Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems

Selective dynamic band gap tuning in metamaterials using graded photoresponsive resonator arrays

The introduction of metamaterials has provided new possibilities to manipulate the propagation of waves in different fields of physics, ranging from electromagnetism to acoustics. However, despite the variety of configurations proposed so far, most solutions lack dynamic tunability, i.e. their functionality cannot be altered post-fabrication. Our work overcomes this limitation by employing a photo-responsive polymer to fabricate a simple metamaterial structure and enable tuning of its elastic properties using visible light. The structure of the metamaterial consists of graded resonators in the form of an array of pillars, each giving rise to different resonances and transmission band gaps. Selective laser illumination can then tune the resonances and their frequencies individually or collectively, thus yielding many degrees of freedom in the tunability of the filtered or transmitted wave frequencies, similar to playing a keyboard, where illuminating each pillar corresponds to playing a different note. This concept can be used to realize low-power active devices for elastic wave control, including beam splitters, switches and filters.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Bridging the gap between annular and can-annular acoustic spectra

In the literature on thermoacoustic instabilities in combustors, a distinction is typically made between annular and can-annular systems because these are the most common gas turbine architectures. In reality, however, annular combustors typically feature discretely symmetric elements, such as burner tubes, and can-annular combustors feature an azimuthally symmetric plenum at the turbine inlet. To better understand the general case in between the annular and can-annular extremes, we analyze the acoustic spectrum of an idealized can-annular combustion chamber with variable geometry, where the length of the axial gap distance beyond the ends of the cans-hence, the coupling strength-may be adjusted. For small gap sizes, the geometry approaches a set of isolated combustor cans, whereas for large gap sizes, it approaches that of pure annular systems. We present two theoretical models based on Bloch wave theory and validate them against finite-element simulations of the Helmholtz equation. We demonstrate that the azimuthal modes transform into the eigenmodes of an annular chamber as the gap is fully opened, and we show that below a certain frequency, all the modes in between the can-annular and annular limits can be classified by their axial and azimuthal mode orders.

Studies on Dual Helmholtz Resonators and Asymmetric Waveguides for Ventilated Soundproofing

Achieving the simultaneity of ventilation and soundproofing is a significant challenge in applied acoustics. Ventilated soundproofing relies on the interplay between local resonance and nonlocal coupling of acoustic waves within a sub-wavelength structure. However, previously studied structures possess limited types of fundamental resonators and lack modifications from the basic arrangement. These constraints often force the specified position of each attenuation peak and low absorption performance. Here, we suggest the in-duct-type sound barrier with dual Helmholtz resonators, which are positioned around the symmetry-breaking waveguides. The numerical simulations for curated dimensions and scattered fields show the aperiodic migrations and effective amplifications of the two absorptive domains. Collaborating with the subsequent reflective domains, the designed structure holds two effective attenuation bands under the first Fabry-Pérot resonance frequency. This study would serve as a valuable example for understanding the local and non-local behaviors of sub-wavelength resonating structures. Additionally, it could be applied in selective noise absorption and reflection more flexibly.

Perfect Resonant Absorption of Guided Water Waves by Autler-Townes Splitting

The control of guided water wave propagation based on the Autler-Townes splitting resonance concept is demonstrated experimentally, numerically, and theoretically. Complete wave absorption is achieved using an asymmetric pointlike scatterer made of two closely spaced resonant side channels connected to a guide and designed so that its energy leakage is in perfect balance with the inherent viscous losses in the system. We demonstrate that the nature of the resonators and guide junction completely controls the positions of the wave numbers at the reflection and transmission zeros on the real axis; the asymmetry of the resonators completely controls their positions on the imaginary axis. Thus, by adjusting these two independent parameters, we obtain a zero reflection and transmission.

Ultrathin Space-Shift Phase-Coherent Cancellation Metasurface for Broadband Sound Absorption

A space-shift phase-coherent cancellation acoustic metasurface is developed, which can achieve broadband low-frequency sound absorption via ultra-thin integrated structure composed of multiple units with weak absorption capability. Through a space-shift design of the channel length, the large-size required in the thickness direction for low-frequency absorption is transferred into an extremely ultra-thin space layer. The units with gradient channel length are compactly arranged in an ultra-thin layer through space folding, a coplanar sound absorption metasurface component with working bandwidth exceeding an octave and thickness of only λ/25 to λ/57 is obtained. As the construction of a special double-hole "bridge" layout, even if the elements are sparsely distributed, strong coupling interactions between the units can sustain. When a certain local phase relationship is satisfied, the coherent cancellation of sound energy can be achieved, so as to reduce the sound reflection and scattering, and enhance the absorption performance. Therefore, from the perspective of phase relationship among units, the present work provides more clear physical image and intuitive theoretical explanation for achieving excellent broadband sound absorption through parallel superposition of multiple units with weak absorption capability. The proposed ultra-thin sound absorbing metasurface can satisfy the thickness limitations and absorption performance requirements in most equipment.

