Impedance Tube Research Articles

Meta-structure based on coupled resonators for low-frequency broadband sound absorption

This work investigates and explains the behavior of an acoustic meta-structure based on different coupled Helmholtz resonators (HR). The analytical formulation of the Maa model is used to represent both the acoustic impedance and the sound absorption mechanism of the absorber. The structures are numerically modeled using finite element method and validated experimentally in an impedance tube considering sound waves of normal incidence. The absorber samples were manufactured in ABS (acrylonitrile butadiene styrene) polymer material with the additive manufacturing technique by extrusion of material. The results of the impedance tube, numerical and theoretical tests showed agreement and the sound absorber showed a sub-wavelength scale with perfect sound absorption ( 0.97) and broadband of 292 Hz in the low frequency region (200 - 600 Hz). We deduced that the excellent experimental result obtained is due to the high resolution used in the sample manufacturing (± 0.1 mm) which minimized manufacture errors. Finally, the influences of the main parameters of the HR panel (width and depth of the micro-slit) on the sound absorption coefficient of the absorber were also analyzed.

Utilizing Waste Cotton/Pigeon Pea Stalk Fibers Composites for Enhanced Sound Absorption and Insulation in Automotive Interiors

ABSTRACT This study investigates the synthesis and characterization of composite materials, pigeon pea stem, and cotton fibers blended in different ratios such as 100/0, 70/30, 60/40, 50/50, 30/70, and 0/100. These composite materials were produced using a compression molding technique. According to ASTM standards, the acoustics, thermal conductivity, and physical characteristics of the composite samples were tested to assess their qualities. The impedance tube method detailed in ASTM E1050 was used to determine the sound absorption coefficients (SAC) for acoustics. The SAC values were measured at six frequencies such as 125, 250, 500, 1000, 2000, and 4000 Hz. The results showed that composite samples made from waste cotton and pigeon pea demonstrated sound absorption values of greater than 80%. Superior sound insulation and absorption, moisture absorption, fiber properties have also been demonstrated by waste composites. Especially, the waste cotton/pea stalk waste fiber composites achieved over 75% sound absorption, while the waste 28% composites performed well in terms of sound absorption, moisture absorption, and fiber properties. Even in humid conditions, the composite samples constructed from used cotton and pigeon pea stalks demonstrated good moisture resistance without reducing their insulating qualities. Soundproofing barriers are composite layers of foam or pigeon pea/cotton.

Bayesian estimation of dissipation and sound speed in tube measurements using a transfer-function model.

This study discusses acoustic dissipation, which contributes to inaccuracies in impedance tube measurements. To improve the accuracy of these measurements, this paper introduces a transfer function model that integrates diverse dissipation prediction models. Bayesian inference is used to estimate the important parameters included in these models, describing dissipation originating from various mechanisms, sound speed, and microphone positions. By using experimental measurements and considering a hypothetical air layer in front of a rigid termination as the material under test, Bayesian parameter estimation allows a substantial enhancement in characterization accuracy by incorporating the dissipation and sound speed estimates. This approach effectively minimizes residual absorption coefficients attributed to both boundary-layer effects and air medium relaxation. The incorporation of dissipation models leads to a substantial reduction (to 1%) in residual absorption coefficients. Moreover, the use of accurately estimated parameters further enhances the accuracy of actual tube measurements of materials using the two-microphone transfer function method.

Geometric optimisation of a multiple coiled-up resonator for broadband and octave band acoustic absorption

This study presents a comprehensive approach to designing sound absorption metamaterials, aiming to achieve broadband absorption capabilities while maintaining a compact thickness, starting from an exceptionally low frequency of 100 Hz. By employing a parallel arrangement of resonators with varying lengths, the proposed approach exploits the envelopes of absorption frequencies to realize broad-spectrum sound absorption.An analytical model is utilized in the geometric optimization phase, accounting for inlet losses and thermo-viscous losses near the walls. The absorption for multiple ducts coupled in parallel is derived using the series and parallel impedance method. A geometric parameterization procedure is implemented to maximize normal incidence acoustic absorption, leading to design optimization for both broadband and octave-band absorbers. Design maps are established to assess acoustic performance and physical space requirements, facilitating informed decision-making in metamaterial design.Prototype fabrication and experimental validation involve 3D printing of optimized geometries using polylactic acid, followed by testing within impedance tubes according to ISO 10534–2 standards. The results demonstrate the effectiveness of the proposed method in achieving broadband sound absorption across specified frequency ranges.

