Assessment of the Measurement and Prediction Methods for the Acoustic Properties of Natural Fiber Samples and Evaluation of Their Properties

ABSTRACT Although some studies have been conducted to show how natural fibers can replace synthetic materials, the use of many natural fibers is still limited. On the other hand, the use of natural fibers can become very common in many applications once their performance is fully understood. This paper aims to present a critical assessment of the acoustic properties of natural fiber samples. First, the methods commonly used for the measurement and prediction of the acoustic properties of natural fiber samples are determined. Second, the common techniques for measuring sound absorption coefficients (SACs) and sound transmission losses (STLs) are presented, and their advantages and limitations are evaluated. After that, the models commonly used for the prediction of acoustic properties are presented. Then, the SACs of many natural fiber samples are presented along with the thickness, bulk density and flow resistivity of the samples. Furthermore, the SACs of the samples are normalized using sample thickness and bulk density, and the sound absorption performance of the fiber samples is evaluated. Based on the results of many natural fiber samples, an empirical model for estimating the SACs of natural fiber samples is presented. Finally, the STLs of some porous natural fiber samples are presented.


Introduction
Development of new materials to replace synthetic materials, such as carbon fibers, has become a necessity due to the adverse effects of chemical-or petroleum-based materials on nature and human health. Due to their biodegradability and sustainability, natural fibers are very promising alternatives to synthetic materials. Natural plant fibers include seed hairs (such as cotton), stem fibers (such as flax and hemp), leaf fibers (such as sisal) and husk fibers (such as coconut). Natural animal fibers include silk and wool. Although some studies have been conducted to show how natural fibers can replace synthetic materials, or to reveal their applications (Das et al. 2020;Gurunathan, Mohanty, and Nayak 2015;Lalit, Mayank, and Ankur 2018;Steffens, Steffens, and Oliveira 2017;Sydow and Sambu et al. 2016 (Continued) samples was presented. In addition, the STLs of some porous natural fiber samples were presented in this study.
The structure of this paper is as follows. First, the techniques commonly used for the measurement of the acoustic properties of natural fiber samples are presented in Section 2. Here, the techniques for measuring both the SACs (Section 2.1) and STLs (Section 2.2) of natural fiber samples are included. The advantages and limitations of the common methods are summarized in Section 2.3. After that, commonly used models to predict the SACs of natural fiber samples are presented in Sections 3.1.1- 3.1.5. The estimation of the physical parameters needed in these models is presented in Section 3.1.6. The mathematical models for the prediction of the SACs of porous samples are evaluated in Section 3.1.7. The prediction of the STLs of structures is presented in Section 3.2. Subsequently, the SACs of many natural fibers are presented in Section 4.1. Both the SACs for 125-2000 Hz and the noise reduction coefficients (NRCs) of the samples are presented. Unlike some review studies in the literature, not only the SACs and thicknesses of the samples are presented, but also their bulk densities and flow resistivities are included. It should be noted that the SACs for different sample thickness, bulk density and flow resistivity values are presented in this study. In addition, by using the bulk density and thickness of the samples, the SACs are normalized, and the sound absorption performance of the samples per unit mass is presented. Furthermore, based on the normalized results of many natural fiber samples, an empirical model for the estimation of the SACs of porous samples is presented. It should be noted that, although there are various studies on the SACs of natural fiber samples (Bhingare, Prakash, and Vijaykumar 2019;Gokulkumar et al. 2020;Kalauni and Pawar 2019;Liao, Zhang, and Tang 2020;Mamtaz et al. 2016;Tang and Yan 2017;Yang et al. 2020), limited number of studies have included the STLs of these materials (Bansod, Mittal, and Mohanty 2016;Bhingare and Prakash 2020;Zhu et al. 2014). The STLs of some porous natural fiber samples are presented in Section 4.2. Finally, some concluding remarks are given in Section 5.

Measurement of acoustic properties
Once the methods commonly used to measure the SACs and STLs of natural fiber samples have been determined, they are presented and discussed here. The evaluations made here about the commonly used methods for measuring the acoustic properties of samples can be used to select the correct measurement technique, and to evaluate the measured results in real applications.