Broadband sound absorption based on impedance decoupling and modulation mechanisms

In sound absorbers, acoustic resistance and reactance are usually coupled together and affect each other, which brings difficulties to impedance matching. An impedance decoupling method is proposed to make acoustic resistance and acoustic reactance vary independently. For the same thickness and perforation rate, acoustic reactance of the perforated panel with tube bundles (PPTBs) varies with the diameter of the tube, but acoustic resistance remains constant. Theoretical and simulated results show that a PPTB absorptive unit can exhibit resonance modes with varying damping states through impedance decoupling. It is found that through well-modulation, the PPTB unit in a slightly over-damped state cannot only maintain high sound absorption coefficients, but also expand the absorption peak bandwidth. Utilizing the mechanism of impedance decoupling, a broadband absorber is designed and evaluated by comprising the PPTB and microperforated panel (MPP). Measurement results indicate that it possesses an average absorption coefficient of 85% spanning more than a 3-octave bandwidth from 160 Hz to 1400 Hz with a deep sub-wavelength thickness. The impedance decoupling method helps to implement sound absorbers with highly efficient low-frequency broadband absorption.

Principles of progressive slow-sound and critical coupling condition in broadband sonic black hole absorber

Recent advances in sonic black hole (SBH) provide new opportunities for controlling sound waves and designing wave manipulation devices. SBH is a device that consists of partitions with gradually decreasing inner radii inserted into an acoustic duct. Several studies have reported that SBH can achieve a broadband sound absorption coefficient close to 1, avoiding the issue of alternating high and low absorption coefficients observed in traditional sound absorbers. However, the fundamental mechanisms and principles behind this behavior are not yet fully understood. This study aims to investigate the detailed sound absorption mechanisms of SBH, including the progressive slow-sound effect and the critical coupling condition that leads to broadband sound absorption. To achieve this goal, an analytical model based on the effective medium approach is developed to investigate the layer-by-layer retardation in sound propagation. The sound absorption coefficient is then determined based on the surface impedance calculation. The effective medium analysis reveals that SBH enables a unique condition to progressively decelerate wave propagation across its layers. As a result, the critical coupling condition becomes more easily established with smoothly increasing SBH partitions and more discretised layers, as elucidated by the complex frequency analysis results. The physical insights gained from this study reveal the distinctive features of SBH compared to classical sound absorbers, paving the way for its engineering applications.

Active control of sound transmission through a floor-level slit

The floor-level slit between the door and the floor is one weak point in building noise insulation. In this paper, an active noise control system is proposed to reduce the sound transmission through a floor-level slit with evenly distributed secondary sources on its top boundary. The system performance is first investigated based on the analytical and numerical models, and simulation results indicate a decrease in active control performance with increasing frequency. The upper limit frequency of 10 dB effective control increases with a higher number of secondary sources, and the corresponding wavelength of the upper limit frequency is approximately the interval between the secondary sources when a plane wave is incident normally. Although the upper limit frequency decreases with the slit height, it approaches a constant when the slit height becomes significantly smaller than the wavelength in the incident sound. The experimental results based on a typical floor-level door slit support the findings in the numerical simulations. For a slit with a width of 0.9 m and a height of 0.005 m, the upper limit frequency of 10 dB noise reduction can reach up to 2830 Hz when ten secondary sources are employed in the experiments.

Recent advances in metasurface design and quantum optics applications with machine learning, physics-informed neural networks, and topology optimization methods

As a two-dimensional planar material with low depth profile, a metasurface can generate non-classical phase distributions for the transmitted and reflected electromagnetic waves at its interface. Thus, it offers more flexibility to control the wave front. A traditional metasurface design process mainly adopts the forward prediction algorithm, such as Finite Difference Time Domain, combined with manual parameter optimization. However, such methods are time-consuming, and it is difficult to keep the practical meta-atom spectrum being consistent with the ideal one. In addition, since the periodic boundary condition is used in the meta-atom design process, while the aperiodic condition is used in the array simulation, the coupling between neighboring meta-atoms leads to inevitable inaccuracy. In this review, representative intelligent methods for metasurface design are introduced and discussed, including machine learning, physics-information neural network, and topology optimization method. We elaborate on the principle of each approach, analyze their advantages and limitations, and discuss their potential applications. We also summarize recent advances in enabled metasurfaces for quantum optics applications. In short, this paper highlights a promising direction for intelligent metasurface designs and applications for future quantum optics research and serves as an up-to-date reference for researchers in the metasurface and metamaterial fields.

Frozen sound: An ultra-low frequency and ultra-broadband non-reciprocal acoustic absorber

The absorption of airborne sound is still a subject of active research, and even more since the emergence of acoustic metamaterials. Although being subwavelength, the screen barriers developed so far cannot absorb more than 50% of an incident wave at very low frequencies (<100 Hz). Here, we explore the design of a subwavelength and broadband absorbing screen based on thermoacoustic energy conversion. The system consists of a porous layer kept at room temperature on one side while the other side is cooled down to a very low temperature using liquid nitrogen. At the absorbing screen, the sound wave experiences both a pressure jump caused by viscous drag, and a velocity jump caused by thermoacoustic energy conversion breaking reciprocity and allowing a one-sided absorption up to 95 % even in the infrasound regime. By overcoming the ordinary low frequency absorption limit, thermoacoustic effects open the door to the design of innovative devices.

3D Printed Graphene-Based Metamaterials: Guesting Multi-Functionality in One Gain

Advanced functional materials with fascinating properties and extended structural design have greatly broadened their applications. Metamaterials, exhibiting unprecedented physical properties (mechanical, electromagnetic, acoustic, etc.), are considered frontiers of physics, material science, and engineering. With the emerging 3D printing technology, the manufacturing of metamaterials becomes much more convenient. Graphene, due to its superior properties such as large surface area, superior electrical/thermal conductivity, and outstanding mechanical properties, shows promising applications to add multi-functionality into existing metamaterials for various applications. In this review, the aim is to outline the latest developments and applications of 3D printed graphene-based metamaterials. The structure design of different types of metamaterials and the fabrication strategies for 3D printed graphene-based materials are first reviewed. Then the representative explorations of 3D printed graphene-based metamaterials and multi-functionality that can be introduced with such a combination are further discussed. Subsequently, challenges and opportunities are provided, seeking to point out future directions of 3D printed graphene-based metamaterials.

