Methodology for Testing Acoustic Absorption of Lightweight Fabrics with 3D Microstructures Using Impedance Tube

Abstract

In this study, the limits of using the impedance tube, or Kundt tube, are examined using the two-microphone method to obtain the normal acoustic absorption coefficient when analyzing the sound absorption properties of lightweight acoustic fabrics. Lightweight porous fabrics with 3D microstructures that have been previously evaluated in reverberation chambers are used. For these materials, a test methodology will be developed in the impedance tube that aims to replicate the conditions of the tests carried out in the reverberation chamber. The samples are tested maintaining the same separation from the final rigid wall and are placed in the impedance tube in two different ways: first, exposing the flat samples to the wave, and second, in pleated format. The results show that it is not possible to consider the results obtained with both methodologies in samples of light textiles with three-dimensional microstructures to be the same. The similarity is limited to low frequencies (100–315 Hz) but bias, excessive dispersion of the data, different global results and shape indicators obtained suggest that both methods are not identical.

1. Introduction

Acoustic conditioning of enclosures is a fundamental aspect to guarantee effective communication and a comfortable stay. This process focuses on controlling sound reflections on the surfaces of the enclosure by absorbing, reflecting and redirecting the energy of sound waves at different frequencies. The resulting reduction in reverberation improves the clarity of the sound perceived by the listener, the intelligibility of speech and the acoustic naturalness of the space.

Acoustic needs change depending on the type of space. For example, an auditorium requires equalization (EQ) and frequency redirection to ensure uniform listening throughout the venue, while a living room may settle for moderate reverberation reduction to allow for clear communication at low volumes. Excessive control of sound reflections can result in an unnatural perception of sound due to the lack of reflections that occur naturally in the environment.

Solutions for acoustic conditioning are diverse and adapt to specific needs of each space. These solutions include elements designed to treat sound in different frequency ranges. For this purpose, different materials, dimensions, arrangements and intrinsic characteristics are experimented with to optimize efficiency in each of the frequency bands. One of the materials commonly used for acoustic conditioning is fabric. It is used not new [1], as it has been used in the form of curtains and stage curtains in theaters and performance halls made of high-density and very thick fabrics [2]. They are especially useful in multipurpose rooms because they allow variable acoustics just by being unfolded or folded. The growing interest in obtaining remarkable acoustic results with smaller elements, making them more useful, has led to the manipulation of the intrinsic structures of these fabrics to improve their acoustic performance [3]. Among these are the so-called lightweight textiles with 3D microstructures [4,5].

There are also several studies that examine the differences between obtaining the absorption coefficient using a reverberation chamber and an impedance tube, quoting classic authors [6,7]. Some studies conclude that the deviation between the results obtained by both methodologies in the acoustic absorption test of various materials is slightly greater in elements with high absorption coefficients [8]. In other studies, with similar materials, it was observed that the maximum absolute value of the errors was not significant for all frequencies, demonstrating the precision of both methods [9]. To further specify the relationship between systems, a model that relates the acoustic absorption coefficient of normal incidence with the acoustic absorption coefficient of random incidence was provided though multivariate linear regression [10]; although, their study is limited to a single absorbent material.

Numerous studies and published works have focused on the characterization of an acoustic absorption coefficient of normal incidence of textiles in impedance tubes. For instance, ref. [11] tested fabrics framed on non-woven polyester fibers and obtained very high absorption coefficients. Ref. [12] studied the effect of an air layer between several layers of fabric and found that adding an air layer between the textile layers significantly improved sound absorption, especially at low frequencies. Additionally, authors such as refs. [13,14] investigated the impact of different structural parameters on the sound absorption properties of textiles.

Regarding the type of fabric, most materials used for the manufacture of these textiles have been analyzed: fabrics made of cotton [15], wool [16], polyester [17] and even natural fibers such as jute fibers [18]. Textile membranes used for the manufacture and coating of headphones have also been tested [19].

However, despite abundant and rigorous existing studies on the acoustic absorption of all types of textiles, no work has developed an impedance tube test methodology using lightweight textiles with 3D microstructures that replicates the conditions of reverberation chamber tests with the same fabrics to verify its validity. This is the gap that this work aims to fill.

In the next section of this article, the characteristics of the analyzed fabrics will be presented and the methodology used to carry out the acoustic absorption tests will be explained.

2. Materials and Methods

This section describes the textile materials tested and the methodology followed to carry out the tests, both in reverberation chamber and in impedance tube. The assembly was carried out in such a way that its results can be comparable.

2.1. Materials

The materials tested consist of four different types of lightweight fabrics featuring 3D microstructures. In this text from now on, we will call them Sample 1 (M1), Sample 2 (M2), Sample 3 (M3) and Sample 4 (M4). All of them are woven with 100% fire-resistant polyester fiber (PES-FR), and each sample has the following characteristics (

Table 1. Characteristics of tested textile sample.

	M1	M2	M3	M4
Composition	100% PES-FR	100% PES-FR	58% PES-FR–42% FR recycled PES	40% PES-FR–60% FR recycled PES
Structure	weave	plain/weave	weave	weave
Number of threads—warp	70/2 CS	32	68	65
Number of threads—weft	Nm/2 CS, 13/1 CS	48	53	42
Yarn count—warp	35	70/2	Nm 450/1 CS	Nm 450/1
Yarn count—weft	35	70/2	Nm 450/3 CS + Nm 100/1 PES-FR + Nm 100/2 CS + Nm 50/8 CS	Nm 450/1 + Nm 100/1 + Nm 70/1 + Nm 3.7
Weight per unit area (g/m2)	295	265	133	161
Contraction: Shrinkage	70°	70°	70°	70°
Warp	−2.8%	−2%	−0.7%	−0.9%
Weft	−2%	−2.9%	−0.9%	−0.5%
Thickness [mm]: 3 positions, pressure 1.00 kPa, pressure-foot 2000 mm2	0.83	0.73	0.94	0.70
Area-specific mass [g/m2]	289	270	272	323
Specific airflow resistance [Pa·s/m]	799	615	557	129

).