Measurement of sound absorption coefficients (SACs)
There are several methods for measuring the SACs of material samples, such as standing-wave-ratio method (or one-microphone impedance tube method), two-microphone transfer function method (or two-microphone impedance tube method), and reverberation room method. The two-microphone transfer function method is delineated in the ISO 10534-2 (ISO (International Organization for Standardization) 1998) and ASTM E1050 (ASTM (American Society for Testing and Materials) 2019a) standards. The reverberation room method is described in the ISO 354 (ISO (International Organization for Standardization) 2003) and ASTM C423 (ASTM (American Society for Testing and Materials) 2017) standards. As mentioned before, the researchers mostly used the two-microphone transfer function method, and there are several studies on the use of the reverberation room method to determine the SACs of natural fiber samples. Therefore, these two methods are presented below.

Two-microphone transfer function method
The schematic picture of the two-microphone transfer function method is shown in Figure 1. In this method, the complex-valued normal-incidence reflection coefficient R can be determined by (Koruk 2014): where ω ¼ 2πf is the angular frequency, H 12 ω ð Þ is the complex-valued acoustic transfer function, which is calculated from the sound pressure signals p 1 to p 2 measured with the two microphones, s is the distance between the two microphones, L is the distance between the right microphone and the test sample, k 0 ¼ ω=c 0 is the wave number of the air, where c 0 is the speed of the sound in the air, and j ¼ ffi ffi ffi ffi ffi ffiffi À 1 p . The normal-incidence SAC is determined as:

Reverberation room method
The schematic drawing of the reverberation room method is shown in Figure 2. In this method, the random-incidence SAC is determined by (Shtrepi and Prato 2020): where S is the sample surface area (m 2 ), and V is the reverberation room volume (m 3 ). Here, c 01 and c 02 are the propagation speeds of sound in the air (m/s) without and with the test sample that can be calculated using c 0 ¼ 343:2 ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 293=T p , where T represents the temperature (K); t 1 and t 2 are the reverberations times measured before and after the test sample is placed in the reverberation chamber or room; and m 1 and m 2 are the power attenuation coefficients of the climatic conditions in the reverberation room without and with the samples that can be calculated according to ISO 9613-1 (ISO (International Organization for Standardization) 1993), respectively.

Measurement of sound transmission losses (STLs)
There are various methods to measure the STLs of material samples, such as sound intensity method, four-microphone transfer matrix method, and conventional two-room method. The sound intensity method is delineated in the ISO 15186-1 standard (ISO (International Organization for Standardization) 2000). The four-microphone transfer matrix method is described in the ASTM E2611 standard (ASTM (American Society for Testing and Materials) 2019b). The conventional tworoom method, in which both rooms are reverberant, is presented in the ASTM E90 standard (ASTM (American Society for Testing and Materials) 2016). It should be noted that, as mentioned earlier, the researchers mostly used the four-microphone transfer matrix method, and there are a few studies on the use of the conventional two-room method to experimentally determine the STLs of natural fiber samples. Therefore, after briefly mentioning the sound intensity method, the other two methods are presented below.

Sound intensity method
In the sound intensity method, in which the sample is placed between the source and receiving room, a microphone on the source side records the sound pressure levels, and an intensity mapping is obtained on the receiving side. The STL of the test sample is calculated using (Lai and Burgess 1991): where L p i is the incident space-averaged sound pressure level in the source room, and L I i and L I t are the incident and transmitted sound intensity levels, respectively. Although only one reverberant room is needed in this method, it is seen that this method is not common in practice today.

Four-microphone transfer matrix method
The schematic picture of the four-microphone transfer matrix method is shown in Figure 3. In this method, the sound pressures measured at four measurement positions, named x 1 to x 4 , can be expressed as (Jung et al. 2008): where A and B indicate the incident and the reflected wave components in the upstream tube, and C and D show the transmitted and the reflected wave components in the downstream tube, respectively. The amplitudes A to D can be derived from the above equations as follows: The problem can be formulated as the following matrix equation (Bolton, Yoo, and Olivieri 2007): As Eq. (2.7) contains only two expressions but four unknowns (T 11 , T 12 , T 21 , and T 22 ), it cannot be solved. Under certain circumstances, it is possible to exploit the reciprocal nature of a sample to generate two additional equations, instead of making a second set of measurements. It is noted that reciprocity requires that the determinant of the transfer matrix is unity (T 11 T 22 -T 12 T 21 = 1). Furthermore, we have T 11 = T 22 for symmetrical systems (Bolton, Yoo, and Olivieri 2007). Now, let's consider a sample of depth h backed by a perfectly anechoic termination, so that it can be assumed that D is identically zero in the downstream tube section. Hence, the normal-incidence sound transmission coefficient T a ¼ C=A is obtained as: Hence, the normal-incidence STL of a sample can be calculated as: Furthermore, if we use equal distance between the two microphones (s 1 ¼ s 2 ¼ s), STL can be written as follows (Jung et al. 2008): where H 12 and H 34 are the acoustic transfer functions, which are calculated from the sound pressure levels p 1 to p 2 and p 3 to p 4 , respectively, and H t ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi S d =S u j j p is the ratio between upstream (S u ) and downstream (S d ) auto-spectrums. It should be noted that the four-microphone transfer matrix method can be used to determine the SACs of test samples as well.