An acoustic impedance design method for tubular structures with broadband sound insulations and efficient air ventilation

In this research, we proposed an acoustic impedance-based design method to increase the soundproofing bandwidths and maintain efficient air ventilation for tubular structures consisting of hollow air-flowing channels. This research has great potential to provide design guidelines based on an acoustic impedance model and even/odd mode analysis for hollow-tube ventilated devices containing resonance and antiresonances. We introduced a thin ventilated structure with a subwavelength thickness of 0.107 λ where λ corresponds to the lowest frequency within the filtering bandwidth, a 19.4 % cross-section open for air passage, and a 10 dB fractional bandwidth of 110.2 % (i.e., 90 % sound energy is blocked), which is broader than that of a conventional Fano-like structure of 44.7 %. To experimentally verify the proposed approach, two prototypes, including lateral-coupled and longitudinal-coupled devices, were designed, fabricated with 3D printing, and experimentally characterized via a commercial-available impedance tube system. The simulations matched the measurements and demonstrated the 10 dB fractional bandwidth of 65 % and 91.5 % and ventilation efficiencies of 21.4 % and 33.4 %, respectively. The main contribution of this work is that the proposed approach can be adopted for lateral or longitudinal coupled ventilated structures with broadband sound insulations and lower the effects of resonance-induced sound transmissions. Besides, the proposed acoustic-impedance model can significantly save the required tremendous computational resources and time compared to FEM simulations. Moreover, the proposed lateral and longitudinal ventilated structures are expected to benefit broadband sound filtering and noise reduction for thin panel or tubular silencers

Estimation of acoustical materials sound absorption coefficient under oblique incidence plane wave and diffuse field via Allard model inversion

A technique for estimating the sound absorption of materials under oblique incidence plane wave and diffuse field excitations is proposed. It requires a mobile loudspeaker and a pair of fixed microphones above a layer of absorbing material. Starting from sound pressure measurements made above the material surface for multiple source positions and by inverting Allard’s propagation model, the proposed method allows for the identification of two effective (or equivalent) parameters, namely, the complex effective density and the complex wave number. Obtaining these parameters makes it possible to estimate the sound absorption coefficient for a plane wave with any angle of incidence or under a diffuse acoustic field by summation over the angles. The results are compared to theoretical values calculated using the Johnson-Champoux-Allard model and to reference measurements obtained using an impedance tube, a small cabin, a large reverberant room, and a sound field synthesis method. One of the limitations of this method lies in the assumptions associated with the Allard model to describe the sound field above the material (assumed to be isotropic, homogeneous, of constant thickness, and to behave like an equivalent fluid). The main advantages are (1) that the sound absorption coefficient can be estimated under oblique incidence plane wave and diffuse acoustic field with values that are always in a physical range (between 0 and 1), and (2) that samples of the order of the square meter without specific preparation can be tested which reduces the constraints associated with impedance tube or reverberant room measurements.

Exploring the acoustic potential of 3D printed micro-perforated panels: A comparative analysis

In the present study, the sound absorption performance of inhomogeneous Micro-Perforated Panels (MPPs) with multiple cavities is investigated. Two models, a three-cavity system and a four-cavity system, are proposed and a numerical study is performed using MATLAB. The models are validated through experimental analysis in an impedance tube. The study meticulously varies the geometrical parameters, including pore diameter, thickness of the MPP, perforation ratio, and back-cavity length. It is found that MPPs with a greater number of sub-cavities have a better sound absorption coefficient than two-cavity systems. The results suggest that the back air cavity is predominantly responsible for multiple peaks, ensuring wideband sound absorption. It is also found that smaller perforation ratios for sub-cavities with larger pore diameters improve sound absorption performance in the lower frequency region. The study indicates that a pore diameter of less than 0.5 mm should be used for better sound absorption above the range of 800–850 Hz, and back cavity length has greater control than pore diameter between 850 Hz and 2000 Hz to make the curve smooth with less fluctuation. The findings have significant implications for the design of MPPs for real-world applications.

