Two-microphone Transfer Function Method Research Articles

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.

Sugar maple (Acer saccharum) waste leaves as a renewable resource for sound absorption: An eco-conscious approach

This study quantitatively investigates the sound absorption coefficient of sugar maple waste leaves, a renewable resource for eco-friendly sound absorption solutions. Chemically treated and untreated sugar maple leaves undergo rigorous evaluation, considering their thickness (2.0 cm), density (1.4 g/cm3 for treated, 1.1 g/cm3 for untreated), and surface porosity. The study employs the two-microphone transfer function method to assess their sound absorption coefficients. Results reveal that chemically treated sugar maple leaves exhibit a notably improved sound absorption coefficient (0.96 at 1550 Hz) compared to untreated leaves (0.93 at 1550 Hz). Furthermore, the treatment substantially enhances the Noise Reduction Coefficient (NRC) (0.422) and Sound Absorption Average (SAA) (0.421). This study signifies a heightened ability to absorb sound across various frequencies, emphasizing the potential of sugar maple waste leaves as sustainable sound absorption materials. The findings contribute to the field of eco-conscious acoustic engineering.

Least-squares approach for improving the accuracy of bulk acoustic property measurements using an impedance tube

The bulk acoustic property (characteristic impedance, propagation wave number, or propagation constant) of porous acoustic material with an impedance tube is generally calculated by the two-cavity method, which is calculated from the specific acoustic impedance obtained by the two-microphone transfer function method (ASTM E1050, ISO 10534-2) or from the transfer matrix measured by the four-microphone transfer matrix method (ASTM E2611). These methods can obtain the bulk acoustic property from the results of up to two measurements with different termination conditions. However, the bulk acoustic property may not be obtained correctly due to calculation singularities caused by the test specimen and/or measurement conditions, and calculation errors caused by setting errors regarding the dimensions or environmental conditions of the tube nd/or test specimen. As a result, to reduce the errors in the bulk acoustic property, workarounds such as measuring the specific acoustic impedance or transfer matrix under multiple termination conditions (n conditions) and averaging the bulk acoustic properties obtained for all combinations of two termination conditions have sometimes been used. Therefore, to improve the error in the bulk acoustic properties, a new calculation method based on the least squares method using all the data measured under multiple termination conditions is proposed.

A resonator installed in a wooden puzzle board greatly enhances sound absorption capability at low frequency: A new approach

Loud noise has become a regular part of life due to growing urbanization and lifestyle changes, making noise pollution a severe health concern. However, eco-friendly materials for low-frequency sound absorption still need improvement. Wooden puzzle-assembled boards are being used to construct wooden buildings in South Korea, but they require better sound absorption performance. Therefore, we have developed a strategy to enhance the sound absorption capability of wooden puzzle-assembled boards by suggesting the installation of a single-frequency resonator on the board. The resonator contains nine pinholes with a 6 mm diameter perforation connected to a 30 mm diameter hole leading to the center hollowed cavity (CHC). We evaluated the sound absorption coefficient (SAC) of the control (i.e., cross-laminated timber (CLT)) and a resonator board. The SAC of the resonator with zero pinholes (i.e., CHC), one pinhole (PH-1), five pinholes (PH-5), and nine pinholes (PH-9) were estimated using a two-microphone transfer function method at low frequencies ranging from 100 to 1600 Hz. The average SAC of PH-9 showed significant improvement at the frequency of 450 Hz (0.637 ± 0.001; 818%) compared to the control samples. The noise reduction coefficient was improved by 239% (0.07 for the control and 0.23 for the PH-9). We compared the experimental results in this study with theoretical results and found that the orientation of the neck length significantly impacted the resonant frequency of the pinhole resonator. This finding provides valuable insights into the design and optimization of pinhole resonators for specific acoustic applications.

