Quadratic Residue Diffuser Research Articles

Insert loss experiment and acoustic impedance theoretical study on the noise barrier with MPP-QRD top structure

The effective edge processing is the key to the performance of noise barrier. To prevent the sound diffraction within the low-medium frequency range, the quadratic residue diffuser (QRD) was combined with microperforated panel (MPP) in this study. The impedance of MPP with different parameters and QRD structure with N = 7 was calculated respectively and the matching degree of the composite structure was obtained. The insertion loss of noise barriers with different MPP-QRD top structures was field measured and compared to the equi-height vertical noise barrier. The results show that the degree of impedance matching between microperforated panels and quadratic residue diffusers is significantly correlated with their performance as the top structure of noise barrier. The acoustic impedance matched MPP-QRD top structure can significantly improve the insertion loss of the vertical noise barrierwith the same height. When the microperforated panel perforation is 3 %, the thickness is 0.8 mm, and the aperture is 0.6 mm, performance of the MPP-QRD structure is the best, the relative insertion loss can reach 4.07 dB.

Understanding diffusion versus scattering devices and how they work

Nearly 50 years ago, Dr. Manfred Schroeder defined the word “Diffuser” as both a process and a product. Since then, many product manufacturers, acousticians and academics have come to use the term for many different products and designs. A careful reading of Dr. Schroeder's 1975 and 1978 papers reveals a lot of significant information as to why certain products are diffusers and why other products do not meet his criteria for diffusion. This paper will show, with the aid of Schroeder's interpretations and modern particle simulations, exactly what he had in mind when he, and others he was working with, created what ultimately became the Quadratic Residue Diffuser or QRD. Additionally, it will show his journey from primitive-root theory to his final quadratic designs. A discussion of the term “Scattering” will also be included to define how Schroeder uses the word and why we need to be careful as to how it is used as well. Test data showing phase models will be used to show the importance of phase manipulation in describing diffusion.

Improved field uniformity in EMC chamber for 6G communication

<span>This paper shows electromagnetic field uniformity in an electromagnetic compatibility (EMC) chamber that is used as a test facility for measuring electromagnetic interference and radiated immunity of 6G communication systems. While not defined yet, 6G radio frequency will work in the wavelength ranges above 95 GHz. With this reason, this paper designed a schroeder-type quadratic residue diffuser for 95 GHz to generate a uniform electromagnetic field in the EMC chamber and studied the field uniformity characteristics in it. To analyze the distribution of electromagnetic fields inside the EMC chamber, finite-difference time-domain (FDTD) numerical analysis method is used. The simulation results show that the EMC chamber with this diffuser satisfies the requirements of international standards and has improved the field uniformity in the chamber.</span>

Sustainable Technology of Wood Charcoal Diffuser for Indoor Acoustical Quality

Wood charcoal is sustainable, renewable, environmentally friendly material using which the acoustic device may be produced. Charcoal made of wood waste materials allows to improve indoor acoustical quality. The current article aims to investigate sound scattering coefficients of quadratic residue diffusers with the covering of oak (Quercus robur) wood charcoal elements. The sound scattering coefficient is calculated due to the reverberation time measurement in the reverberation chamber. The calculation results of the scattering coefficient show the growth of scattering in the frequencies – the highest value reached 0.88 (diffuser N7 with charcoal). The effectiveness of diffusers to diffuse sound waves increases as the number of wells grows. The diffuser with 80 % charcoal elements showed a higher scattering coefficient comparing to the diffuser without charcoal elements.