Interpenetrating Hollow Microlattice Metamaterial Enables Efficient Sound-Absorptive and Deformation-Recoverable Capabilities

Owing to the pervasive noise and crash hazards, tough microlattices with sound absorption capabilities are sought-after. However, typical truss microlattices are unable to fulfill this requirement. To overcome this, herein, we report a new design strategy for truss microlattices via introducing the concept of interpenetrating hollow struts, which thereby constitutes a novel interpenetrating hollow microlattice metamaterial (IHMM). The design is based on interweaved unit cells of a hollow octet-truss (HOT) and a hollow rhombic dodecahedron-like (HRDL) truss. Experimentally demonstrated, the IHMM displays a synergistic gain in both sound absorption and mechanical properties that substantially surpass that of its constituent lattices. High sound absorption coefficients (α > 0.99) and broad half-absorption (3.2 kHz) are observed, with the average α being 110.6 and 85.3% higher than those of the HOT and HRDL, respectively. The sound absorption mechanism is attributed to the presence of cascaded Helmholtz resonance, which is then fully elucidated by impedance and damping analyses. The IHMM also outperforms its constituents in specific strength. A simultaneous high strength (4 MPa) and recoverability (80% strain) and pseudo-reusability are also observed. The mechanisms behind the mechanical reinforcement and exceptional robustness are thoroughly revealed. Overall, this work offers insights into developing multifunctional engineering materials.

Low frequency attenuation of acoustic waves in a perforated pipe

This paper presents new experimental and numerical evidence that perforations in a pipe wall result in a low-frequency bandgap within which sound waves rapidly attenuate. These perforations are modelled as an acoustically soft boundary condition on the pipe wall and show that a low frequency bandgap is created from 0 Hz. The upper bound of this bandgap is determined by the dimensions and separation of the perforations. An analytical model based on the transfer matrix method is proposed. This model is validated against numerical predictions for the pipe with varying perforation geometries. A numerical study is undertaken to model the effect of perforations with ideal acoustically soft boundary conditions and surrounded with an air gap. Close agreement is found between the numerical and analytical models. Experimental evidence shows that the width of the bandgap is accurately predicted with the numerical and analytical models.

New Class of Multifunctional Bioinspired Microlattice with Excellent Sound Absorption, Damage Tolerance, and High Specific Strength

Although mutually independent, simultaneous sound absorption and superior mechanical properties are often sought after in a material. One main challenge in achieving such a material will be on how to design it. Herein, we propose a bamboo-inspired design strategy to overcome the aforementioned challenges. Building on top of the basic octet-truss design, we introduce a hollow-tube architecture to achieve lightweight property and mechanical robustness and a septum-chamber architecture to introduce acoustic resonant cells. The concept is experimentally verified through samples fabricated using selective laser melting with the Inconel 718 alloy. High sound absorption coefficients (>0.99) with broadband spectra, damage-tolerant behavior, high specific strength (up to 81.2 MPa·cm3/g), and high specific energy absorption of 40.1 J/g have been realized in this design. The sound absorption capability is attributed to Helmholtz resonance through the pore-and-cavity morphology of the structure. Microscopically speaking, dissipation primarily occurs via the viscous frictional flow and thermal boundary layers on the air and microlattice interactions at the narrow pores. The high strength is in turn attributed to the near-membrane state of stress in the plate structures and the excellent strength of the base material. Overall, this work presents a new design concept for developing multifunctional metamaterials.

Multifunctional sound-absorbing and mechanical metamaterials via a decoupled mechanism design approach

Multifunctional materials are in high demand for practical engineering applications. Owing to the ubiquitous noise and impact energy hazards in many settings, traditional materials and conventionally designed metamaterials are incapable of preventing these types of hazard simultaneously. Herein, we report a new paradigm, via a decoupled approach, in the design of acousto-mechanical multifunctional metamaterials. We leverage the morphology of a Helmholtz resonator, such that the sound-absorbing and mechanical components are designed independently. For sound absorption, we adopt a coherent coupling design for a favorable resonant response, while for the mechanical response, we adopt customized struts. We then demonstrate our concept via 3D printing. Experimentally measured remarkable broadband absorption in the practical low-frequency range (<1.0 kHz) is achieved. Absorption mechanisms are attributed to viscous and thermal boundary dissipation. Compression tests also reveal that the metamaterials are highly deformation resilient with a recovery of up to 98%, owing to both the lattice structure design and the viscoelastic behavior of the base material. Through this decoupled design, we further demonstrate the potential of our metamaterials in customizable absorption, strength, pseudo-reusability, and impact resistance. The proposed design paradigm broadens the horizon for the design of multifunctional materials, offering an impetus to their exploration for practical applications.