The characteristics of the samples were obtained in accordance with ISO 9053-1 and ISO 5084 standards [20,21].

In the samples, the arrangement of the fabric can be seen at first sight, forming the three-dimensional microstructures that provide greater acoustic absorbing capacity. In Figure 1, the structure of Sample 4 can be observed both visibly and under an optical microscope. The microscope used is a Kyowa Bio-Pol 2, with flat-field lenses, and the image has been obtained with 10× magnification. In Figure 1b, the darker mass formed by very fine threads corresponds to the white part of image 1a. It can be seen in the upper right corner of the image how it passes over the net formed by perpendicular crossing of threads that intersect in groups of three.

2.2. Reverberation Chamber

Lightweight textiles with 3D structures previously presented using ISO 354 were tested [22].

The interrupted noise signal method was used to carrier out the tests. The reverberation chamber used has a volume of V = 199.6 m³ and a surface area of S = 216 m². It is equipped with six omnidirectional microphones, four speakers and twelve composite metal plates hanging in a curved arrangement and settled irregularly to increase diffusivity. The reverberation chamber complies in all cases with the specifications of the ISO 354 standard [22].

For each type of lightweight fabric with 3D microstructures, two tests were carried out: one as a flat hanging curtain and the other as a pleated hanging curtain. Therefore, a total of eight tests were performed (four types of fabric and two tests for each).

The assembly details of the tested arrangements were as follows:

• In all cases, the tests were conducted without an enclosure frame.
• The fabrics were always hung directly from the ceiling, suspended from a metal rail with a height of 90 mm, and overlapped the rail by 60 mm.
• In all cases, a distance of 150 mm from the reflective wall was maintained

For flat hanging curtains, the type of arrangement used was a G-150 arrangement type according to ISO 354 [22] (Section 6.2.1 and Appendix B.5). Dimensions of the fabrics tested were as follows (

Table 2. Actual test surfaces of flat samples.

	MF 1	MF 2	MF 3	MF 4
Actual test area [m2]	3.50 × 2.93	3.52 × 2.95	3.53 × 2.94	3.50 × 2.95
Total area [m2]	10.26	10.38	10.38	10.32

).

For pleated curtains, the following arrangements used a G-100 arrangement, according to ISO 354 [22] (Section 6.2.1 and Appendix B.5). Dimensions of the fabrics tested were as follows (

Table 3. Actual test surfaces of pleated samples.

	MP 1	MP 2	MP 3	MP 4
Actual test area [m]	3.49 × 2.93	3.51 × 2.95	3.52 × 2.94	3.50 × 2.95
Total area [m2]	10.23	10.35	10.35	10.32

).

During the installation of pleated curtains, twice as much lightweight fabric with 3D microstructures was used compared to the assembly of flat samples. The pleats of pleated curtains have an approximate depth of 21 cm in the central area of the curtain.

In all cases, the acoustic absorption was calculated based on the rate of sound level decrease in the chamber, and the results were expressed in terms of acoustic absorption coefficient in one-thirds octave bands between 100 Hz and 5000 Hz, with values ranging between 0 and 1.

2.3. Impedance Tube

Methodology used in performing tests in the impedance tube is fundamental to guarantee the reliability and reproducibility of results obtained. The methodological process followed is described in detail below, which covers everything from sample preparation to the execution of acoustic tests, including the calibration phases, experimental setup and data analysis.

2.3.1. General Descriptions

The device used in the tests is an impedance tube, a widely used acoustic measurement system for characterizing the acoustic properties of absorbing materials. This tube allows for the determination of the acoustic absorption of various materials by measuring the variations in sound pressure generated when a sound wave hits the material under study. The tube used in this study has the following technical characteristics:

• Frequency range: 50 Hz to 5700 Hz;
• Maximum sound pressure level (SPL): 150 dB;
• Background noise: <30 dB;
• Microphones:
• For free-field, ½ inch;
• Nominal sensitivity: 50 mV/Pa at 250 Hz;
• Frequency response: ±2 dB, 3.15 Hz–20 kHz;
• Dynamic range: 14–150 dB referenced to 20 μPa;
• Output impedance: <50 Ω, capacitance: 20 pF at 1000 Hz;
• Distance between microphones: 29.2 mm (50.8 mm between sample and nearest microphone);
• Tube inner diameter: 34.9 mm.

The tube has been validated in several intercomparing studies with laboratories throughout Europe, which has proven its reliability in the tests carried out. Specifically, in 2014, 2016 and 2018, the tube was subjected to intercomparing tests among nine laboratories, obtaining satisfactory results in all occasions.

The top cut-off frequency of the tube is 5700 Hz, according to the specifications of the device. For the tests, the process parameters were initially configured, including environmental conditions, resolution, number of repetitions and calibration of the microphones.

2.3.2. Sample Preparation and Cutting

Sample preparation is one of the most critical stages of the experimental process, as the quality and accuracy of the samples directly affect the validity of the results obtained. Samples of lightweight textiles with 3D microstructures must be prepared in appropriate sizes and shapes to fit correctly in to the impedance tube, without creating irregularities that may affect the propagation of the sound wave. To make the comparison as realistic as possible with the tests carried out in a reverberant chamber according to ISO 354 [22], two different types of samples were prepared, flat and pleated samples, with their particular specificities described below.