Sound diffusion with spatiotemporally modulated acoustic metasurfaces

Traditional sound diffusers are quasi-random phase gratings attached to reflecting surfaces to introduce spatiotemporal incoherence into the backscattered acoustic field. Early designs consisted of periodically tiled diffuser grating unit cells to cover large surfaces. However, spatial periodicity leads to coherent constructive and destructive interference, which is undesirable for achieving acoustic diffusivity. This problem was partially addressed by using aperiodic tiling of unit cells based on pseudorandom sequences. While an aperiodic diffuser spacing can overcome the problems introduced by spatial periodicity, the improvements in performance come at the expense of increased thickness. In this work, we investigate spatiotemporal modulation of the surface acoustic admittance of a metasurface diffuser to improve sound diffusion. Using semi-analytical and finite element models, we demonstrate that the effects of the spatial periodicity can be mitigated without introducing an aperiodic spatial spacing, thus simultaneously minimizing diffuser thickness and improving diffusivity of the backscattered field. We develop a semi-analytical model that employs Fourier series expansion to determine the scattered sound field from a surface admittance consisting of a quadratic residue diffuser whose individual well admittances are modulated in a traveling wave fashion with modulation frequency, ωm, amplitude, Ym, and a wavenumber that matches the unit cell length, Λ. We observe significant improvement in diffusion due to the fact that the spatiotemporal modulation scatters sound into additional frequency-wavenumber pairs associated with harmonics of ωm and their diffraction orders. The semi-analytical model results are verified using a time-domain finite element model and compared with periodic and aperiodic diffuser designs.

Sound-scattering properties of Sierpinski triangle fractal structures in the near field

This paper proposes a new design of an acoustic diffuser based on the construction rules of the Sierpinski triangle in order to broaden the effective diffusion frequency range. The diffuser is made of triangular blocks of different sizes attached to a plane surface. The effects of the number of fractal iterations, the height of triangular blocks, and arrangements of the blocks on the normal-incidence diffusion coefficients in the near field are examined through numerical simulations based on the boundary element method (BEM) in the frequency range of 100 Hz – 5 kHz. Furthermore, measurement results will be presented to validate the diffusion performance presented by the numerical simulations. The diffusion performance of a conventional quadratic residue diffuser (QRD) is compared to confirm the advantage of the designed diffuser for broadening the effective frequency range. It shows that the fractal patterns with various sizes of blocks improve diffusion performance compared to the conventional QRD of the same size, especially in the mid-low frequency range below 1 kHz.

Expanded test frequency band and improved field uniformity in a reverberation chamber for networked system by dual-band quadratic residue diffusers

Expanded test frequency band and improved field uniformity in a reverberation chamber for networked system by dual-band quadratic residue diffusers

Comparison Failure and Successful Methodologies for Diffusion Measurements Undertaken inside Two Different Testing Rooms

The scattering phenomenon is known to be of great importance for the acoustic quality of a performance arts space. The scattering of sound can be achieved in different ways: it can be obtained by the presence of architectural and/or decorating elements inside a room (e.g., columns, statues), by the geometry and roughness of a surface (e.g., Quadratic Residue Diffuser (QRD)) and by the diffraction effect occurring when a sound wave hits the edges of an obstacle. This article deals with the surface scattering effects and the diffusion phenomenon only related to MDF and plywood panels tested by disposing the wells both horizontally and vertically. The test results undertaken inside a semi-reverberant room and inside a large reverberant room have been compared to highlight the success and the failure of the measuring methodologies. In detail, according to the existing standards and regulations (i.e., ISO 17497—Part 2), diffusion measurements have been undertaken on a few selected types of panel: two QRD panels (made of Medium Density Fiberboard (MDF) and plywood) with and without a smooth painted solid wood placed behind the QRD. The panels have been tested inside two rooms of different characteristics: a semi-anechoic chamber (Room A) and a large reverberant room (Room B). The volume size influenced the results that have been analyzed for both chambers, showing an overlap of reflections on panels tested inside Room A and a clear diffusion response for the panels tested inside Room B. In terms of the diffusion coefficient in all the octave bands between 125 Hz and 8 kHz, results should not be considered valid for panels tested in Room A because they were negatively impacted by extraneous reflections, while they are reliable for panels tested in Room B.