Adjustable Sound Absorber of Multiple Parallel-Connection Helmholtz Resonators with Tunable Apertures Prepared by Low-Force Stereolithography of Photopolymer Resin

The variable noise spectrum for many actual application scenarios requires a sound absorber to adapt to this variation. An adjustable sound absorber of multiple parallel-connection Helmholtz resonators with tunable apertures (TA-MPCHRs) is prepared by the low-force stereolithography of photopolymer resin, which aims to improve the applicability of the proposed sound absorber for noise with various frequency ranges. The proposed TA-MPCHR metamaterial contains five metamaterial cells. Each metamaterial cell contains nine single Helmholtz resonators. It is treated as a basic structural unit for an array arrangement. The tunable aperture is realized by utilizing four segments of extendable cylindrical chambers with length l₀, which indicates that the length of the aperture l is in the range of [l₀, 4l₀], and that it is tunable. With a certain group of specific parameters for the proposed TA-MPCHR, the influence of the tunable aperture with a variable length is investigated by acoustic finite element simulation with a two-dimensional rotational symmetric model. For the given noise spectrum of certain actual equipment with four operating modes, the TA-MPCHR sample with a limited total thickness of 40 mm is optimized, which is made of photopolymer resin by the low-force stereolithography, and its actual average sound absorption coefficients for the frequency ranges of 500-800 Hz, 550-900 Hz, 600-1000 Hz and 700-1150 Hz reach 0.9203, 0.9202, 0.9436 and 0.9561, respectively. Relative to common non-adjustable metamaterials, the TA-MPCHR made of photopolymer resin can reduce occupied space and improve absorption efficiency, which is favorable in promoting its practical applications in the noise pollution prevention.

Models for resonant acoustic metasurfaces with application to moth wing ultrasound absorption

Taking as bioinspiration the remarkable acoustic absorption properties of moth wings, we develop a simple analytical model that describes the interaction between acoustic pressure fields, and thin elastic plates incorporating resonant sub-structures. The moth wing is an exemplar of a natural acoustic metamaterial; the wings are deeply subwavelength in thickness at the frequencies of interest, the absorption is broadband and the tiny scales resonate on the moth wing acting in concert. The simplified model incorporates only the essential physics and the scales are idealized to flat rigid rectangular plates coupled via a spring to an elastic plate that forms the wing; all the components are deep-subwavelength at desired frequencies. Based on Fourier analysis, complemented by phenomenological modelling, our theory shows excellent agreement with simulation mimicking the moth-wing structure. Moth wings operate as broadband sound absorbers employing a range of scale sizes. We demonstrate that a random distribution of scale sizes generates a broadband absorption spectrum. To further illustrate the potential of the model, we design a deeply sub-wavelength acoustic counterpart of electromagnetically induced reflectance. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Reduction of the occlusion effect induced by earplugs using quasi perfect broadband absorption

Passive earplugs are used to prevent workers from noise-induced hearing loss. However, earplugs often induce an acoustic discomfort known as the occlusion effect. This phenomenon corresponds to an increased auditory perception of the bone-conducted part of physiological noises at low-frequency and is associated with the augmentation of the acoustic pressure in the occluded earcanal. In this work, we report a new concept of passive earplugs for mitigating the occlusion effect between 100 Hz and 1 kHz. The strategy consists in reducing the input impedance of the earplug seen from the earcanal by using quasi-perfect broadband absorbers derived from the field of meta-materials. The proposed "meta-earplug" is made of 4 critically coupled Helmholtz resonators arranged in parallel. Their geometry is optimized using an evolutionary algorithm associated with a theoretical model of the meta-earplug input impedance. The latter is validated against a finite-element approach and impedance sensor measurements. The meta-earplug is manufactured by 3D printing. Artificial test fixtures are used to assess the occlusion effect and the insertion loss. Results show that the meta-earplug induces an occlusion effect approximately 10 dB lower than foam and silicone earplugs while it provides an insertion loss similar to the silicone earplug up to 5 kHz.

Absorption characteristics of large acoustic metasurfaces

Metasurfaces formed of arrays of subwavelength resonators are often tuned to 'critically couple' with incident radiation, so that at resonance dissipative and radiative damping are balanced and absorption is maximized. Such design criteria are typically derived assuming an infinite metasurface, whereas the absorption characteristics of finite metasurfaces, even very large ones, can be markedly different in certain frequency intervals. This is due to the excitation of surface waves, intrinsic to resonant metasurfaces and especially meta-resonances, namely collective resonances where the surface waves form standing-wave patterns over the planar metasurface domain. We illustrate this issue using a detailed model of a Helmholtz-type acoustic metasurface formed of cavity-neck pairs embedded into a rigid substrate, with geometric and dissipation effects included from first principles (R. Brandão and O. Schnitzer, Wave Motion, 97, 102583, 2020). This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

Fundamental constraints on broadband passive acoustic treatments in unidimensional scattering problems

In a passive lossy acoustical system, sum rules derived from passivity explicitly relate the broadband response to the spatial dimension of the system, which provide important design criteria as well. In this work, the theory of Herglotz function is applied systematically to derive sum rules for unidimensional scattering problems relying on passive acoustic treatments which are generally made of rigid, motionless and subwavelength structures saturated by air. The rigid-boundary reflection, soft-boundary reflection and transmission problems are analysed. The derived sum rules are applied for guiding the designs of passive absorbers and mufflers: the required minimum space is directly predicted from the target (i.e. the desired absorption or transmission-loss spectra) without any specific design. Besides, it is possible to break this type of sum rules and fundamental constraints in particular cases. This property, if well used, could result in ultra-compact absorbers working at long wavelength up to infinity.