FLAT SAMPLES: For the cutting of flat samples, precision blades specifically designed for this purpose were used. These circular blades have the right diameter to be set in the impedance tube. However, when trying to cut fabrics with flexible and thin physical properties, such as those used in this study, it was observed that the blades did not achieve clean cuts. The movement of the lightweight textiles during the cutting process caused slight fraying and irregular edges, which invalidated the sample for use in tube tests.

As an alternative, a high-precision scalpel and a compass with a drawing pen were used to make the cuts manually, allowing greater control over the shape and size of the samples. Although this process is slower and more laborious, it proved to be the most effective for obtaining fabric samples with clean edges and without deformation (see Figure 2). To ensure the regularity of the cuts, an extruded polystyrene sheet was used as a base, which facilitated the penetration of the scalpel; also, the same piston from the impedance tube was used to ensure the circular shape of the cut.

This process was repeated for all lightweight textiles with 3D microstructures under study, guaranteeing that multiple optimal samples were obtained for each material, which allowed for reduced variability and statistically consistent results. Quality control in the sample manufacturing stage is essential to avoid defects that may alter the results of acoustic tests.

PLEATED SAMPLES: Obtaining pleated specimens that maintained an accurate circular shape was a considerable technical challenge due to the difficulty of ensuring that the folds did not alter the cross-section of the sample.

To overcome this difficulty, molds were designed in CAD software 2025 version, which were later 3D printed. These molds consisted of two cylinders with a circular section, a wavy shape and a slightly rough surface that facilitated the pressing of lightweight fabrics with 3D microstructures and their fitting to the pleated shape without damaging the folds. These molds made it possible to obtain folds in a stable and precise way (Figure 3a,b).

Once molds were printed, the samples were cut manually, ensuring that the fabric did not fray and that the folds maintained their precise shape (Figure 4).

The process of cutting the pleated samples also required special care in handling the lightweight textiles to prevent the folds would unfold during the assembly process in the tube. To achieve this, a manual method was employed, using metal tweezers to set the samples inside the tube while maintaining the shape of the folds.

2.3.3. Setup of Samples in Impedance Tube

The aim was to ensure that test conditions were as close as possible to those applied in the tests carried out with the same lightweight textiles with 3D microstructures in the reverberation chamber. Once the samples were properly cut and prepared, they were set up in the impedance tube, maintaining in all cases their pleats and the distance of 150 mm between the sample and the metal piston. To ensure that pleats remain intact, the sample is set in the mold, but once positioned in the tube, the mold is removed from the back. This way, samples are perfectly pleated and will no longer move. The assembly was similar to the procedure used when testing samples with decompression termination, but in this case, they maintained the distance of 150 mm.

To succeed this, a tube of greater length and exactly the same diameter was used, which allowed the microphones to be placed in the appropriate positions and to maintain the distance of 150 mm between the sample and the reflective wall (metal piston). See Figure 5a,b.

As can be seen in Figure 5a,b, the folds obtained with such a small circular section (34.9 mm in diameter) are 15 mm in size. With this assembly of the pleated samples, it has been possible to keep the sample at the same distance of 15 cm that separated the curtain from the back wall in the reverberant chamber (Figure 6). However, it has been impossible to obtain folds of similar dimensions (21 cm) to those obtained by hanging a curtain with an approximate surface area of 10 m².

2.3.4. Conducting the Test

With the samples correctly placed and the system calibrated, the tests were carried out on the impedance tube following the instructions of the ISO 10534-2 standard [23]. During the measurements, the sound pressure was monitored and the responses of the samples were recorded as a function of frequency variations.

Each lightweight fabric sample was exposed to three tests, with the aim of obtaining an average absorption value that would faithfully reflect the acoustic properties of the material under controlled conditions. The resolution of the measurements (800 lines) and the number of repetitions (600) were adjusted to ensure the consistency of the data obtained.

This section of the article has provided a detailed description of samples and methodology used in the tests, considering all relevant aspects from preparation, assembly and performance of the tests. In the next sections, results obtained and data analysis will be presented to evaluate the acoustic absorbing behavior of the different lightweight textiles with 3D microstructures and their statistical comparison with the results obtained in the reverberation chamber.

3. Results

In this section, the results obtained for the absorption coefficient in third-octave frequency bands will be presented, organized and in different tables, both in the reverberant chamber according to ISO 354 [22] and in the impedance tube according to ISO 10534-2 [23]. This section also shows the values of the practical acoustic absorption coefficient α_p in octave bands and the weighted acoustic absorption coefficient α_w determined from the practical acoustic absorption coefficients α_p in octave bands from 250 Hz to 4000 Hz. These are calculated in accordance with ISO 11654 [24].

3.1. Results Obtained in Reverberation Chamber

The results of the random-incidence acoustic absorption coefficient for the four samples of lightweight polyester textiles with 3D microstructures set in a flat arrangement are shown below (Figure 7).

Table 4. Expression of acoustic absorption results in reverberant chamber for four flat samples.