Improved sound diffuser performance using spatiotemporally modulated metasurfaces

Conventional sound diffuser designs consist of a periodic arrangement of variable depth wells which result in a quasi-random spatial distribution of the reflected phase and minimal energy loss. Diffuser performance depends on geometric parameters such as well depth, number of elements per diffuser period, and in-plane dimensions. We previously showed that coiled-space acoustic metasurfaces (AMS) can significantly reduce diffuser depth while maintaining the performance when compared to classical quadratic residue diffusers (QRD) [Kang and Haberman, J. Acoust. Soc. Am., 149(4), A141 (2021)]. However, all conventional and AMS diffuser performance is limited by geometry due to the linear relationship between frequency and wavelength. Here we consider spatiotemporal modulation of an AMS to control and improve sound diffusion using a technique inspired by nonreciprocal vibrations in Euler beams [Goldsberry et al., Phys. Rev. B 102 (2020)]. A theoretical model is developed using the classical grating equation augmented with a surface impedance that is modulated as a travelling wave function. Properly selected modulation parameters lead to increased diffusion coefficients associated with scattering into harmonics of the temporal modulation frequency and nonreciprocal scattering patterns dependent on the spatiotemporal modulation. Diffuser performance is demonstrated and investigated through the angular dependence of the scattered field magnitude.

An experimental investigation into the scattering properties of maximum length sequence diffusers and quadratic residue diffusers

Since the invention of Schroeder diffusers, extensive studies have been carried out on the prediction and measurement of diffusion coefficients and correlation scattering coefficients in the far field, providing valuable referring data for public. However, as another important evaluation index, the random-incidence scattering coefficients of Schroeder diffusers, which are popularly used in geometric room acoustic models for accurate predictions, have not yet been systematically studied in the diffusing field. This paper presents an experimental study on the scattering coefficients of two well-known Schroeder diffusers (maximum length sequence (MLS) diffusers and quadratic residue diffusers (QRDs)) in one 1:10 scaled-down reverberation room. The scattering coefficients of these Schroeder diffusers were compared to discover their variation laws as a function of well depth, well width, sequence length and the ratio of the maximum well depth to the wave length. To validate the accuracy and reliability of the scaled-down measurements, the scattering coefficients of six MLS diffusers, as well as their standard deviations, were also measured in a full-size reverberation room. The results measured in this study provide engineers and acousticians with some useful reference data in room acoustics design.

Experimental demonstration of a two-dimensional sound diffusing acoustic metasurface with subwavelength thickness

Acoustic diffusers are surfaces that minimize the strength of room modes in small- and medium-sized rooms and reduce specular reflections in large spaces. Since diffusers are surface treatments that are mounted to walls of interior spaces, it is desirable to reduce their thickness in order to maximize usable space. Traditional diffuser designs, such as the quadratic residue diffuser (QRD) make use of variable depth wells to control the local phase of the reflected field. In these designs, well depth is directly proportional to the reflected phase, rendering the overall thickness dependent on the design frequency. Coiled-space (CS) structures are good candidates to minimize diffuser thickness while maintaining performance. However, CS structures have tortuous channels which are susceptible to viscous losses which can degrade diffuser performance. This work presents a CS design for a 2D QRD (N = 7) diffuser with minimal viscous losses and λ/8 thickness, a 4x reduction compared to traditional QRD. Six unit-cell designs were optimized, fabricated, and measured in an impedance tube. Measured reflection coefficients are in a good agreement with predictions. The 3D diffusion performance of the CS and traditional diffusers were measured on multiple planes orthogonal to the diffuser surface with CS and traditional designs performing comparably.