A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress-relaxation

We present a unified framework for the study of wave propagation in homogeneous linear thermo-visco-elastic (TVE) continua, starting from conservation laws. In free-space such media admit two thermo-compressional modes and a shear mode. We provide asymptotic approximations to the corresponding wavenumbers which facilitate the understanding of dispersion of these modes, and consider common solids and fluids as well as soft materials where creep compliance and stress relaxation are important. We further illustrate how commonly used simpler acoustic/elastic dissipative theories can be derived via particular limits of this framework. Consequently, our framework allows us to: (i) simultaneously model interfaces involving both fluids and solids and (ii) easily quantify the influence of thermal or viscous losses in a given configuration of interest. As an example, the general framework is appliedto the canonical problem of scattering from an interface between two TVE half spaces in perfect contact. To illustrate, we provide results for fluid–solid interfaces involving air, water, steel and rubber, paying particular attention to the effects of stress relaxation.

Broadband impedance modulation via non-local acoustic metamaterials

Causality of linear time-invariant systems inherently defines the wave-matter interaction process in wave physics. This principle imposes strict constraints on the interfacial response of materials on various physical platforms. A typical consequence is that a delicate balance has to be struck between the conflicting bandwidth and geometric thickness when constructing a medium with desired impedance, which makes it challenging to realize broadband impedance modulation with compact structures. In pursuit of improvement, the over-damped recipe and the reduced excessive response recipe are creatively presented in this work. As a proof-of-concept demonstration, we construct a metamaterial with intensive mode density that supports strong non-locality over a frequency band from 320 Hz to 6400 Hz. Under the guidelines of the over-damped recipe and the reduced excessive response recipe, the metamaterial realizes impedance matching to air and exhibits broadband near-perfect absorption without evident impedance oscillation and absorption dips in the working frequency band. We further present a dual-functional design capable of frequency-selective absorption and reflection by concentrating the resonance modes in three frequency bands. Our research reveals the significance of over-damped recipe and the strong non-local effect in broadband impedance modulation, which may open up avenues for constructing efficient artificial impedance boundaries for energy absorption and other wave manipulation.

Confined acoustic line modes within a glide-symmetric waveguide

Confined coupled acoustic line-modes supported by two parallel lines of periodic holes on opposite surfaces of a glide-symmetric waveguide have a hybrid character combining symmetric and anti-symmetric properties. These hybrid coupled acoustic line-modes have a near constant group velocity over a broad frequency range as no band gap is formed at the first Brillouin zone boundary. We show that the hybrid character of these confined modes is tuneable as a function of the spacing between the two surfaces. Further we explore how the band-gap reappears as the glide symmetry is broken.

Compact resonant systems for perfect and broadband sound absorption in wide waveguides in transmission problems

This work deals with wave absorption in reciprocal asymmetric scattering problem by addressing the acoustic problem of compact absorbers for perfect unidirectional absorption, flush mounted to the walls of wide ducts. These absorbers are composed of several side-by-side resonators that are usually of different geometry and thus detuned to yield an asymmetric acoustic response. A simple lumped-element model analysis is performed to link the dependence of the optimal resonators surface impedance, resonance frequency, and losses to the duct cross-sectional area and resonator spacing. This analysis unifies those of several specific configurations into a unique problem. In addition, the impact of the potential evanescent coupling between the resonators, which is usually neglected, is carefully studied. This coupling can have a strong impact especially on the behavior of compact absorbers lining wide ducts. To reduce the evanescent coupling, the resonators should be relatively small and therefore their resonances should be damped, and not arranged by order of increasing or decreasing resonant frequency. Finally, such an absorber is designed and optimized for perfect unidirectional absorption to prove the relevance of the analysis. The absorber is 30 cm long and 5 cm thick and covers a single side of a 14.8 × 15 cm2 rectangular duct. A mean absorption coefficient of 99% is obtained experimentally between 700 and 800 Hz.

How the waveguide acoustic black hole works: A study of possible damping mechanisms

The acoustic black hole (ABH) effect in waveguides is studied using frequency-domain finite element simulations of a cylindrical waveguide with an embedded ABH termination composed of retarding rings. This design is adopted from an experimental study in the literature, which surprisingly showed, contrary to the structural counterpart, that the addition of damping material to the end of the waveguide does not significantly reduce the reflection coefficient any further. To investigate this unexpected behavior, we model different damping mechanisms involved in the attenuation of sound waves in this setup. A sequence of computed pressure distributions indicates occurrences of frequency-dependent resonances in the device. The axial position of the cavity where the resonance occurs can be predicted by a more elaborate wall admittance model than the one that was initially used to study and design ABHs. The results of our simulations show that at higher frequencies, the visco-thermal losses and the damping material added to the end of the setup do not contribute significantly to the performance of the device. Our results suggest that the primary source of damping, responsible for the low reflection coefficients at higher frequencies, is local absorption effects at the outer surface of the cylinder.

Acoustic Metamaterials for Low-Frequency Noise Reduction Based on Parallel Connection of Multiple Spiral Chambers

Acoustic metamaterials based on Helmholtz resonance have perfect sound absorption characteristics with the subwavelength size, but the absorption bandwidth is narrow, which limits the practical applications for noise control with broadband. On the basis of the Fabry–Perot resonance principle, a novel sound absorber of the acoustic metamaterial by parallel connection of the multiple spiral chambers (abbreviated as MSC-AM) is proposed and investigated in this research. Through the theoretical modeling, finite element simulation, sample preparation and experimental validation, the effectiveness and practicability of the MSC-AM are verified. Actual sound absorption coefficients of the MSC-AM in the frequency range of 360–680 Hz (with the bandwidth Δf1 = 320 Hz) are larger than 0.8, which exhibit the extraordinarily low-frequency sound absorption performance. Moreover, actual sound absorption coefficients are above 0.5 in the 350–1600 Hz range (with a bandwidth Δf2 = 1250 Hz), which achieve broadband sound absorption in the low–middle frequency range. According to various actual demands, the structural parameters can be adjusted flexibly to realize the customization of sound absorption bandwidth, which provides a novel way to design and improve acoustic metamaterials to reduce the noise with various frequency bands and has promising prospects of application in low-frequency sound absorption.