Conventional two-room method
The schematic drawing of the conventional two-room method is shown in Figure 4. In this method, in which both the source and receiving rooms are diffuse or reverberant, the STL of a partition with surface area S can be expressed in terms of the average sound pressure level in the source room (L p i ) and in the receiving room (L p t ) as (Lai and Burgess 1991): where A is the absorption of the receiving room.

Summarizing and comparing the common methods for measuring acoustic properties
Acoustic tests are performed using small cylindrical samples (about 15/30 to 100 mm in diameter) in the two-microphone transfer function (a) and four-microphone transfer matrix (b) methods, while larger samples (several meters in size) or complete objects are used in the reverberation room (c) and conventional two-room (d) methods. The first two methods (a and b) are widely used in practice, because impedance tubes are very suitable for laboratory measurements due to their small sizes, they require small-sized samples (limited wasted material), and the measurement time is short (a few minutes). However, with these two methods (a and b), only normal-incidence SACs and STLs in a limited frequency range that is imposed by tube dimensions (Koruk 2014) can be measured. Furthermore, the mounting condition of the test sample in the tubes can affect the SACs and STLs measured in these two methods (a and b). The random incidences of sound wave in the reverberation room (c) and conventional two-room (d) methods are close to the practical conditions, therefore these methods (c and d) are considered to be superior to the other two methods (a and b). Furthermore, the SACs and STLs of test samples for a broad frequency range with limited edge effect can be obtained by these methods (c and d). However, these methods (c and d) require large samples (wasted material), and the working space for the rooms is much larger than the impedance tube facility that makes these methods impractical for laboratory measurements. Therefore, for example, small-scale reverberation rooms have been proposed to determine randomincidence SACs of test samples, but they have same drawbacks, such as edge effect and limited lower frequency range (Shtrepi and Prato 2020). The methods commonly used to measure the acoustic properties of material samples in practice and their advantages and disadvantages are presented in Figure 5.

Prediction of acoustic properties
After determining the commonly used models for the prediction of the SACs of natural fiber samples, these models are presented compactly and evaluated here. In addition, the prediction of the STLs of structures is presented. The evaluations made here about the common models for predicting the acoustic properties of structures can be exploited to use the models correctly, and to assess the measured and predicted results in practice.

Prediction of sound absorption coefficients (SACs)
It is worth remembering that SAC is related to the reflection coefficient R as follows (Allard and Attala, 2009): Therefore, we need to determine R ω ð Þ to calculate α ω ð Þ. The reflection coefficient at the surface of a layer is the ratio of the pressures created by the outgoing and ingoing waves at the surface of the layer. Having the surface acoustic impedance Z ω ð Þ, the reflection coefficient can be calculated by (Allard and Attala, 2009): where Z 0 ¼ ρ 0 c 0 is the impedance of the air outside the material, c 0 is the speed of sound in the air, and ρ 0 is the density of the air. The surface acoustic impedance at normal incidence for a hard-backed sample with the thickness of h is given by (Kino 2015): where ϕ is the porosity of the sample, and k ω ð Þ is the wave number of the air in the sample. The characteristic impedance Z c ω ð Þ and the wave number k ω ð Þ, which are a function of frequency, can be estimated by the following equations (Kino 2015):  where ρ ω ð Þ and K ω ð Þ are the so-called dynamic density and bulk modulus of the air in the sample. It is seen that we need (a) k (or ρ and K) and (b) Z c to calculate α. There are different methods to determine these parameters in the literature. As mentioned before, the researchers mostly used the Delany-Bazley model as well as its modified versions and Johnson-Champoux-Allard model to predict the acoustic properties of natural fiber samples.