Investigation on Low-Frequency and Broadband Sound Absorption of the Compact Anechoic Coating Considering Hydrostatic Pressure

The anechoic coating capable of absorbing sound energy in low frequencies within broadband is essential to conceal underwater vehicles. However, the geometric deformation and modification of mechanical parameters under hydrostatic pressure affect the prediction of absorption performance in deep water environments. An anechoic coating embedded with tandem resonant voids is proposed in this work to achieve quasi-perfect low-frequency and broadband absorption. The analytical method based on the effective medium approach and numerical simulation are performed to estimate the effects of hydrostatic pressure on sound absorption. When additionally considering the dynamic mechanical parameters of the compressed viscoelastic medium, the original absorption humps in low frequencies are inclined to higher band, accompanied by the expanded absorption bandwidth. Then, the tandem coating specimen is measured in a water-filled impedance tube. The experimental spectra are consistent with the analytical and numerical results under various hydrostatic pressures, demonstrating the efficient absorption (α > 0.7) in broadband low frequencies via ordinary pressure. At the same time, the absorption spectrum under higher hydrostatic pressures is also verified in the tube. Consequently, this work paves the way for a broadband low-frequency underwater absorber design and provides an efficient method to characterize the low-frequency and broadband absorption from the coupled resonant coatings in deep water environments.

Development of Louvered Noise Barrier with Changeable Sound Insulation from Waste Tire Rubber and Investigation of Acoustic Properties

In line with circular economy principles, the recycling and reuse of tire rubber waste are considered highly advanced and environmentally friendly waste disposal methods. Through the repurposing of tire rubber waste, the goal is to minimize environmental impact while creating a louvered noise barrier with sound attenuation capabilities. The acoustic properties of the structure made of used tire rubber granulate are investigated in this research. Firstly, nine rubber granulate plates of different fractions, thickness, and density were produced. Two plates with the best results were selected after an impedance tube analysis of their sound absorption (α) and sound transmission loss (DTL). These plates were used as a filler in the structure of the louvers. The efficiency of the structure and its dependence on the tilting angle of the louvers and the number of plates were investigated in a semi-anechoic sound-absorbing chamber. The maximum sound level reduction observed was 17.3 dB (in the 8000 Hz frequency band), and the maximum equivalent sound level loss (LAeq) was 7.3 dBA.

Efficient broadband sound absorption exploiting rainbow labyrinthine metamaterials

In this work, we demonstrate in a proof of concept experiment the efficient noise absorption of a 3D printed panel designed with appropriately arranged space-coiling labyrinthine acoustic elementary cells of various sizes. The labyrinthine unit cells are analytically and numerically analysed to determine their absorption characteristics and then fabricated and experimentally tested in an impedance tube to verify the dependence of absorption characteristics on cell thickness and lateral size. The resonance frequency of the unit cell is seen to scale approximately linearly with respect to both thickness and lateral size in the considered range, enabling easy tunability of the working frequency. Using these data, a flat panel is designed and fabricated by arranging cells of different dimensions in a quasi-periodic lattice, exploiting the acoustic ‘rainbow’ effect, i.e. superimposing the frequency response of the different cells to generate a wider absorption spectrum, covering the target frequency range, chosen between 800 and 1400 Hz. The panel is thinner and more lightweight compared to traditional sound absorbing solutions and designed in modular form, so as to be applicable to different geometries. The performance of the panel is experimentally validated in a small-scale reverberation room, and an absorption close to ideal values is demonstrated at the desired frequencies of operation. Thus, this work suggests a design procedure for noise-mitigation panel solutions and provides experimental proof of the versatility and effectiveness of labyrinthine metamaterials for tunable mid- to low-frequency sound attenuation.