Transfer function model-based Bayesian estimation of dissipation and sound speed in impedance tube measurements

The air dissipation, mainly due to the boundary effect at interior walls of impedance tubes, is noteworthy for normal incidence measurements of acoustic materials using the transfer function method. This work proposes a transfer function model-based Bayesian approach to estimate the dissipation factors. Other parameters, such as the sound speed and the microphone positions, are also critical, therefore, estimated as well, along with the dissipation. The measurement of the empty impedance tube with a rigid termination applies the two-microphone transfer function method. A hypothetical air layer assumed in front of the rigid backing enables the numerical comparison between the air layer’s theoretical and experimental transfer function values. Experimental results incorporating the estimated dissipation coefficient validate the accuracy of the proposed approach. Furthermore, the estimated parameters are incorporated into further evaluations of material properties using the transfer function method, which effectively reduces the residual absorption error of the impedance tube measurement.

Multi-objective optimisation of automobile sound package with non-smooth surface based on grey theory and particle swarm optimisation

This paper studies a multi-objective optimisation design of the sound package with non-smooth surface, for enhancing the acoustic performance and reducing the material weight. The sound absorption performances of porous materials were predicted by using two-microphone transfer function method combined with finite element method (FEM). Smooth surface and triangular surface were chosen for analysis to compare sound absorption performances. Moreover, an orthogonal experiment was designed to compare sound absorption performance and material mass among different sound packages. Thus, the multi-objective design was converted into a single objective with grey correlation degree. Furthermore, the average grey correlation degree of parameter variables was analysed. On this basis, the optimal combination was selected by using particle swarm optimisation (PSO) algorithm. From the optimisation data, triangular surface sound package material with the optimal surface parameters and thickness was numerically simulated. The simulation result shows that sound absorption performance was improved while the material mass decreased.

Experimental study of smart sound absorber using multimode electromechanical coupling control in the low-frequency range

To construct a smart sound absorber in the low-frequency range with a wide control band, a piezoelectric ceramic (PZT) shunted with multiple resonance circuit is attached onto a micro-perforated panel (MPP) to perform as a smart sound absorber. The absorption can be controlled by the shunt circuit parameters conveniently. This smart micro-perforated panel (MPP) is investigated experimentally to explore the feasibility and design procedure in practical use. Based on the coupling among the acoustical, electrical, and mechanical fields, the proposed broadband sound absorber can achieve good acoustic performance on subwavelength scales. The electrical response of the shunt circuit is tested with a Network Analyzer. The acoustic performance of the smart sound absorber is measured in an impedance tube with the two-microphone transfer function method. The experimental results validate that the shunt circuit can resonate with the PZT patch at multiple frequencies, and hence improve the sound absorption of the smart absorber at these frequencies.

Investigation of broadband sound absorption of smart micro-perforated panel (MPP) absorber

A smart micro-perforated panel (MPP) is investigated in order to enhance sound absorption performance of MPP absorbers, especially at low frequencies. The smart MPP consists of a conventional MPP and a surface-bonded piezoelectric ceramic (PZT) shunted with single- or multiple-resonance circuit. A three-dimensional (3D) finite element model is used to investigate the coupling effects between MPP and the shunted PZT. The numerical results demonstrate three energy-dissipation mechanisms: mechanical damping, electrical shunt damping, and Helmholtz resonance of the MPP. The effects of different multimode shunt design methods are explored so as to intensify the panel vibration and hence improve sound absorption. A low-frequency broadband sound absorber can then be constructed based on the strong coupling among the acoustical, electrical, and mechanical domains. Several absorption peaks induced by electromechanical coupling are found in the frequencies lower than the Helmholtz resonance frequency of MPP. The electrical and mechanical responses of the proposed absorber are investigated in detail. In the experiment, the transfer function of the shunt circuit of the proposed absorber is tested with a network analyser, and the sound absorption coefficients are measured in the impedance tube based on the two-microphone transfer function method. Fair agreement between experimental and numerical results is obtained.