Delany-Bazley model
The Delany-Bazley model (Delany and Bazley 1970) is a relatively simple technique for the estimation of the acoustic parameters of a layer of isotropic and homogenous porous material. This model allows to replace a layer of fibrous material, with porosity close to one (ϕ � 1), by a layer of equivalent fluid. The complex wave number k and the characteristic impedance Z c were measured by Delany and Bazley (1970) for a large range of frequencies using many fibrous samples with porosity close to unity (Allard and Attala, 2009). According to these measurements, the quantities k and Z c depend mainly on the frequency ω and on the flow resistivity σ of the porous media. A proper fit of the measured values of k and Z c was obtained with the following expressions (Progneaux, Bouillard, and Deraemaeker 2015): where k 0 ¼ ω=c 0 is the wave number of the air outside the sample, σ is the flow resistivity, and c 1 À c 8 are the Delany-Bazley regression constants ( Table 2). The importance of the Delany-Bazley model is its simplicity and application for a wide range of materials with 0:01 < ω 2πσ < 1:0 (Fouladi, Ayub, and Nor 2011). This empirical model can provide reasonable estimations of k and Z c in the approximative frequency range defined by the relation 0:01 < ω 2πσ < 1:0, and it is widely used in practice for its simplicity (only one parameter, σ, is needed to describe the acoustic behavior of a porous sample).

Delany-Bazley-Miki model
After the work by Delany and Bazley (1970), several authors suggested slightly different empirical expressions of k and Z c for specific frequency ranges and different porous samples (Dunn and Davern 1986;Miki 1990). In the case of multiple layers, Miki (1990) recognized that the real part of the surface impedance when computed with the Delany-Bazley model sometimes becomes negative at low frequencies (indicating a nonphysical result), and new coefficients were proposed. The so-called Delany-Bazley-Miki model has the same formula structure as the Delany-Bazley model; however, the coefficients (c 1 , c 3 , c 5 and c 7 ) and the degrees (c 2 , c 4 , c 6 and c 8 ) are different (Progneaux, Bouillard, and Deraemaeker 2015). The Delany-Bazley-Miki model regression constants are listed in Table 3.

Johnson-Champoux-Allard model
The geometry of fibrous samples was not considered in the Delany-Bazley model (Delany and Bazley 1970) and its modified versions (Dunn and Davern 1986;Miki 1990). A significant improvement in the description of the viscous forces was carried out by Johnson, Koplik, and Dashen (1987). Allard and Champoux (1992) obtained, from the geometry of the porous samples, new simple equations that give similar results in the range of validity of the equations of Delany and Bazley (1970), and they are based on a physical representation of the acoustical phenomena associated with the different physical properties of the porous materials. The so-called Johnson-Champoux-Allard model (Allard and Champoux 1992) is a rigid-frame model, where the solid phase of the frame remains motionless. In addition to the static air flow resistivity (σ) used in the Delany-Bazley model and its modified versions, the open porosity, high-frequency limit of tortuosity (α 1 ), viscous characteristic length (Λ), and thermal characteristic length (Λ 0 ) are used in this model. It should be noted that Λ and Λ 0 relate the viscous and thermal losses, respectively (Fouladi, Ayub, and Nor 2011).
In order to take into account the inertial and the viscous couplings between the air and the frame in an air-saturated rigid-frame porous sample, the equilibrium density ρ 0 is replaced by the dynamic density ρ ω ð Þ that depends on frequency in the Johnson-Champoux-Allard model (Allard and Champoux 1992). Dynamic density that is proposed by Johnson, Koplik, and Dashen (1987) is given by (Allard and Champoux 1992;Kino 2015;Kino and Ueno 2008): ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi where η is the viscosity of air. The tortuosity relates ρ ω ð Þ and ρ 0 according to (Allard and Champoux 1992): In the case of cylindrical pores making an angle θ with the direction of propagation, α 1 is equal to (Allard and Champoux 1992): The viscous characteristic length introduced by Johnson, Koplik, and Dashen (1987) is given by (Allard and Champoux 1992): where the integral in the numerator is evaluated over the volume of the pore, and v r ð Þ is the velocity of an inviscid fluid in the pore. The integral in the denominator is taken over the surface of the pore, and v r ω ð Þ is the velocity of the same inviscid fluid at the surface of the pore wall. Champoux and Allard (1991) presented an expression for the dynamic bulk modulus for the same porous sample based on the previous study (Johnson, Koplik, and Dashen 1987) given by (Kino 2015;Kino and Ueno 2008): jΛ 02 ρ 0 P r ω ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 1 þ jρ 0 Λ 0 2 P r ω 16η q � � À 1 (3:12) where P 0 is the atmospheric pressure, γ is the specific heat ratio of the air, and P r is the Prandtl number of the air. The thermal characteristic length is given by (Allard and Champoux 1992): It should be noted that the equation of Λ 0 is equivalent to the equation of Λ without the squared velocity weighting (Allard and Champoux 1992).