Investigation of sound absorption on a polymeric acoustic metamaterial using 3D printing process

AbstractThis paper presents the design and characterization of DENORMS (Designs for Noise‐Reducing Materials and Structures) cell‐based acoustic metamaterial developed using a 3D printing technique. The metamaterial's acoustic absorption properties were investigated through experimental testing and numerical simulations. The experimental testing of the acoustic metamaterial was conducted in an impedance tube using a two‐microphone method. The numerical simulations were carried out using a thermoviscous module. The simulations allowed for a deeper understanding of the influence of geometric parameters on the absorption coefficient, providing valuable insights for optimizing the design. It was observed that upon increasing the spherical diameter while maintaining the same cylindrical diameter and cylindrical length resulted in an increase in the absorption coefficient throughout the frequency range. It was also observed that upon increasing the cylindrical diameter, there was a significant decrement of absorption coefficient, and upon increasing the length of the cylinder, there was a shift of response toward lower frequency. The augmentation in cell count from 9 to 24 led to a rise in the absorption coefficient and a shift of the response toward lower frequencies. The findings highlight the significance of photopolymer 3D printing in tailoring complex geometries for enhanced performance of the acoustic metamaterial.Highlights Photopolymeric resin used for DENORMS cell‐based acoustic metamaterial. High cleanability and accuracy of digital light processing 3D printing technique. Usage of thermoviscous model for simulation of sound absorption behavior. Use of two microphone impedance tube to determine sound absorption coefficient. Geometric parameters significantly affect the absorption coefficient.

Exploration of Voids, Acoustic Properties and Vibration Damping Ratio of Cyperus Pangorei Rottb Fiber and Ramie Fiber Reinforced with Epoxy Resin Hybrid Composites.

Noise pollution is a major threat to the health and well-being of the entire world; this issue forces researchers to find new sound absorption and insulating material. In this paper, the sound absorption coefficient and vibration damping factor of panels manufactured from Cyperus pangorei rottb and ramie fiber reinforced with epoxy resin are explored. Cyperus pangorei rottb grass fiber and ramie fiber are widely available natural fibers. Cyperus pangorei rottb grass fiber is used in mat manufacturing, whereas ramie is widely used as a fabric. Using both of these fibers, six variant panels using a vacuum resin infusion process (VRIP) were fabricated. The panels were named C, R, CR, RCR-Flat, RCR-Curved, and RCR-Perforated. All the panels were tested for the sound absorption coefficient using an impedance tube with a frequency ranging up to 6300 Hz. Modal analysis was carried out by using the impulse hammer excitation method. A micro X-ray computed tomography (CT) scan was used to study the voids present in the panels. The results were compared among the six variants. The results show that the RCR-curved panel had the highest sound-absorbing coefficient of 0.976 at a frequency range between 4500 Hz to 5000 Hz. These panels also showed better natural frequency and damping factors. The presence of internal voids in these panels enhances sound absorption properties. These panels can be used at higher frequencies.

Broadband low-frequency sound insulation of stiffened sandwich PFGM doubly-curved shells with positive, negative and zero Poisson's ratio cellular cores