An Evaluation on Acoustic Behavior of Untreated Tree Trunks Depending on Bark Physical Properties and Fiber Cell Structure

ABSTRACT In recent years, noise pollution generated by increasing global urbanization has become an important issue. This study focused on determining the sound absorption coefficients (SACs) of untreated tree trunks as natural fiber-based materials and predicting their noise reduction coefficients (NRCs). It also evaluated the effects of noise reduction using numerical data. One of the most effective acoustic characteristics is the normal incidence SAC; this was obtained for trunks belonging to species of black locust, narrow-leafed ash, stone pine, silver lime, sweet chestnut, sessile oak, maritime pine, cedar, and plane in the frequency range of 50–6000 Hz using an impedance tube based on a two-microphone transfer function method. The absorbance of sound was found to correlate with the tree species, trunk diameter, bark shape, and the bark’s fibrous structure. The results confirmed that when compared with deciduous species, the trunks of coniferous species exhibit higher NRC values which were recorded as 0.302 ± 0.005 for stone pine and 0.233 ± 0.004 for cedar. Furthermore, the surface morphology of the outer bark of different tree species obtained via scanning electron microscopy revealed that significant variations exist in the microstructure of the bark’s fiber cells.

Sound Absorption Measurements of Bio-Sourced Esparto-Fibres : Effect of the Compression

The use of absorbent materials such as fibrous materials is considered as an innovative solution to solve noise problems. The purpose of this research paper is to study the acoustic absorption of a new bio-sourced fibrous material called "Alfa fibers", in order to use it as an absorbent material to reduce reverberation time in the building construction domain (theatre, cinema, conference room, ...). For that, a set of 36 samples was designed and prepared for different thicknesses and different densities in order to evaluate the effect of thickness variation and density variation on sound absorption performance. An experimental study was carried out to measure the sound absorption coefficient at normal incidence, using the ISO 10534-2 standard method known as two-microphone transfer function method. All tests were performed in a Kundt tube with a diameter of 10 cm, in the frequency range (50-1600 Hz). These measurements show that the absorption coefficient can reach a value of 0.9 around 1000 Hz. The experimental results clearly show that sound absorption improves when the thickness of the samples increases, or when the density increases to an optimal value of 300Kg/m3 from which absorption performance begins to decrease. At low frequencies, sound absorption can be improved by creating an air gap between the sample and the rigid bottom.

Silica aerogel/polyester blankets for efficient sound absorption in buildings

In this paper sound absorption characteristics of silica aerogel/polyester (PET) blankets are investigated. PET fibers were made on an industrial scale compact melt spinning line and then processed on a laboratory scale needling line to produce nonwoven fabrics. The silica aerogel blankets were prepared by in situ synthesis of silica aerogel on the nonwoven fabrics via a two-step sol-gel process of tetraethoxysilane which was followed by drying at ambient pressure. In order to achieve aerogel particles with different pore structure and properties, various synthesis conditions were used. The nonwoven samples were characterized in terms of thickness, fiber diameter, porosity and pore size by X-ray micro-computed tomography and scanning electron microscopy. Moreover, nitrogen adsorption analysis was carried out to determine the specific surface area and pore structure of aerogel particles.The effect of pore structure, physical properties and hydrophobicity of aerogel particles on sound absorption coefficient (SAC) of blankets was investigated using two-microphone transfer function method. Also, the effect of sol volume and nonwoven thickness was investigated. The results indicated that at all frequency levels, silica aerogel/PET blankets enjoy higher SAC than their untreated counterparts. It was found that, SAC is strongly affected by the pore structure of aerogel particles. Silica aerogels with lower bulk densities, larger pore size and higher porosities exhibited better sound absorption performance. The results also indicated that hydrophobic aerogel blankets exhibit higher SAC as compared with hydrophilic blankets. The results also showed that the thickness of nonwoven fabric strongly affects the SAC of aerogel blankets.

Experimental Study of Acoustic Performance of Porous Metals at High Temperatures

Based on an improved two-microphone transfer function method, a testing system for the exploration of acoustic performance of porous materials under high temperature conditions was developed with porous foam copper as one of research objects. The acoustic performances of some porous metallic materials were studied in the temperature range of 300°C to 700°C under the premise of ensuring the temperature stability that makes the measurement uncertainty be ± 6°C at high temperatures. The sound absorption coefficient and the acoustic impedance ratio of porous coppers at different ambient temperatures were acquired accordingly. And then the influence of the variation of temperature fields on the acoustic properties of porous metals was analyzed. The experimental results are in good agreement with the theoretical analysis, which proves the rationality of design of the device and provides important references and specific guidance for future study of the acoustic properties of porous metal materials.