Flat Samples
Frq Hz	MF1			MF2			MF3			MF4
	αs	σ	αp	αs	σ	αp	αs	σ	αp	αs	σ	αp
100	0.03	0.013	0.05	0.01	0.010	0.05	0.03	0.013	0.05	0.00	0.009	0.05
125	0.07	0.017		0.06	0.015		0.06	0.015		0.02	0.011
160	0.08	0.016		0.07	0.015		0.08	0.016		0.07	0.015
200	0.18	0.021	0.30	0.18	0.021	0.30	0.19	0.022	0.30	0.14	0.018	0.25
250	0.30	0.025		0.28	0.024		0.29	0.025		0.20	0.020
315	0.45	0.029		0.42	0.028		0.44	0.029		0.34	0.024
400	0.65	0.032	0.75	0.62	0.031	0.75	0.64	0.032	0.75	0.51	0.027	0.60
500	0.80	0.033		0.79	0.033		0.79	0.033		0.60	0.027
630	0.85	0.032		0.84	0.032		0.87	0.032		0.62	0.026
800	0.83	0.029	0.75	0.83	0.029	0.70	0.85	0.029	0.75	0.58	0.023	0.55
1000	0.76	0.027		0.74	0.027		0.75	0.027		0.51	0.021
1250	0.63	0.025		0.59	0.024		0.58	0.024		0.52	0.022
1600	0.70	0.026	0.70	0.65	0.025	0.70	0.67	0.026	0.70	0.60	0.024	0.60
2000	0.75	0.028		0.72	0.028		0.73	0.028		0.60	0.025
2500	0.70	0.028		0.66	0.027		0.68	0.028		0.59	0.026
3150	0.76	0.033	0.75	0.73	0.032	0.75	0.74	0.033	0.75	0.62	0.030	0.65
4000	0.76	0.038		0.73	0.037		0.73	0.037		0.63	0.035
5000	0.77	0.048		0.74	0.048		0.74	0.048		0.64	0.046
αw	0.60 (H)			0.60 (H)			0.60 (H)			0.55 (H)

presents the results obtained in third-octave bands between 100 and 5000 Hz when tested in a standardized reverberation chamber, with calculations of the values of the practical acoustic absorption coefficient α_p in octave bands, the weighted acoustic absorption coefficient α_w and its corresponding shape indicator.

Below, the results of the random-incidence sound absorption coefficient for the four samples of lightweight polyester textiles with 3D microstructures set in a pleated arrangement are shown. Again, the results in third-octave bands between 100 and 5000 Hz are presented in a table (

Table 5. Expression of acoustic absorption results in reverberation chamber for four pleated samples.

Pleated Samples
	MP1			MP2			MP3			MP4
Fq. Hz	αs	σ	αp	αs	σ	αp	αs	σ	αp	αs	σ	αp
100	0.07	0.019	0.15	0.05	0.016	0.15	0.06	0.018	0.15	0.05	0.016	0.10
125	0.16	0.026		0.15	0.025		0.17	0.027		0.13	0.023
160	0.22	0.027		0.19	0.025		0.23	0.028		0.17	0.023
200	0.34	0.031	0.55	0.31	0.029	0.50	0.34	0.031	0.55	0.36	0.033	0.50
250	0.53	0.038		0.46	0.034		0.51	0.037		0.45	0.033
315	0.77	0.044		0.68	0.040		0.75	0.043		0.64	0.038
400	0.85	0.040	0.95	0.74	0.036	0.85	0.82	0.039	0.90	0.76	0.036	0.80
500	0.97	0.038		0.86	0.035		0.91	0.036		0.83	0.034
630	0.97	0.035		0.90	0.033		0.92	0.034		0.79	0.030
800	0.95	0.032	1.00	0.91	0.031	0.95	0.92	0.031	0.95	0.82	0.029	0.85
1000	0.98	0.033		0.93	0.031		0.98	0.033		0.84	0.029
1250	1.03	0.034		0.97	0.033		1.01	0.034		0.83	0.030
1600	1.01	0.033	1.00	0.93	0.031	0.95	1.00	0.033	1.00	0.85	0.030	0.85
2000	1.00	0.034		0.94	0.032		0.99	0.033		0.83	0.030
2500	0.98	0.033		0.95	0.033		0.97	0.033		0.85	0.031
3150	1.01	0.037	1.00	0.95	0.036	0.95	1.01	0.037	1.00	0.89	0.035	0.90
4000	1.00	0.042		0.97	0.041		1.02	0.042		0.90	0.040
5000	0.99	0.051		0.96	0.051		1.00	0.052		0.88	0.050
αw	0.85 (H)			0.80 (H)			0.85 (H)			0.80 (H)

) and are tested in a standardized reverberation chamber, with the calculations of the practical acoustic absorption coefficient α_p in octave bands, the weighted acoustic absorption coefficient α_w and its corresponding shape indicator.

The results of the flat samples obtain absorption coefficients with very low values at low frequencies (less than 400 HZ), close to zero at the lowest frequencies (100 HZ) and with rising values reaching α = 0.45 for M_F1 at 315 Hz.

In frequency bands between 400 and 1600 Hz, the absorption coefficients increase progressively until they reach their maximums (M_F3 α = 0.87) at 630 Hz in all cases. From 630 Hz, the coefficients decrease until they reach their relative minimum between 1000 and 1250 Hz. At high frequencies (2000 to 5000 HZ), the results show fluctuations but remain within a controlled range of α between approximately 0.6 and 0.8.

The results of the pleated samples obtain low absorption coefficients at frequencies below 400 HZ, close to zero at the lowest frequencies (100 HZ) and with rising values to reach α = 0.77 for M_P1 at 315 Hz.

In the frequency bands between 400 and 1600 Hz, the absorption coefficients increase progressively until they reach their maximums (M_P1 α = 1.03 to 1250 Hz). From 1600 Hz onwards, the coefficients remain with small fluctuations at values close to the maximums.

The results show, as expected, that pleated samples, due to their larger contact surface with sound waves created by the folds, present greater absorption across nearly all frequencies compared to flat samples. This fact is also reflected in all cases when comparing their weighted sound absorption coefficients.