Expanded test frequency band and improved field uniformity in a reverberation chamber for networked system by dual-band quadratic residue diffusers

Expanded test frequency band and improved field uniformity in a reverberation chamber for networked system by dual-band quadratic residue diffusers

Simulation-validated generative design of acoustical arrays with diffusion and absorption

This paper presents several new results for on-going efforts in combining computational design methods and acoustical needs. Past investigations employed rule-based design strategies that expanded upon current monolithic deployment of quadratic residue diffusers (QRD) in the field. The algorithm generated novel, and visually diverse arrays of N = 7 QRD panels. The arrays generated visually strayed from the typical appearance of QRD arrays; appearing more expressive as rules were applied. Furthermore, evaluation metrics including a visual complexity coefficient and 3-D polar plots from PML-FEM simulations provided visual evidence that a relationship exists between the appearance of an array and its corresponding acoustical response. Building on this previous work, representative arrays generated by the output of the algorithms with expanded parameters will be presented alongside updated evaluation metrics. The algorithm uses an expanded set of simulation-validated rules that include non-square grid configurations, multiple design frequencies, a varying number of wells, and incorporate zones of absorption. These new arrays, along with results and discussion of acoustical response to these rules, will be presented. Using these expanded parameters absorption, field of room acoustics design is opened up to wide-ranging visual design possibilities that are fully cooperative and incorporated with the acoustic response.

Acoustic metasurfaces as sound diffusers and diffsorbers

Acoustic metasurfaces (AMS) may offer additional design space for the creation of sound diffusers and diffsorbers. We present the design and experimental characterization of an AMS created to diffuse sound fields using a treatment of uniform thickness. The AMS unit cell designs were chosen to minimize viscous losses while enabling control of reflected phase at each point of the AMS. The design geometry was then optimized with a parametric sweep of unit cell dimensions using finite element (FE) models where the target phase shifts are associated with a one- and two-dimensional quadratic residue diffuser (QRD). Samples were fabricated using additive manufacturing and impedance tube measurements were conducted to validate FE predictions. Modeled and measured reflection coefficients were shown to be in good agreement. The scattered field was then measured in an anechoic chamber using the logarithmic frequency modulated chirp excitation and the deconvolution methods to provide narrowband and broadband estimates of sound diffusion performance. Overall performance is presented for narrow-band and broadband considerations. The AMS response is compared and contrasted with traditional QRD designs, highlighting differences in frequency- and angle-dependence as well as temporal diffusion and absorption. [S.N.L. is managed and operated by NTESS under DOE NNSA Contract No. DE-NA0003525.]

A diffuser language: Designing quadratic residue diffuser arrays with shape grammars

This paper presents research on a rule-based approach to designing creative acoustic diffuser arrays. A shape grammar-influenced design method is specified that uses shape rules to recursively design arrays of quadratic residue diffusers (QRD) in a way that is neither mechanical nor deterministic. Shape grammar-based generative systems have already been shown to be capable of being used in architecture and engineering to create languages of functional objects but have not yet been extended into the realm of acoustics. The grammar presented by this paper produces a QRD-based acoustic diffusion language that breaks habits in QRD deploying techniques, which is lacking outside of using known equations that give known forms. The grammar can include different design frequencies and open the possibilities of different and non-uniform, intentional diffusion treatment. This paper will specify and demonstrate the formation rules, and discuss on how in combination with material specifications, this design method can generate broadband QRD arrays that address both performative and aesthetic criteria in new and surprising ways.

Fractal diffusers as noise barrier top-edge devices

With every passing decade, the issue of noise pollution has worsened in urban areas and the usefulness of noise barriers have increased. To improve the effectiveness of noise barriers in limited frequency bandwidth, a few researchers have reported that quadratic residue diffusers as noise barrier top-profiles have shown promising noise attenuation, albeit in their narrow frequency bandwidth. It has been reported for room acoustics that the frequency bandwidth of quadratic residue diffusers may significantly be extended by a nested or fractal design. Therefore, the aim of this work is to investigate the potential of fractal acoustic diffusers for noise barrier application. Upon conducting a numerical analysis of 1-D fractal diffuser as noise barrier top-profile using finite element method, it is observed that fractal diffusers outperformed T-barriers in both the shadow zone and the transition zone. Hence, fractal acoustic diffusers are promising candidates for our application as these have good diffusion properties in the integrated frequency bandwidth. If properly designed, the fractal diffuser top-edge device can be used to enhance noise attenuation over extended frequency bandwidth.