Johnson-Champoux-Allard-Lafarge model
The Johnson-Champoux-Allard-Lafarge model is based on the study by Johnson, Koplik, and Dashen (1987) to describe viscous and inertial dissipative effects inside the porous sample and the studies by Champoux and Allard (1991) and Lafarge et al. (1997) to describe the thermal dissipative effects. The dynamic density used in this model is the same as the one for the Johnson-Champoux-Allard model given in Eq. (3.8). Different from the Johnson-Champoux-Allard model, the thermal static permeability (q 0 0 ) is used for the low-frequency behavior of thermal effects in the Johnson-Champoux-Allard -Lafarge model (Lafarge et al. 1997). As a result, the dynamic bulk modulus is given as: ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 1 þ j where c p is the specific heat of the air at constant pressure, and κ is the thermal conductivity of the air.

Biot-Allard model
In addition to the parameters used in the Johnson-Champoux-Allard-Lafarge model, the Biot-Allard model takes into account the loss factor (η s ), density (ρ s ), Poisson's ratio (v s ) and Young's modulus (E s ) of the frame of the porous sample (Allard and Atalla, 2009). Overall, in this model, the surface impedance is calculated using (Allard and Atalla, 2009;Fouladi, Ayub, and Nor 2011): ζ 1 ¼ C 1 δ 2 1 À ω 2 ρ 11 ω 2 ρ 12 À C 2 δ 2 1 ζ 2 ¼ C 1 δ 2 2 À ω 2 ρ 11 ω 2 ρ 12 À C 2 δ 2 2 (3:19) ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi Here, δ 1 and δ 2 are the wave numbers of the compressional frame-borne and air-borne waves, ζ 1 and ζ 2 are the ratios of the velocities for the two compressional waves, and Z a 1 and Z a 2 and Z s 1 and Z s 2 are the characteristic impedances corresponding to transmission in air and frame, respectively (Allard and Atalla, 2009). The air bulk modulusK is the same with the one for the Johnson-Champoux-Allard-Lafarge model given in Eq. (14).

Calculation of the physical parameters
There is a need to calculate the flow resistivity of the sample to calculate its SACs using the Delany-Bazley model. In addition to flow resistivity, it is necessary to determine the viscous and thermal characteristic lengths and the tortuosity of the porous sample to calculate its SACs using the Johnson-Champoux-Allard model. Furthermore, in addition to all the mentioned parameters above, the thermal static permeability is needed to calculate the SACs of a porous sample using the Johnson-Champoux-Allard-Lafarge and Biot-Allard models. Now, let's present some models for the estimation of these parameters. It should be noted that there are different models to predict flow resistivity (Cox and D'Antonio 2004;Mechel 2008). For example, for random fiber orientation, flow resistivity can be estimated using: where r f is the fiber radius. Please note that the air viscosity is around η ¼ 1.82 × 10 −5 kgm −1 s −1 at 20 ° C and 101.3 kPa. Similarly, the other air parameters needed in calculation of the SACs of a porous sample are c p ¼ 1002 J/kg/K, γ ¼ 1:4, P r ¼ 0:71 and κ ¼ 0:026 W/m/K at 20 °C and 101.3 kPa. The porosity ϕ can be predicted using: where ρ f is the fiber density, and ρ s is the bulk or sample density. The tortuosity of porous samples can be estimated using (Bansod, Mittal, and Mohanty 2016): (3:28) The viscous and thermal characteristic lengths of the porous sample can be calculated using (Allard and Champoux 1992;Kino 2015): where l is the total length of the fiber per unit volume given by: The static thermal permeability based on cylindrical pores assumption can be estimated using (Lafarge et al. 1997):