3.2. Results Obtained in Impedance Tube

The results obtained in the four samples of lightweight polyester textiles with 3D microstructures tested in flat arrangement in impedance tubes are shown below (Figure 8). From each flat textile sample, three tests were carried out, presenting as a final result the arithmetic mean of the three tests. In the same way as was conducted for the results obtained in the reverberant chamber,

Table 6. Expression of acoustic absorption results in impedance tube for four flat samples.

Flat Samples
	MF1			MF2			MF3			MF4
Fq Hz	αs	σ	αp	αs	σ	αp	αs	σ	αp	αs	σ	αp
100	0.06	0.031	0.05	0.11	0.015	0.10	0.10	0.042	0.10	0.00	0.000	0.05
125	0.03	0.012		0.04	0.044		0.10	0.015		0.02	0.006
160	0.10	0.021		0.13	0.076		0.14	0.046		0.07	0.006
200	0.27	0.047	0.45	0.29	0.101	0.40	0.21	0.032	0.35	0.16	0.006	0.25
250	0.45	0.070		0.40	0.025		0.37	0.029		0.24	0.012
315	0.63	0.087		0.52	0.062		0.55	0.040		0.37	0.015
400	0.77	0.084	0.75	0.66	0.030	0.70	0.68	0.031	0.70	0.48	0.021	0.55
500	0.81	0.078		0.74	0.031		0.74	0.040		0.56	0.010
630	0.72	0.064		0.68	0.010		0.67	0.032		0.57	0.006
800	0.55	0.068	0.40	0.52	0.015	0.40	0.51	0.032	0.40	0.46	0.006	0.35
1000	0.30	0.035		0.27	0.006		0.27	0.015		0.27	0.000
1250	0.40	0.015		0.40	0.015		0.41	0.010		0.27	0.012
1600	0.92	0.023	0.70	0.90	0.010	0.70	0.90	0.015	0.70	0.79	0.006	0.65
2000	0.56	0.044		0.53	0.015		0.54	0.015		0.57	0.012
2500	0.67	0.017		0.68	0.015		0.68	0.012		0.54	0.012
3150	0.58	0.032	0.65	0.56	0.006	0.65	0.56	0.012	0.65	0.61	0.012	0.65
4000	0.78	0.012		0.78	0.006		0.79	0.006		0.74	0.006
5000	0.66	0.006		0.67	0.000		0.66	0.012		0.64	0.000
αw	0.50 (MH)			0.50 (H)			0.50 (H)			0.45 (H)

shows the final results obtained in third-octave bands between 100 and 5000 Hz, using the two-microphone method to obtain the normal acoustic absorption coefficient. The table also shows the values of the practical sound absorption coefficient α_p in octave bands, the weighted sound absorption coefficient α_w and its shape indicator.

Next, the results of the normal incidence acoustic absorption coefficient for the four samples of lightweight polyester textiles with 3D microstructures set in a pleated arrangement are shown. Again, the results in third-octave bands between 100 and 5000 Hz are presented in a table (

Table 7. Expression of acoustic absorption results in impedance tube for four pleated samples.

Pleated Samples
	MP1			MP2			MP3			MP4
	αs	σ	αp	αs	σ	αp	αs	σ	αp	αs	σ	αp
100	0.13	0.015	0.20	0.11	0.010	0.15	0.09	0.023	0.15	0.08	0.010	0.15
125	0.17	0.006		0.13	0.000		0.13	0.023		0.09	0.015
160	0.33	0.010		0.27	0.012		0.28	0.026		0.21	0.017
200	0.48	0.006	0.65	0.40	0.006	0.55	0.43	0.031	0.60	0.33	0.015	0.45
250	0.65	0.010		0.56	0.006		0.59	0.035		0.47	0.017
315	0.81	0.010		0.72	0.006		0.76	0.026		0.62	0.017
400	0.92	0.006	0.95	0.85	0.000	0.85	0.88	0.020	0.85	0.74	0.017	0.80
500	0.96	0.006		0.90	0.010		0.90	0.038		0.82	0.015
630	0.90	0.015		0.81	0.031		0.82	0.010		0.82	0.010
800	0.66	0.006	0.45	0.68	0.021	0.45	0.68	0.026	0.45	0.64	0.060	0.40
1000	0.36	0.012		0.37	0.021		0.37	0.021		0.31	0.020
1250	0.38	0.000		0.29	0.015		0.34	0.006		0.28	0.006
1600	0.92	0.012	0.75	0.87	0.000	0.70	0.90	0.010	0.70	0.76	0.015	0.60
2000	0.62	0.012		0.65	0.031		0.63	0.021		0.55	0.012
2500	0.66	0.012		0.56	0.026		0.62	0.012		0.52	0.010
3150	0.62	0.012	0.70	0.66	0.035	0.70	0.63	0.015	0.70	0.58	0.006	0.65
4000	0.80	0.006		0.75	0.010		0.79	0.006		0.69	0.010
5000	0.68	0.012		0.65	0.006		0.66	0.010		0.61	0.000
αw	0.55 (LMH)			0.55 (MH)			0.55 (LMH)			0.50 (MH)

), when tested in an impedance tube, with the calculations of the values of the practical acoustic absorption coefficient α_p in octave bands, the weighted acoustic absorption coefficient α_w and its corresponding shape indicator.

As in previous occasions, we will describe the results obtained by dividing them into low (<400 Hz), medium (between 400 and 1600 Hz) and high frequencies (>1600 Hz).

The results of the flat samples show absorption coefficients with very low values at low frequencies, close to or equal to zero at the lowest frequencies (100 Hz) and with increasing values to reach a maximum of α_s = 0.63 for M_F1 at 315 Hz.