Underwater metamaterial absorber with impedance-matched composite

By using a structured tungsten-polyurethane composite that is impedance matched to water while simultaneously having a much slower longitudinal sound speed, we have theoretically designed and experimentally realized an underwater acoustic absorber exhibiting high absorption from 4 to 20 kHz, measured in a 5.6 m by 3.6 m water pool with the time-domain approach. The broadband functionality is achieved by optimally engineering the distribution of the Fabry-Perot resonances, based on an integration scheme, to attain impedance matching over a broad frequency range. The average thickness of the integrated absorber, 8.9 mm, is in the deep subwavelength regime (~λ/42 at 4 kHz) and close to the causal minimum thickness of 8.2 mm that is evaluated from the simulated absorption spectrum. The structured composite represents a new type of acoustic metamaterials that has high acoustic energy density and promises broad underwater applications.

A decoupling-design strategy for high sound absorption in subwavelength structures with air ventilation

A strategy based on the decoupling design of two elementary structures, both made of coiled-up channels, is proposed. One channeling structure is designed for blocking sound transmission, while the other element is used for absorbing sounds at low-transmission frequencies. Based on this strategy, the sound-absorbing sample with air ventilation is fabricated and its high-absorption capability is demonstrated experimentally. The expanding of sound absorption bandwidth by combining different absorptive channels into the sample structure is also demonstrated. The proposed method provides a new route towards broadband high sound absorption in ventilated structures.

Low-Frequency, Open, Sound-Insulation Barrier by Two Oppositely Oriented Helmholtz Resonators

In this work, a low-frequency, open, sound-insulation barrier, composed of a single layer of periodic subwavelength units (with a thickness of λ/28), is demonstrated both numerically and experimentally. Each unit was constructed using two identical, oppositely oriented Helmholtz resonators, which were composed of a central square cavity surrounded by a coiled channel. In the design of the open barrier, the distance between two adjacent units was twice the width of the unit, showing high-performance ventilation, and low-frequency sound insulation. A minimum transmittance of 0.06 could be observed around 121.5 Hz, which arose from both sound reflections and absorptions, created by the coupling of symmetric and asymmetric eigenmodes of the unit, and the absorbed sound energy propagating into the central cavity was greatly reduced by the viscous loss in the channel. Additionally, by introducing a multilayer open barrier, a broadband sound insulation was obtained, and the fractional bandwidth could reach approximately 0.19 with four layers. Finally, the application of the multilayer open barrier in designing a ventilated room was further discussed, and the results presented an omnidirectional, broadband, sound-insulation effect. The proposed open, sound-insulation barrier with the advantages of ultrathin thickness; omnidirectional, low-frequency sound insulation; broad bandwidth; and high-performance ventilation has great potential in architectural acoustics and noise control.

Ultra-sparse metamaterials absorber for broadband low-frequency sound with free ventilation

An absorptive device for broadband low-frequency sound with ventilation is essential but challenging in acoustic engineering, which is subjected to the narrow-band limitation and difficulty of balancing high-efficiency absorption and excellent ventilation. Here, we have theoretically and experimentally demonstrated an ultra-sparse (with filling ratio of 53.7%) broadband metamaterial absorber which can efficiently absorb (absorptance  >90%) sound energy ranging from 307 to 341 Hz, while enabling air to flow freely. The broadband absorber is constructed by parallel coupling four ventilated metamaterials absorbers (VMAs) showing different operating frequencies. Each VMA is composed of three folded Fabry-Pérot resonators as paste components, which are patched subsequently to the walls of a waveguide and correspondingly act as dark, middle, and bright modes following the coupled mode theory. In the VMA, the dark mode is highly over-damped to absorb sound energy, while the bright mode is highly under-damped to be an effective acoustic soft boundary, and the middle mode in-between should be slightly over-damped to strengthen the absorptions. Further investigation demonstrates that broadband high-efficiency absorption is robust against oblique incident angles. The proposed VMA provides a clear scheme for efficiently absorbing low-frequency sound while allowing free air flow simultaneously, which may prompt versatile applications in noise control.

Influence of interference among parallel absorbers on acoustic characteristics of an absorbing panel

This paper proposes a modified theory for synthesizing the acoustic impedance of an absorbing panel by considering the interference among parallel absorbers. The absorbing panel comprises periodically distributed absorbers with different acoustic characteristics, and the periodic distribution allows the impedance of the panel to be characterized by that of a unit cell. However, at frequencies between the resonances of the absorbers in the unit cell, the unit-cell impedance given by traditional theory deviates significantly from that given by a finite-element model. Inspecting the flow field near the surface of the unit cell reveals that the out-of-phase flow plays an important role in the interaction among the parallel absorbers and induces the deviation. A modified theory is proposed by multiplying the original resultant impedance by a factor that considers the interaction. The modified theory is verified by numerical results for several typical absorbing panels with different patterns of unit cells and different geometrical parameters of absorbers, and experimental validation is also carried out. As further evidence for the correctness and universality of the modified theoretical model, a comparison is presented with the mutual-radiation-impedance theoretical model based on a Helmholtz resonator array panel. The results of validation on different absorbing panels and the comparison with the mutual-radiation-impedance method show that the modified theoretical model is better at predicting the absorption coefficient than is the traditional theory.