Compared to the conventional cellular cores, the cellular cores auxetic metamaterials with negative and zero Poisson's ratios have unique mechanical deformation characteristics, which can be further applied to modeling lightweight sandwich structures. Based on that, the sound transmission characteristics of a novel stiffened sandwich porous functionally graded materials (PFGM) doubly-curved shells with full Poisson's ratio characteristic range cellular cores are investigated in this study. The adjustment of material properties of PFGM face sheets in the thickness direction is achieved through power law based on component volume fraction, and the core layer consists of cellular cores with positive, negative, and zero Poisson's ratios (PPR, NPR, and ZPR). Two common types of stiffened sandwich shell types, namely, the shell with PFGM face sheets and metal-rich cellular cores (type-A), and the ceramic-rich cellular cores (type-B), are discussed, and the Hamilton's principle is used to derive the governing equations. By applying normal velocities continuity conditions at the fluid-structure interface to consider fluid-structure coupling, which is further analytically solved using Navier's technology, and the average sound transmission loss (STL) with broadband low-frequency is described. The effectiveness of the established theoretical model is confirmed by comparing it with previously published results, experimental and simulated results obtained by impedance tube and COMSOL commercial software. A systematic comparison is conducted on the performance of stiffened sandwich PFGM doubly-curved shells with full Poisson's ratio characteristic range cellular cores, and the results show superior performance in the sound insulation for the sandwich shell with ZPR cellular cores, considerably at a broad low-frequency range of 220–2040 Hz, in comparison with the sandwich shell with NPR cellular cores and conventional PPR cellular cores types. This work's findings can serve as a benchmark for future studies and help to design and create engineering sandwich structures with improved sound insulation properties.

Non-destructive reverberant testing of natural fibrous samples in a diffused acoustic field environment

A hexahedron reverberation box was utilized to measure the reverberation time of samples in a diffuse acoustic field. The aim of this study is to design a mathematical model that accurately represents the correlation between frequency and absorption coefficient for analysis. The same was obtained by aligning the noise absorption coefficients (NACs) determined through an impedance tube and calculated based on the reverberation time. The analysis indicated that jute fiber exhibits superior performance compared to other natural fibers, such as rock and glass wool, in the attenuation of sound frequencies above 2200 Hz. The results motivated further investigation over jute nonwoven fabric to conduct layer analysis (1–7) and to examine the impact of thickness. Thereby, a dataset was compiled consisting of 11 fibrous samples (nine natural and two commercial fibers) and jute nonwoven fabric. The empirical model was developed regardless of the type of fiber or thickness of the nonwoven fabric, and it was successfully validated for three additional fibers (banana, pineapple, and ramie). The predictive model exhibited a high level of accuracy in estimating the NAC, displaying a strong similarity to that of impedance tube measurements. The achieved mean absolute error ranges for the predictions are between 0.02 and 0.03 only. The main discovery of this study revolves around the recognition of frequency of sound as a crucial variable and its application in predicting the NAC for the samples.

A machine learning approach for predicting the Johnson-Champoux-Allard parameters of a fibrous porous material

Porous fibrous materials have been widely used as acoustic treatments for noise attenuation. Their acoustic properties are typically characterized by Johnson-Champoux-Allard (JCA) model, which includes five dominant parameters, i.e., open porosity, flow resistivity, tortuosity, viscous characteristic length, and thermal characteristic length. The JCA parameters depend on the microstructure configuration of the material, which can be attained by experimental measurements or numerically analyzing the flow field inside the microstructure, but significant efforts to predict the parameters are typically required. This study proposes a machine learning approach based on an artificial neural network (ANN) for predicting the JCA parameters of a fibrous material. Two geometric parameters that can characterize the fibrous material, i.e., the radius of the fiber and the equivalent throat size between neighbouring fibers, are set as inputs for the prediction model, while the five JCA parameters are set as outputs. The datasets for the network are prepared from finite element simulations. Results confirm that the trained model can predict the JCA parameters accurately and reliably based on the micro-structural geometric parameters. Finally, the model is further validated by the measured acoustic characteristics of a metal-based fibrous material in an impedance tube. The machine learning model opens up possibilities to facilitate the design of advanced porous materials.

Fundamental acoustics concepts taught through the development of an impedance tube

As part of its mission to educate students, Applied Research Laboratories, The University of Texas at Austin (ARL:UT) employs student technicians to assist on a variety of ongoing research projects. Recently, an undergraduate student technician was tasked with the design and fabrication of a low-cost impedance tube for use in characterizing acoustic materials. To assist the student in developing a set of design requirements, and to determine whether preliminary data were being accurately collected and processed, a set of homework problems were developed to teach the student the fundamental concepts in acoustics necessary for impedance tube development. Homework problems required utilizing both travelling- and standing-wave solutions to the one-dimensional (1D) Helmholtz equation, as well as a basic understanding of the relationships between pressure, particle velocity, and acoustic impedance. Homework solutions were compared with 3D finite element simulations and with experimental data collected using the impedance tube. We felt that these homework problems were effective at conveying basic ideas in acoustics to a student with no prior knowledge in the subject, and how those concepts could be used to solve real-world problems.