Characterization of acoustic diffusion using refracto-vibrometry

Refracto-vibrometry is a relatively new measurement technique that is sensitive to variations in the optical refractive index of a medium caused by changes in acoustic pressure within that medium (the acousto-optic effect). It has so far been employed primarily as a qualitative visualization tool for airborne sound propagation because determining sound pressure level at a point using the technique is difficult and inefficient. Instead, the authors propose that this optical technique is well suited for determining dimensionless quantities, such as coefficients describing scattering uniformity from a surface. A new measurement and analysis process relying on refracto-vibrometry has been developed and used to determine acoustic diffusion coefficients through purely optical means for the first time. A quadratic residue diffuser is used as an arbitrary test surface, and refracto-vibrometry measurements of its polar response have been performed and results compared to a boundary element model. The benefits and limitations of the optical method over the traditional microphone-based approach are discussed.

Diffusion unwrapped, new testing that reveals real data

The concept of acoustic diffusion and devices that create diffuse properties has been around for well over 40 years. While there have been a number of test methods that have purported to show diffusion from these devices, the evidence of this is questionable at best. The author, along with others, has developed a new test method that can differentiate between specular and diffuse reflections as well as show many other characteristics desirable for acousticians and designers. This test method, being developed in coordination with ASTM, allows the user to see many different components of diffusion including polar responses, frequency response, attenuation, and phase characteristics, a key component of understanding a diffuse reflections. At the same time, the test method also shows the character of specular reflections, which difference is quite clear in the output data. The paper will also show how devices, from quadratic residue diffusers to geometric shapes, do not necessarily have the frequency response or diffuse reflections that we have assumed for many years. Many different examples will be presented as well as the different data outputs required to see how a diffuser actually performs.

Boundary Element Modelling of a Novel Simple Enhanced Bandwidth Schroeder Diffuser Offering Comparable Performance to a Fractal Design

It is well established that Schroeder diffusers may be used as surface treatment to promote diffuse sound fields in auditoria over a target frequency range. Quadratic Residue Diffusers are very effective within a design frequency bandwidth, and this frequency bandwidth may be significantly extended by a nested or fractal design. Publicly available data typically publish diffusion coefficients separately for the parent diffuser and the child diffuser, with some ambiguity surrounding the effect the two levels have on each other, and the performance at ‘crossover’ frequencies. This paper uses an optimised 2D boundary element method to investigate the differences in results when the parent and child diffusers are modelled separately, and as an integrated design. It is found that the scattering properties of the child diffuser are significantly modified by the well of the parent diffuser in which it is placed. More interestingly, the excellent scattering properties of the fractal design may be achieved with only a minor loss of bandwidth using a far simpler and more robust geometry in which the child diffuser is replaced by a concave surface at the base of the well in the parent diffuser. The paper outlines the optimisation of the boundary element code for this task, and compares results for a variety of well bottom shapes with the fractal design.

The effects of materials on the performance of acoustic diffusers

Over the years, many different theories about the effects of material mass, finishes, coverings such as fabrics, porosity, and other physical attributes of diffuser design have been put forth. These theories have included excess absorption and/or reduced diffusion being caused by different woods or other materials being used as well as different types of paints and finishes. This paper is a study on the veracity of those theories and the effects of assorted materials in the construction and implementation of acoustic diffusers. The study will include the use of a specific diffuser design utilizing a periodic design with specific frequency ranges better known as quadratic residue diffusers. Tests will be conducted to look at specific absorption results and the correlation to diffusion efficiency, if any. In addition, different styles of QRD's will be utilized to see if any designs can overcome the various attributes in design used in diffusion. Standard and customized testing procedures will be used to derive the information presented in the paper.