In frequency bands between 400 and 1600 Hz, the absorption coefficients progressively increase until they reach their relative maximums around 500 Hz, decrease quickly until reaching a minimum at 1000 Hz and then increase again until their absolute maximums, which in all cases are obtained at 1600 Hz. The difference between these maximums and minimums in mid-frequencies is large in all cases (±0.52~0.62). This difference affects the calculation of the weighted acoustic absorption coefficients (α_w) and their shape indicators.

At high frequencies (2000 to 5000 HZ), the results show fluctuations, but they remain with a more controlled range of α, with maximum differences close to ±0.2.

The pleated samples obtain relatively low absorption coefficients in the 125 Hz octave, but these values increase rapidly, reaching a peak maximum value in α_s = 0.81 for M_P1 at 315 Hz.

In frequency bands between 400 and 1600 Hz, the absorption coefficients increase progressively until they reach their maximum at 500 Hz in all cases. Starting from 500 Hz, the coefficients decrease sharply, until they reach their relative minimum around 1250 Hz. This abrupt decline significantly affects the calculation of the weighted acoustic absorption coefficients (α_w), and the abrupt irregularities greatly influence its shape indicators.

At high frequencies (2000 to 5000 Hz), the results show fluctuations but remain within a controlled α range of approximately ±0.2.

The results show that pleated samples offer a higher absorption between 100 and 1000 Hz. These differences are not as great as in the case of the reverberation chamber tests. This fact is considered normal since we remember that the dimensions of the folds tested in both cases are not equivalent, being much smaller in the samples tested in impedance tubes.

Between 1250 and 5000 Hz, the flat samples occasionally exhibit slightly higher acoustic absorption values, which do not correspond to the expected results.

So far, the results obtained from both the reverberant chamber and the impedance tube have been presented, and the distribution of the data across the range of frequencies of interest has been described. In the next section, the results will be analyzed in detail, comparing both methodologies.

4. Discussion

This section of the article compares the results presented above and analyzes the similarities and differences obtained. In the first part, the results are presented graphically. Next, statistical methodology was used to analyze the similarity between the results for the two acoustic absorption coefficients—random and normal incidence—calculated in the four lightweight textiles with 3D microstructures. In each case, it is stated whether the compared results can be considered statistically similar.

The section concludes with a comparison between weighted sound absorption coefficients (α_w) and shape indicators.

Figure 9 shows the absorption coefficients obtained for the eight samples tested in a flat arrangement in the same chart. The values labeled with the letter R are the acoustic absorption coefficients of random incidence (tested in a reverberation chamber), in third-octave frequency bands between 100 and 5000 Hz, for the four samples of lightweight polyester textiles with 3D microstructures framed in a flat arrangement. The values with the letter I are the acoustic absorption coefficients for normal incidence (tested in an impedance tube), in third-octave frequency bands between 100 and 5000 Hz, for the same four samples of lightweight polyester fabrics with 3D microstructures set in a flat arrangement. It is interesting to note that this graph shows that around the frequency of 1000 Hz, the absorption coefficients obtained in the impedance tube decrease. Vibrations of the solid phase of poro-elastic material samples in impedance tubes can significantly affect their acoustic absorption, particularly in specific frequency bands like around 1000 Hz. This behavior is related to the sample size and boundary conditions within the tube, rather than being an intrinsic property of the material. This explains why it does not appear in tests conducted in the reverberation chamber.

We therefore have four data pairs (M_F1 R-M_F1 I; M_F2 R-M_F2 I; M_F3 R-M_F3 I; and M_F4 R-M_F4 I), each expressed in third-octave frequency bands between 100 and 5000 Hz and measured using two methods (reverberation chamber and impedance tube) mentioned above, totaling eight series.

To compare both methodologies, each data series is paired with its identical counterpart obtained using the other measurement method in the 18 third-octave frequency bands, and an arithmetic subtraction of the values obtained in each case is performed. The result is the difference Δ α_s (by frequencies) between both testing methods (

Table 8. Differences between methodologies and hypothesis testing for the eight flat samples.

Flat Fabric Samples
Frequency [Hz]	Δ αs1	Δ αs2	Δ αs3	Δ αs4
100	−0.03	−0.10	−0.07	0.00
125	0.04	0.02	−0.04	0.00
160	−0.02	−0.06	−0.06	0.00
200	−0.09	−0.11	−0.02	−0.02
250	−0.15	−0.12	−0.08	−0.04
315	−0.18	−0.10	−0.11	−0.03
400	−0.12	−0.04	−0.04	0.03
500	−0.01	0.05	0.05	0.04
630	0.13	0.16	0.20	0.05
800	0.28	0.31	0.34	0.12
1000	0.46	0.47	0.48	0.24
1250	0.23	0.19	0.17	0.25
1600	−0.22	−0.25	−0.23	−0.19
2000	0.19	0.19	0.19	0.03
2500	0.03	−0.02	0.00	0.05
3150	0.18	0.17	0.18	0.01
4000	−0.02	−0.05	−0.06	−0.11
5000	0.11	0.07	0.08	0.00
Statistics
Mean	0.045	0.043	0.054	0.024
Standard deviation	0.177	0.177	0.176	0.104
t-statistic	0.077	1.037	1.313	0.975
p-value	0.296	0.314	0.207	0.343

).

The results can be considered statistically equal if α_s follows a normal distribution with a mean of zero.

To carry out this analysis, a widely known and validated test, the Student’s t-test, is used. The test compares a variable with a mean of zero to an estimate of its standardized deviation constructed with -n independent data points. Like any statistical test referring to its standard deviation, it is necessary to determine if the sample comes from a normal distribution.