Evaluation of the models
The aforementioned mathematical models for the prediction of the SACs of porous samples are evaluated here. For this purpose, first, the SACs of a natural fiber sample are calculated using the models mentioned above, and the results are compared in Figure 6. The properties of this porous sample made from natural hemp fibers are h = 40 mm, ϕ ¼ 0:93, σ ¼ 4920 Ns/m 4 , α 1 ¼ 1:05, ^¼ 115 μm, ^0 ¼ 170 μm, and ρ s ¼ 88 kg/m 3 (Santoni et al. 2019). Using Eq. (3.32), the thermal static permeability for this sample is calculated to be 3.7 × 10 −9 m 2 . Here, the shear modulus of the frame is assumed to be G s = 200000 (1 + 0.1 j) Pa. It is seen that the SACs predicted by the Johnson-Champoux-Allard, the Johnson-Champoux-Allard-Lafarge and Biot-Allard models are close to each other, and they are close to the experimental results. However, there are some differences between the results predicted by the Delany-Bazley (or Delany-Bazley-Miki) model and the experimental results. The small peak related to the frame resonance seen in the experimental curve between 750 and 850 Hz is successfully predicted by the Biot-Allard model. However, as can be seen, the effect of the frame resonance on the SACs of the porous sample is negligible. Another point is that, although the Delany-Bazley model produces negative SACs at low frequencies (i.e. f < 100 Hz), there is no negative value produced by the Delany-Bazley-Miki model. The regression constants in the Delany-Bazley model can be tuned to match experimental results and predictions for specific frequency ranges and different porous samples. Unlike the Delany-Bazley model or its modified versions, the Johnson-Champoux-Allard and Johnson-Champoux-Allard-Lafarge models can predict some local maxima and minima seen in the experimental SAC curves. Furthermore, the Johnson-Champoux-Allard-Lafarge model can produce more accurate SACs at low frequencies, because static thermal permeability is used to describe the low-frequency behavior of thermal effects in this model (Lafarge et al. 1997). Unlike all the models mentioned above, the Biot-Allard model can predict frame resonances. It should be noted that, for many porous materials including natural fiber samples excited by an incident acoustic wave, it is possible to assume that their frames are rigid, either due to the high value of the elastic modulus, or the high density, or because of special test conditions (Raj, Fatima, and Tandon 2020;Santoni et al. 2019). Therefore, the Johnson-Champoux-Allard and Johnson-Champoux-Allard-Lafarge models can produce the same SACs as the Biot-Allard model when the flow resistivity is not too high and the shear modulus of the frame is not too low (Moussatov, Ayrault, and Castagnede 2001;Wang, Kuo, and Chen 2008).

Prediction of sound transmission losses (STLs)
A typical STL curve is shown in Figure 7. There are specific material properties that dominate each frequency region. The stiffness of the sample determines the first frequency region that is between 0 and natural frequency (ω ij ). The behavior of the curve is determined by the mass of the sample in frequency range between natural and critical frequencies (ω ij and ω c ). The part of the STL curve above the critical frequency is called the coincidence region, and the damping of the sample dominates this region. Based on these boundaries, the STLs of a sample is estimated using (Tadeu and Mateus 2001;Wang et al. 2011): where � ρ is the sample surface density. Although the STLs of a sample can be estimated using the Johnson-Allard equivalent fluid model based on the transfer matrix, boundary and finite element methods (Alhijazi et al. 2020;Bansod, Mittal, and Mohanty 2016), the models presented here are very practical for the estimation of the STLs of structures, and to evaluate the measured results. In addition to the sample surface density � ρ, there is a need to determine the natural and critical frequencies of the sample to use these models. The natural frequency of a sample is given by: ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi E s h 3 12ρ s h 1 À v 2 s À � s (3:34) where a, h, ρ s , E s , and v s are the diameter, thickness, density, Young's modulus, and Poisson's ratio of the sample, respectively. Here, i and j are the nodal diameters and circles of the modes, whereas λ 2 ij are the modal constants. For example, the modal constants are 10.22 and 39.77 for the modes (0,1) and (0,2), respectively, for a clamped circle sample (Dragonetti et al. 2020). The critical frequency of a sample can be determined using (Norton and Karczub 2003): ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi

Acoustic properties
The SACs at different frequencies and NRCs for many natural fibers are presented here. Unlike some review studies in the literature, not only the SACs and thicknesses of the samples are presented, but also their bulk densities and flow resistivities are included in the tables here. In addition, the SACs of the samples are normalized using their bulk density and thickness, hence the sound absorption performance of the samples per unit mass is presented. Based on the normalized results of many natural fiber samples, an empirical model for the estimation of the SACs of porous samples is presented. Although there are various studies on the SACs of natural fiber samples, limited number of studies included the STLs of these materials, therefore the STLs of some natural fiber samples are presented in this section.