Spiral sound-diffusing metasurfaces based on holographic vortices

In this work, we show that scattered acoustic vortices generated by metasurfaces with chiral symmetry present broadband unusual properties in the far-field. These metasurfaces are designed to encode the holographic field of an acoustical vortex, resulting in structures with spiral geometry. In the near field, phase dislocations with tuned topological charge emerge when the scattered waves interference destructively along the axis of the spiral metasurface. In the far field, metasurfaces based on holographic vortices inhibit specular reflections because all scattered waves also interfere destructively in the normal direction. In addition, the scattering function in the far field is unusually uniform because the reflected waves diverge spherically from the holographic focal point. In this way, by triggering vorticity, energy can be evenly reflected in all directions except to the normal. As a consequence, the designed metasurface presents a mean correlation-scattering coefficient of 0.99 (0.98 in experiments) and a mean normalized diffusion coefficient of 0.73 (0.76 in experiments) over a 4 octave frequency band. The singular features of the resulting metasurfaces with chiral geometry allow the simultaneous generation of broadband, diffuse and non-specular scattering. These three exceptional features make spiral metasurfaces extraordinary candidates for controlling acoustic scattering and generating diffuse sound reflections in several applications and branches of wave physics as underwater acoustics, biomedical ultrasound, particle manipulation devices or room acoustics.

Bilayer ventilated labyrinthine metasurfaces with high sound absorption and tunable bandwidth

The recent advent of acoustic metamaterials offers unprecedented opportunities for sound controlling in various occasions, whereas it remains a challenge to attain broadband high sound absorption and free air flow simultaneously. Here, we demonstrated, both theoretically and experimentally, that this problem can be overcome by using a bilayer ventilated labyrinthine metasurface. By altering the spacing between two constituent single-layer metasurfaces and adopting asymmetric losses in them, near-perfect (98.6%) absorption is achieved at resonant frequency for sound waves incident from the front. The relative bandwidth of absorption peak can be tuned in a wide range (from 12% to 80%) by adjusting the open area ratio of the structure. For sound waves from the back, the bilayer metasurface still serves as a sound barrier with low transmission. Our results present a strategy to realize high sound absorption and free air flow simultaneously, and could find applications in building acoustics and noise remediation.

Multiband asymmetric sound absorber enabled by ultrasparse Mie resonators

On the quest towards efficiently eliminating noises, the development of a subwavelength sound absorber with the capability of free ventilation remains challenging. Here, we theoretically propose and experimentally demonstrate an asymmetric metamaterial absorber constructed by tuned Mie resonators (MRs) with unbalanced intrinsic losses. The lossy MR layer is highly dissipative to consume the sound energy while the lossless one acts as an acoustically soft boundary. Thus, the absorber presents quasi-perfect absorption (95% in experiment) for sound waves incident from the port nearer the dissipative MR and large-amount reflection (71% in experiment) from the opposite port. Moreover, the fluid dynamics investigation confirms the superior character of free air circulation owing to the ultrasparsity (volume filling ratio as low as 5%) of the absorber and its robustness to the velocity of airflows. Due to the multiple-order resonant modes of MR, we further demonstrate the flexibility of a methodology to extend asymmetric absorptions into multibands. Coupled mode analysis is employed to reveal the physical mechanism and further indicates that sparsity can be tuned by attentively controlling the reference leakage factor and intrinsic loss.

Generative adversarial networks for the design of acoustic metamaterials

Metamaterials are attracting increasing interest in the field of acoustics due to their sound insulation effects. By periodically arranged structures, acoustic metamaterials can influence the way sound propagates in acoustic media. To date, the design of acoustic metamaterials relies primarily on the expertise of specialists since most effects are based on localized solutions and interference. This paper outlines a deep learning-based approach to extend current knowledge of metamaterial design in acoustics. We develop a design method by using conditional generative adversarial networks. The generative network proposes a cell candidate regarding a desired transmission behavior of the metamaterial. To validate our method, numerical simulations with the finite element method are performed. Our study reveals considerable insight into design strategies for sound insulation tasks. By providing design directives for acoustic metamaterials, cell candidates can be inspected and tailored to achieve desirable transmission characteristics.

Elastic bandgap widening and switching via spatially varying materials and buckling instabilities

Efficient control over elastic wave transmission is often critical in the design of architected materials. In this work, lattices that achieve buckling induced band gaps are designed with spatially varying material properties to leverage both effects for enhanced wave control. Each unit cell exhibits a large shape change when subjected to an external activation. Unit cells with discrete material properties are then arranged in different spatial configurations. Numerical simulations for transmission through the example structures demonstrate both bandgap widening due to different material properties in adjacent unit cells and switching at different deformation states.