The results obtained show p-values higher than the significance level (set at 0.05) in all cases; so, the null hypothesis cannot be rejected with a 95.0% confidence level. However, a more detailed analysis reveals important differences when dividing the data into three frequency groups: high (5 K–2 K Hz), medium (1.6 K–400 Hz) and low (315–100 Hz).

High-Frequency Group 5 K–2 K Hz: The results obtained with the impedance tube show much greater variability than those obtained in the reverberant chamber. The means of the differences Δ α_s are almost zero for the four lightweight textiles, but the standard deviation reaches values close to 0.1 in all cases. Standard deviation quantifies the variation in or dispersion of the dataset. It should be noted that we are evaluating the differences between absorption coefficient results, whose values range from zero to one. Therefore, a standard deviation close to or greater than 0.1 is an important dispersion.

Medium-Frequency Group 1.6 K–400 Hz: In this frequency range, the variability of the results obtained with the impedance tube intensifies to the extreme. The means of the differences Δ α_s are greater or close to 0.1 for the four lightweight textiles (it should be zero), and the standard deviations reach maximum values of 0.24 for Δ α_s1 and minimum values of 0.15 for Δ α_s4. So, the dispersion of the data is excessive.

Low-Frequency Group 315–100 Hz: At low frequencies, the results are much closer between the two measurement methods. The means of the differences Δ α_s are close to zero in all four cases. The standard deviation is also close to zero, with results whose first value appears in the second decimal place, except for Sample 3. However, the tests mostly show a slight bias since most of the results obtained with the impedance tubes are slightly higher than those obtained in the reverberant chamber.

Up to this point, the results obtained with lightweight textiles with 3D microstructures tested in a flat arrangement have been analyzed. From now on, the results obtained with lightweight textiles tested in a pleated arrangement will be presented. Let us remember, before starting, that the pleats in both systems are not of the same dimensions.

Figure 10 shows the absorption coefficients obtained for the eight samples tested in a pleated arrangement on the same chart. The values with the letter R are the values of the acoustic absorption coefficients of random incidence (tested in a reverberation chamber), in central third-octave frequency bands between 100 and 5000 Hz, for the four samples of lightweight polyester textiles with 3D microstructures framed in a pleated arrangement. The values with the letter I are the values of the acoustic absorption coefficients of normal incidence (tested in an impedance tube), in central bands of third-octave frequency bands between 100 and 5000 Hz, for the same four samples of lightweight polyester textiles with 3D microstructures set in a pleated arrangement. In the results from the impedance tube at frequencies close to 1000 Hz, the same phenomenon explained in the graph of flat samples is observed.

Again, we have four data pairs (M_P1 R-M_P1 I; M_P2 R-M_P2 I; M_P3 R-M_P3 I; and M_P4 R-M_P4 I), each expressed in third-octave frequency bands between 100 and 5000 Hz, and two measurement methods (reverberant chamber and impedance tube), which, together with the eight series related to the flat samples, make a total of sixteen series.

Just as was conducted when studying the flat samples, each data series is paired with its counterpart from another measurement method in the 18 frequency bands of third-octave frequency bands, and an arithmetic subtraction of the values obtained in each case is performed. The result is the Δ difference (by frequencies) between the two test methods.

The results can be considered statistically equal if they follow a normal distribution of Δ and have a mean of zero.

When analyzing the possible normality of the samples, we find that the values of standardized bias and standardized kurtosis for each dataset are within the expected range for data from a normal distribution.

Again, the null hypothesis to be tested with the t-test is that both methodologies obtain the same results, with the alternative hypothesis being that each methodology obtains different results.

Table 9. Differences between methodologies and hypothesis testing for the eight pleated samples.

Pleated Fabric Samples
Frequency [Hz]	Δ αs1	Δ αs2	Δ αs3	Δ αs4
100	−0.06	−0.06	−0.03	−0.03
125	−0.01	0.02	0.04	0.04
160	−0.11	−0.08	−0.05	−0.04
200	−0.14	−0.09	−0.09	0.03
250	−0.12	−0.10	−0.08	−0.02
315	−0.04	−0.04	−0.01	0.02
400	−0.07	−0.11	−0.06	0.02
500	0.01	−0.04	0.01	0.01
630	0.07	0.09	0.10	−0.03
800	0.29	0.23	0.24	0.18
1000	0.62	0.56	0.61	0.53
1250	0.65	0.68	0.67	0.55
1600	0.09	0.06	0.10	0.09
2000	0.38	0.29	0.36	0.28
2500	0.32	0.39	0.35	0.33
3150	0.39	0.29	0.38	0.31
4000	0.20	0.22	0.23	0.21
5000	0.31	0.31	0.34	0.27
Statistics
Mean	0.154	0.146	0.173	0.153
Standard deviation	0.250	0.239	0.236	0.190
t-statistic	2.617	2.588	3.102	3.418
p-value	0.018	0.019	0.006	0.003

shows the Δ α_s values for each pair of pleated samples in the third-octave central bands, the mean results, the standardized deviations, the t-statistic values and the p-values obtained for the hypothesis testing across the full frequency range.

The results obtained show p-values below the significance level (set at 0.05) in all cases, allowing us to reject the null hypothesis with a 95.0% confidence level. In the case of pleated samples, when analyzing the data by frequencies, there are also differences as in the flat sample results.

High-Frequency Group 5 K–2 K Hz: The means of the differences Δ αs are below zero but higher than in the case of flat samples. The standard deviation reaches values above 0.2 in all cases except Sample 4, meaning that this standard deviation close to or above 0.2 represents significant dispersion, as the range is from zero to one.