Analysis of the error sources of the two-microphone transfer function method for measuring absorption coefficient in the free field using numerical modeling

Extension of the two-microphone transfer function absorption coefficient measurement technique from impedance tubes to the free field introduces several error sources. The three-dimensional nature of the sound field necessitates consideration of factors that are not relevant in an enclosed tube below the cutoff frequency. The impedance tube technique has been modified to account for non-planar wave propagation due to an acoustic point source. The sound field contamination from sample edge diffraction has generally restricted use of the technique to frequencies such that wavelengths are small relative to sample dimensions. This requires the use of very large test panels for low frequencies. Numerical models of the two-microphone free field technique have been created to quantify these effects. Each effect was isolated to better understand its independent impact on the accuracy of the technique. Finally, a series of experimental tests were conducted to validate the numerical modeling results.

Effect of characterization of porous metal fiber media on sound absorption coefficient

Porous metal fiber media (PMFM) is a kind of advanced structural and functional material, and it has attracted a wide spread attention owing to excellent sound absorption performance. The sound absorption property of PMFM is mainly influenced by the fiber diameter, the average pore size and thickness of PMFM. In the paper, three stainless steel fibers with the diameters (∅) of 8, 12 and 20 μm were used to make PMFM with the average pore sizes of 10, 20, 30 and 40 μm and the thicknesses of 1, 2 and 3 mm by air-laid and sintering processes. The sound absorption coefficients of PMFM were tested in impedance tube using two-microphone transfer-function method according to ISO 10534-2 and ASTM E1050-98 international standards at room temperature. The results show that when the frequency ranges from 50 Hz to 6,400 Hz in material with the average pore size of 20 μm and the thickness of 3 mm and the fiber diameter of ∅8 μm, the average sound absorption coefficient is the highest.

An improved two-microphone transfer function method for measuring oblique absorption coefficient in the free field using numerical modeling

The use of the two-microphone free field transfer function technique has remained unchanged since its development. In practice, finite sample sizes limit measurement fidelity due to edge effects. The sound field contribution from edge diffraction has generally restricted the technique from use at low frequencies (<300 Hz) and required test panels greater than several square meters in area. This effort intends to characterize the diffraction contribution to the sound field for relatively small panels. Using numerical modeling, samples of like acoustic properties were excited by a point source at normal incidence to quantify the diffraction term. Following validation via comparison with impedance tube data, the diffraction term was incorporated in an updated derivation of the complex reflection coefficient equation and validated experimentally for a known reference material at both normal and oblique incidence. The goal of this work is to validate measurements of oblique absorption coefficient in an anechoic chamber for panels smaller than one square meter at frequencies down to 100 Hz.

Exploration into the sources of error in the two-microphone transfer function impedance tube method

The two-microphone transfer function method has become the most widely used method of impedance tube testing. Due to its measurement speed and ease of implementation, it has surpassed the standing-wave ratio method in popularity despite inherent frequency limitations due to tube geometry. Currently, the two-microphone technique is described in test standards ASTM E1050 and ISO 10534-2 to ensure accurate measurement. However, while detailed for correct test execution, the standards contain vague recommendations for a variety of measurement parameters. For instance, it is only stated in ASTM E1050 that “tube construction shall be massive so sound transmission through the tube wall is negligible.” To quantify this requirement, damping of the tube was varied to determine how different loss factor values effect measured absorption coefficient values. Additional sources of error explored are the amount of required absorbing material within the tube for reflective material measurements, additional calibration methods needed for test of excessive reflective materials, and alternate methods of combating microphone phase error and tube attenuation.

