damping Ratio

The variation in the damping ratio, denoted by ζ, is presented in Figure 10. From the point of view of spectral damping, all categories and types of plates present damping ratios of a maximum of 0.2 (the few exceptions—for the plates in the first group—can be treated separately, without considerable influence on the overall ensemble). The spectral spread of the values also has a similar structure for both groups; namely, it presents higher values at frequencies below 2000 Hz and lower ones (<0.1) above this value.

Figure 10. Damping ratio variation: (a) wood species for violin top plate; (b) wood species for violin back plate.

Each system has a Q-factor depending on its construction. In vibration testing, the Q-factor relates to the sharpness of a resonance. Resonance occurs when the drive frequency of the sine test profile equals the test item’s natural frequency, which amplifies the frequency to a potentially damaging level. The resonance sharpness is determined by the ratio of its center frequency and half-power bandwidth. Most studies use the calculation relationship of the quality factor (Q⁻¹) as the ratio between the half-value width of the resonance peak and the peak frequency [3,4,7,8,9,39].

In Table 3, the values of damping ratio, quality factor, and resonance response time in the case of dominant frequency are presented. The Q-factor also relates to a resonance’s response time. Resonance with a low Q value covers a wider range of frequencies and has a faster response time, meaning the resonance responds faster to changes in amplitude. A product with a high-Q resonance typically has a longer response time, meaning it will take longer to see an effect at the response location when the input amplitude changes. The demand response time should be slower than the resonance. In Table 3, the expected response time was calculated for a resonance with a frequency-to-time equation. It can be noted that tropical species have a longer response time, and from spectral analysis, the frequency spectrum is richer than in temperate species. Some properties have a greater weight when classifying the material as a resonant wood. Ref. [40] but also ref. [41] considers that the close connection with the elastic moduli and acoustic radiation recommends density as the main criterion for the selection of wood with acoustic qualities. Refs. [41,42,43] emphasize the importance of acoustic radiation, while refs. [43,44] claim the importance of the damping factor. Ref. [44] designates loudness as the most important acoustic parameter. Damping parameters are crucial when choosing wood for plucked or struck string instruments and have a lower value in the case of bowed instruments, where the state of vibration of the strings is continuous [9,43,44,45]. In conclusion, the acoustic quality of wood for musical instruments must be assessed through a multi-criteria analysis regarding physical, elastic, and acoustic characteristics, as well as considering the combination of species used for the soundboard.

Table 3. The damping ratio, quality factor, and resonance response time.

Wood Species	Damping Ratio, ζ, for Dominant Frequency	Quality Factor Q (1/2 ζ)	Resonance Response Time (sec.)
Norway spruce	0.0176	28	0.0309
Taiwania	0.0239	21	0.0330
Japanese cedar	0.0252	20	0.0329
Maple	0.0145	34	0.0222
Willow	0.0164	30	0.0172
Poplar	0.0218	23	0.0272
Chinese parasol	0.0264	19	0.0320

4. Conclusions

The paper presented an extensive analysis of the physical and acoustic properties of some species with potential for use in musical instruments. In addition to determining the density and sound propagation velocities and the acoustic characteristics derived from this, the frequency spectra and vibrational characteristics of the violin boards of the seven investigated species were determined. The most important findings are summarized in Table 4.

Table 4. Obtained results of the physical, elastic, and acoustic characteristics.

Acoustic and Dynamic Properties	Norway Spruce	Taiwania	Japanese Cedar	Maple	Willow	Poplar	Chinese Parasol
Density (kg/m3)	430 (45)	357 (30)	392 (20)	640 (43)	450 (44)	420 (27)	280 (20)
Sound velocity (m/s)	5875 (423)	3573 (282)	4310 (825)	4653 (247)	4820 (268)	4872 (166)	4325 (182)
DMOE (MPa)	14,500 (2500)	4834 (461)	9724 (488)	13,570 (1500)	9997 (1965)	9994 (617)	5336 (463)
Acoustic radiation (m4 kg−1 s−1)	15.22 (1.007)	10.088 (0.254)	13.167 (0.400)	7.790 (0.259)	11.082 (1.112)	11.339 (0.695)	15.585 (0.801)
Acoustic impedance (×106 N s m−3)	2.43 (0.268)	1.26 (0.048)	1.96 (0.081)	3.06 (0.133)	2.12 (0.335)	2.01 (0.094)	1.25 (0.068)
Dominant frequency (Hz)	922	635	604	1550	842	1770	592
Quality factor Q	28	21	20	34	30	23	19

Since the purpose of this study was to estimate which other wood species could replace the established species (spruce and maple), all the determined parameters were compared with the reference species. Of these, Japanese cedar and Chinese parasol wood show a high potential for their use in the violin body.