Medium-Frequency Group 1.6 K–400 Hz: In this frequency range, the variability of the results obtained using the impedance tube also intensifies. The means of the differences Δ αs are above 0.2 in the four lightweight textiles when they should be zero, and the standard deviations also reach maximum values. Therefore, the data dispersion is excessive.

Low-Frequency Group 315–100 Hz: Similar to the flat samples, at low frequencies, the results are much closer between the two measurement methods, and the means of the differences Δ αs are close to zero. The standard deviation is also close to zero, with the tests mostly showing a slight bias as most of the results obtained in the impedance tube are slightly higher than those obtained in the reverberation chamber, except for Sample 4.

This confirmed the alternative hypothesis that each methodology obtains different results.

In this section, the results have been analyzed and the two methodologies have been statistically compared, leading to the following results and conclusions.

5. Conclusions

The acoustic absorption coefficients for random incidence were obtained in central third-octave frequency bands between 100 and 5000 Hz by testing four types of lightweight textiles with 3D microstructures in a reverberation chamber by placing the textile samples hanging flat at a distance of 15 cm from the wall.

Additionally, a testing methodology in an impedance tube has been developed to replicate the conditions of the tests carried out in the reverberation chamber. The samples were tested maintaining the same separation from the rigid final wall (15 cm) in both methods, and they were placed in the impedance tube, exposing the flat textile samples to the wave.

The acoustic absorption coefficients of normal incidence were obtained, in central third-octave bands between 100 and 5000 Hz, by testing four types of lightweight textiles with 3D microstructures placed flat in impedance tube. The results obtained from two methods were statistically compared.

The results obtained when comparing both methodologies with flat samples are as follows:

• Indicate that the p-values are above the significance level.
• Consequently, with a confidence level of 95.0%, the hypothesis that both methodologies obtain similar results cannot be rejected.
• However, significant differences appear depending on the frequency: In central third-octave bands between 100 and 315 Hz, the results obtained in the impedance tube are slightly higher than those obtained in a reverberation chamber, presenting a bias. In central third-octave bands between 400 and 1600 Hz, there is an excessive dispersion between the results of both methods, although some compensate for others. In central third-octave bands between 2000 and 5000 Hz, the dispersion is less but not negligible.
• When comparing the values of the weighted acoustic absorption coefficient (α_w) (Table 4 and Table 6), the differences are statistically significant. Higher overall values are obtained when testing in the reverberation chamber for the four types of lightweight textiles with 3D microstructures.

The main conclusion of this part of the study is that statistically it is not possible to consider the results obtained with both methodologies in samples of lightweight textiles with 3D microstructures framed flat to be the same. Despite some similarity, the bias, excessive dispersion of the data and different overall results obtained suggest that both methods are not identical. The differences are statistically significant.

The same happens, but is even more evident, when comparing the textile samples arranged in a pleated fashion.

The acoustic absorption coefficients of random incidence were obtained, in central third-octave bands between 100 and 5000 Hz, by testing four types of lightweight textiles with 3D microstructures in a reverberation chamber, placing the textile samples hanging pleated at a distance of 15 cm from the wall.

Again, a testing methodology in the impedance tube was developed to replicate as closely as possible the conditions of the tests carried out in the reverberation chamber. The samples were tested maintaining the same separation from the rigid final wall (15 cm) in both methods, and they were placed in the impedance tube exposing the pleated textile samples to the wave. However, the folds obtained in both setups were not similar. In the impedance tube, the pleats were 15 mm, and in the reverberation chamber arrangement, the folds were 21 cm.

The acoustic absorption coefficients of normal incidence were obtained, in central third-octave bands between 100 and 5000 Hz, by testing four types of lightweight textiles with 3D microstructures placed pleated in the impedance tube. The results obtained from both methods were statistically compared.

The results obtained when comparing both methodologies with pleated samples are as follows:

• Show p-values below the significance level.
• Therefore, with a confidence level of 95.0%, the hypothesis that both methodologies obtain similar results can be rejected.
• When comparing the values of the weighted acoustic absorption coefficient (α_w) and their shape indicators (Table 5 and Table 7), statistically both methodologies show differences. The shape indicator means that the acoustic absorption coefficient at the indicated frequencies is considerably higher than the values of the offset reference curve used to calculate the weighted acoustic absorption coefficient (α_w). Its expression should be taken as a warning that recommends observing the entire curve of the acoustic absorption coefficient and not just its overall expression.
• The overall values obtained when testing in a reverberation chamber are, in all cases, much higher than those obtained in an impedance tube in the four types of lightweight textiles with 3D microstructures. The shape indicators for textiles tested in a reverberation chamber are all H (high frequencies) and change considerably when testing pleated samples in the impedance tube, appearing as H, M and L, which reveals the excessive dispersion of results obtained in tests across all frequency ranges, which is not typical in any type of commercial absorbent materials.

Therefore, even by testing the pleated samples, it is not possible to consider the results obtained with both methodologies as equal in lightweight textile samples with three-dimensional microstructures. The t-test and the different overall results clearly show that both methodologies obtain different results, and the shape indicators suggest that testing pleated samples in an impedance tube is not reliable. The differences are statistically significant.

A methodology has been developed for an impedance tube that simulates the conditions of a reverberation chamber. This advancement would be significant as it allows for more accurate measurements of acoustic properties in controlled environments and a cleaner procedure when using small samples.

However, it is important to note that the impedance tube is not a tested system for measuring the absorption of fabrics placed at a distance from a rigid wall. This limitation suggests that while the impedance tube can provide valuable data under certain conditions and for some frequencies, the low ones, it may not be suitable for all types of acoustic measurements, particularly those involving complex spatial configurations.