The Comparison of Sound Absorption of Kapok-Based Fiber Nonwoven Fabrics

As a natural fiber, kapok fiber has the high hollow degree that is very good for sound absorption. Four different kinds of kapok-based fiber nonwoven fabrics, made by kapok fiber mixing with hollow polyester, viscose fiber, PP fiber and cotton fiber respectively, were made and the sound absorption coefficients were measured in the frequency region of 100 - 6300 Hz by using a two-microphone transfer-function method. The comparisons of the sound absorption for four types of materials with similar thickness and densities with no air gap and with 1 cm, 3 cm air gap were made. The results indicate that the sound absorption of kapok/hollow polyester fiber nonwoven fabrics is superior to those of other three ones and kapok/hollow polyester fiber nonwoven fabrics can be used for sound-absorbing materials in engineering.

Microstructure-based calculations and experimental results for sound absorbing porous layers of randomly packed rigid spherical beads

Acoustics of stiff porous media with open porosity can be very effectively modelled using the so-called Johnson-Champoux-Allard-Pride-Lafarge model for sound absorbing porous media with rigid frame. It is an advanced semi-phenomenological model with eight parameters, namely, the total porosity, the viscous permeability and its thermal analogue, the tortuosity, two characteristic lengths (one specific for viscous forces, the other for thermal effects), and finally, viscous and thermal tortuosities at the frequency limit of 0 Hz. Most of these parameters can be measured directly, however, to this end specific equipment is required different for various parameters. Moreover, some parameters are difficult to determine. This is one of several reasons for the so-called multiscale approach, where the parameters are computed from specific finite-element analyses based on some realistic geometric representations of the actual microstructure of porous material. Such approach is presented and validated for layers made up of loosely packed small identical rigid spheres. The sound absorption of such layers was measured experimentally in the impedance tube using the so-called two-microphone transfer function method. The layers are characterised by open porosity and semi-regular microstructure: the identical spheres are loosely packed by random pouring and mixing under the gravity force inside the impedance tubes of various size. Therefore, the regular sphere packings were used to generate Representative Volume Elements suitable for calculations at the micro-scale level. These packings involve only one, two, or four spheres so that the three-dimensional finite-element calculations specific for viscous, thermal, and tortuous effects are feasible. In the proposed geometric packings, the spheres were slightly shifted in order to achieve the correct value of total porosity which was precisely estimated for the layers tested experimentally. Finally, in this paper some results based on the self-consistent estimates are also provided.

Finite element computation of elliptical vocal tract impedances using the two-microphone transfer function method

A two-microphone transfer function (TMTF) method is adapted to a numerical framework to compute the radiation and input impedances of three-dimensional vocal tracts of elliptical cross-section. In its simplest version, the TMTF method only requires measuring the acoustic pressure at two points in an impedance duct and the postprocessing of the corresponding transfer function. However, some considerations are to be taken into account when using the TMTF method in the numerical context, which constitute the main objective of this paper. In particular, the importance of including absorption at the impedance duct walls to avoid lengthy numerical simulations is discussed and analytical complex axial wave numbers for elliptical ducts are derived for this purpose. It is also shown how the direct impedance of plane wave propagation can be computed beyond the TMTF maximum threshold frequency by appropriate location of the virtual microphones. Virtual microphone spacing is also discussed on the basis of the so-called singularity factor. Numerical examples include the computation of the radiation impedance of vowels /a/, /i/, and /u/ and the input impedance of vowel /a/, for simplified vocal tracts of circular and elliptical cross-sections.

Sound reflection in an acoustic impedance tube terminated with a loudspeaker shunted by a negative impedance converter

A system for the absorption of sound at the termination of an acoustic tube using an electrodynamic loudspeaker connected to a shunt circuit is presented. A theoretical model of the electrodynamic loudspeaker in the acoustic tube is used for the calculation of the frequency dependence of the ideal shunt circuit impedance, which yields perfect sound absorption in broad frequency range. It is shown that both the real and imaginary parts of the shunt circuit impedance must be negative in the considered system. The required negative values of the shunt circuit impedance are achieved using a negative impedance converter. Frequency dependences of the reflection coefficient were measured in the acoustic impedance tube using the two-microphone transfer function method. Greatly reduced values of sound absorption coefficient were achieved in a narrow frequency range. The stability, applicability of the sound absorption system, and broadening its frequency range are discussed.