Sound absorption coefficients (SACs)
The SACs and NRCs of common natural fiber samples, including coconut, cotton, flax, hemp, jute, kapok, kenaf, ramie and sisal are listed in Table 4. Since the SACs of porous samples are strongly dependent on the bulk density, thickness and flow resistivity of the samples, they are clearly indicated in Table 4. In addition, the diameter and density of the fibers are included in Table 4. For comparison purposes, in addition to the SACs of the natural fiber samples, the SACs of the natural jute felt and wool, synthetic polyester fiber and glass wool samples are listed in Table 4. It is seen that the SACs of many natural fiber samples, such as cotton, flax, jute, kapok and ramie can be higher than those of glass wool samples of the same thickness. Almost all natural fiber samples given here have better sound absorption performance than polyester fiber samples of the same thickness. The NRCs of various natural fiber samples with a thickness of 40 mm are plotted in Figure 8a. It is seen that the SACs of the jute and flax fiber samples are higher than those of the other samples. However, it should be noted that, although the thicknesses of these samples are the same, their bulk densities (masses) are quite different. In order to obtain a parameter that reflects the effect of the specimen mass, the NRC of the sample is divided by its thickness (h) and bulk density (ρ s ): The results obtained using this new normalized parameter for the natural fiber samples in Figure 8a are plotted in Figure 8b. It is clearly seen that the coconut, date palm, hemp, kenaf, and sisal fiber samples have higher sound absorption per unit mass than the flax, jute and ramie fiber samples. The results clearly show that the sound absorption performance per unit mass for the kapok sample is very high compared to the other samples. Similarly, the SACs can be normalized using h and ρ s : The normalized SACs and NRCs for all the samples in Table 4 are calculated and listed in Table 5. The results show that, for some natural fiber samples, such as hemp and kapok, the sound absorption performance per unit mass can be higher than that of polyester fiber and glass wool samples. The NRCs and normalized NRCs of the natural fiber samples in Figure 8 are plotted in Figure 9 as a function of the bulk density. It is seen that there is no correlation between NRC and bulk density ( Figure 9a). However, there is a strong correlation between the normalized NRC (or NRC 0 ) and bulk density (i.e. R 2 = 0.97) as seen in Figure 9b. Now, the normalized NRCs and SACs for different frequencies are plotted as a function of the bulk density for all natural fiber samples with different thicknesses in Table 4 to see whether there is a relationship between the normalized parameters and the bulk density. Overall, the normalized SACs for 500, 1000 and 2000 Hz and the normalized NRCs are plotted in Figure 10. It is seen that there is a good correlation between the normalized SAC and the bulk density for 500, 1000 and 2000 Hz (R 2 > 0.8), and a perfect correlation between the normalized NRC and the bulk density (R 2 = 0.92) for different natural fiber samples with different thickness and flow resistivity values. The relationship between the normalized NRC and bulk density is given by Aρ À τ s . Hence, the following expression can be written: Thus, we can write the following empirical model for the estimation of the SACs of porous samples:   The values of A and τ determined for the SACs at different frequencies and NRC are listed in Table 6. Requiring only the bulk density and thickness of the sample, this simple empirical model can be used for rough estimation of the SACs of a porous sample, and to evaluate the measured results.

Sound transmission losses (STLs)
The STLs of some porous natural fiber samples as well as their averages are listed in Table 7. As expected, it is seen that STL increases as the bulk density and thickness of the sample increases. The STLs of some natural fiber samples with a thickness of 30 mm are plotted in Figure 11. It is seen that the natural fiber samples have low STLs. The low STLs of natural fiber samples are due to their high porosity and low density. On the other hand, the STLs of some natural fiber samples such as jute are higher than those of the acoustic foams such as polypropylene. Overall, in addition to the sound absorption provided by natural fiber structures, their insulation capability can provide a considerable sound transmission loss in practical applications. It should be noted that there are only a few studies on the STLs of natural fiber samples, so it seems that more research is needed on the STLs of natural fiber samples. For the desired values of the SACs and STLs of a porous sample, the bulk density, thickness, and flow resistivity of the sample need to be optimized.