Design of an improved impedance tube to measure sound absorption coefficients of flexible textile materials

Textile materials have demonstrated significant potential in sound noise reduction due to their porous, lightweight, and easily processed nature. However, the current experimental setup for measuring the sound absorption of small-sized samples is expensive. Additionally, there is a lack of suitable equipment for measuring the sound absorption of flexible textiles as it is challenging to mount flexible samples into an impedance tube. This paper presents the design, fabrication, and testing of impedance tubes specifically designed for measuring the sound absorption coefficients of textile materials. The impedance tubes were designed based on the transfer function and two-microphone methods, with diameters of 100 mm and 30 mm. These tubes covered frequency ranges from 200–1600 Hz and 500–6400 Hz, respectively. Furthermore, improved sample holders were developed to mount flexible textile materials without altering the acoustic impedance characteristics of the front surface of the test sample. Validation experiments were conducted on melamine foams, and the results were compared with those obtained from the commercial B&K 4206 setup. The results obtained from the designed setup showed good agreement with those from the B&K 4206 system. The maximum error observed was 8% at 2800 Hz for the 30 mm diameter tube and 8.3% at 1600 Hz for the 100 mm diameter tube. Finally, the designed system was used to measure the sound absorption coefficients of textile materials with varying densities. The results obtained were consistent with the material properties, demonstrating the effectiveness of the designed setup.

Dissipation estimation for the impedance tube measurement using Bayesian inference

Although air dissipation is usually neglected in the impedance tube measurement, it affects the accuracy of the measurement results. Multiple effects contribute to the sound dissipation in an impedance tube, like the boundary layer effect or relaxation effect. This work formulates a transfer function model incorporating different dissipation. Bayesian inference is applied to estimate the acoustic dissipation in an impedance tube. Critical parameters in dissipation models are estimated based on the transfer function measured from an empty impedance tube. Nested sampling is applied to get an accurate approximation of parameters. The results of the analysis demonstrate that the critical parameters estimated by the Bayesian method are accurate. The accurate estimated dissipation helps improve the accuracy of impedance measurement with the material under test.

The feasibility of building an impedance tube to measure sound absorption coefficients of materials

This presentation focuses on the design and build of an impedance tube to measure sound absorption coefficients of materials. A practical approach was taken to develop an impedance tube from readily available ‘off the shelf’ materials, with the ultimate goal of determining feasibility and accuracy of such a build. The design theory from multiple sources will be discussed, as well as a detailed breakdown of the dimensions and materials used for the apparatus. Measurement methodologies, testing set-up and data processing techniques are also presented to contextualize the results. Finally, comparisons of the tube results are made to existing known sound absorption coefficient data of materials to ultimately assess the accuracy of the low-cost impedance tube and any deficiencies. Methods to improve the design of the tube are also explored, as well as future design improvements.

Design and construction of the Texas Christian University impedance tube

The two-microphone impedance tube test method is a well-established and widely used technique for determining the acoustic absorption coefficient and impedance ratio of materials. This method uses two closely spaced microphones to simultaneously measure the incident and reflected sound waves. A two-microphone impedance tube measurement system made of 6061-T6 Aluminum with a diameter of 3 inches, a 0.5 inch wall thickness, and microphones spaced 2.7 inches apart has been constructed for undergraduate research at Texas Christian University (TCU). These geometrical values suggest a usable frequency range of 50 Hz to 2637.77 Hz as referenced in ASTM Standard E1050-19. Validation of the system was achieved by taking measurements on Owen Corning Type 705 pressed fiberglass board with a 1-inch thickness and comparing them to absorption data provided by the manufacturer. Additional validation measurements were taken without a test sample in place. All validation tests suggest that the TCU impedance tube is an accurate measurement system.