Concluding remarks
A critical assessment of the acoustic properties of natural fiber samples was performed in this paper. The contributions of this study are summarized as follows. The common techniques for both the measurement and prediction of the SACs and STLs of natural fiber samples were determined, presented, and evaluated. The SACs of many natural fibers, including coconut, cotton, flax, hemp, jute, ramie and sisal fibers, which are the world's major plant fibers, were presented along with the thickness, bulk density and flow resistivity of the samples. The SACs of the samples were normalized using their thickness and bulk density, and the sound absorption performance of the samples per unit mass was presented. Based on the normalized results of many natural fiber samples, an empirical model for the estimation of the SACs of porous samples was presented. The STLs of some natural fiber samples were presented.  • The two-microphone transfer function method is commonly used in practice, and there are several studies on the use of the reverberation room method to determine the SACs of natural fiber samples. It is worth remembering that the two-microphone transfer function method is delineated in the ISO 10534-2 and ASTM E1050 standards, and the reverberation room method is described in the ISO 354 and ASTM C423 standards. • The four-microphone transfer matrix method is commonly used in practice, while there are a few studies on the use of the conventional two-room method to determine the STLs of natural fiber samples. It is noted that the four-microphone transfer matrix method is delineated in the ASTM E2611, and the conventional two-room method is explained in the ASTM E90 standard. • Although they require small test samples, and they are quite practical, only normal-incidence SACs and STLs in a limited frequency range that is imposed by tube dimensions can be measured with impedance tube tests, and the mounting condition of the test sample in the tubes can affect the SACs and STLs measured in impedance tube tests. On the other hand, the random-incidence SACs and STLs with limited edge effect for a wide frequency range can be measured via the reverberation room and two-room methods. The advantages and limitations of these methods are summarized in Section 2.3 and Figure 5. • The Delany-Bazley and Johnson-Champoux-Allard models are widely used to predict the acoustic properties of natural fiber samples. There is a need to calculate the flow resistivity of the sample to calculate its SACs using the Delany-Bazley model. In addition to the flow resistivity, it is necessary to determine the viscous and thermal characteristic lengths and the  tortuosity of the porous sample to calculate its SACs using the Johnson-Champoux-Allard model. In addition to all the parameters mentioned above, thermal static permeability is required to calculate the SACs of a porous sample using the Johnson-Champoux-Allard-Lafarge and Biot-Allard models. The Johnson-Champoux-Allard and Johnson-Champoux-Allard-Lafarge rigidframe models can predict not only the general trend, but also local maxima and minima seen in the experimental SAC curves. Furthermore, the Biot-Allard deformable-frame model can predict frame resonances. All these models are compared and evaluated in Section 3.1.7.  • Although the STLs of a sample can be estimated using the Johnson-Allard equivalent fluid model based on the transfer matrix, boundary and finite element methods, the basic models presented in Section 3.2 can be used for rough estimation of the STLs of samples, and to evaluate the experimental results. While the main input in these models is the sample surface density, it is necessary to calculate the natural and critical frequencies of the sample to use these models. • Not only the SACs and NRCs for widely used natural fibers, including coconut, cotton, flax, hemp, jute, kapok, kenaf, ramie and sisal, but also the bulk density, thickness and flow resistivity of the samples are listed in Table 4. Furthermore, the SACs and NRCs of the samples are normalized using the thickness and bulk density of the samples to obtain a parameter for sound absorption reflecting the effect of mass, and the results are listed in Table 5. It is seen that the SACs of many natural fiber samples, such as cotton, flax, jute, kapok and ramie can be higher that the SACs of polyester fiber and glass wool samples of the same thickness. For some natural fiber samples, such as hemp and kapok, the sound absorption performance per unit mass can be higher than that of polyester fiber and glass wool samples. • The results show that there is a good correlation between the normalized SAC and the bulk density for different frequencies, and a perfect correlation between the normalized NRC and the where A and τ are some constants (given in Table 6 for different frequencies), and h and ρ s are the sample thickness and bulk density, respectively. This simple empirical model can be used for rough estimation of the SACs of a porous sample, and to evaluate the measured results.
• The results show that natural fiber samples have low STLs due to their high porosity and low density. On the other hand, the STLs of some natural fiber samples such as jute are higher than those of the acoustic foams such as polypropylene. However, it is observed that more research is needed on the STLs of natural fiber samples. Yang, W., and L. Yan. 2012. Sound absorption performance of natural fibers and their composites. Science China-Technological Sciences 55 (8)