Planar acoustic scattering by a multi-layered split ring resonator

The problem of two-dimensional acoustic scattering of time-harmonic plane waves by a multi-ringed cylindrical resonator is considered. The resonator is made up of an arbitrary number of concentric sound-hard split rings with zero thickness. Each ring opening is oriented in any direction. The acoustics pressure field in each layered region enclosed between adjacent rings is described by an eigenfunction expansion in polar coordinates. An integral equation/Galerkin method is used to relate the unknown coefficients of the expansions between adjacent regions separated by a ring. The multiple scattering problem is then formulated as a reflection/transmission problem between the layers, which is solved using an efficient iterative scheme. An exploration of the parameter space is conducted to determine first, the conditions under which the lowest resonant frequency can be minimised, and second, how non-trivial resonances of the multi-ring resonators can be explained from those of simpler arrangements, such as a single-ring resonator. It is found here that increasing the number of rings while alternating the orientation lowers the first resonant frequency, and exhibits a dense and nearly regular resonant structure that is analogous to the rainbow trapping effect.

Angle-Dependent Absorption of Sound on Porous Materials

Sound-absorbing materials are usually measured in a reverberation chamber (diffuse field condition) or in an impedance tube (normal sound incidence). In this paper, we show how angle-dependent absorption coefficients could be measured in a factory-type setting. The results confirm that the materials have different attenuation behavior to sound waves coming from different directions. Furthermore, the results are in good agreement with sound absorption coefficients measured for comparison in a reverberation room and in an impedance tube. In addition, we introduce a biofiber-based material that has similar sound absorption characteristics to glass-wool. The angle-dependent absorption coefficients are important information in material development and in room acoustics modeling.

Inverse design of acoustic metamaterials based on machine learning using a Gauss–Bayesian model

Acoustic metamaterials (AMs) have attracted a substantial amount of attention in recent decades where the parameter design plays an important role. However, conventional design methods generally rely on analytical physical models and require a very large number of evaluations of acoustic performance. Here, we propose and experimentally demonstrate an inverse-design method for AMs based on machine learning using a Gauss–Bayesian model. As a result of the cycle of training and prediction and the use of adaptive acquisition functions, this method allows the parameters of AMs to be efficiently designed for specific functionalities without the need for physical models. Considering the significance of low-frequency ventilated sound absorption, we present a design for a typical acoustic metamaterial absorber with multiple structural parameters that facilitate high sound absorption at low frequencies. In the design process, the parameters were adaptively adjusted to improve the sound absorption performance at low frequencies using only 37 evaluations, and this high absorption performance was verified by the agreement of numerical and experimental results. Because of its low cost, high flexibility, and independence from physical models, this method paves the way for tremendous opportunities in the design of various AMs for particular desired functionalities.

Subwavelength broadband sound absorber based on a composite metasurface

Suppressing broadband low-frequency sound has great scientific and engineering significance. However, normal porous acoustic materials backed by a rigid wall cannot really play its deserved role on low-frequency sound absorption. Here, we demonstrate that an ultrathin sponge coating can achieve high-efficiency absorptions if backed by a metasurface with moderate surface impedance. Such a metasurface is constructed in a wide frequency range by integrating three types of coiled space resonators. By coupling an ultrathin sponge coating with the designed metasurface, a deep-subwavelength broadband absorber with high absorptivity (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${>}80\%$$\end{document}>80%) exceeding one octave from  185 Hz to  385 Hz (with wavelength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}λ from 17.7 to 8.5 times of thickness of the absorber) has been demonstrated theoretically and experimentally. The construction mechanism is analyzed via coupled mode theory. The study provides a practical way in constructing broadband low-frequency sound absorber.

Dual frequency sound absorption with an array of shunt loudspeakers

Transformer noise is dominated by low frequency components, which are hard to be controlled with traditional noise control approaches. The shunt loudspeaker consisting of a closed-box loudspeaker and a shunt circuit has been proposed as an effective sound absorber by storing and dissipating the electrical energy converted from the incident sound. In this paper, an array of shunt loudspeakers is proposed to control the 100 Hz and 200 Hz components of transformer noise. The prototype under tests has a thickness of 11.8 cm, which is only 1/28 of the wavelength of 100 Hz. The sound absorption performance of the array under random incidence is analyzed with the parallel impedance method, and the arrangement of array elements is optimized. The test results in a reverberation room show that the proposed array has sound absorption coefficients of 1.04 and 0.93 at 100 Hz and 200 Hz, respectively, which provides potential of applying this type of thin absorbers for low-frequency sound control.

Cochlea-inspired design of an acoustic rainbow sensor with a smoothly varying frequency response

A number of physical arrangements for acoustic rainbow sensors have been suggested, where the aim is to separate different frequency components into different physical locations along the sensor. Although such spatial discrimination has been achieved with several designs of sensor, the resulting frequency responses at a given position along the sensor are generally not smoothly varying. In contrast, the cochlea provides an interesting natural example of a rainbow sensor, which has an exponential frequency distribution and whose response does vary smoothly with frequency. The design of a rainbow sensor is presented that has a number of discrete resonators and an exponential frequency distribution. We discuss the conditions for a smoothly varying frequency response in such a sensor, as part of a broader design strategy. It is shown that the damping within the resonators determines the trade-off between the frequency resolution and the number of elements required to achieve a smooth response. The connection is explained between this design and that of an effective acoustic absorber. The finite number of hair cells means that the cochlea itself can be thought of as being composed of discrete units and the conditions derived above are compared with those that are observed in the cochlea.

Tailored elastic surface to body wave Umklapp conversion

Elastic waves guided along surfaces dominate applications in geophysics, ultrasonic inspection, mechanical vibration, and surface acoustic wave devices; precise manipulation of surface Rayleigh waves and their coupling with polarised body waves presents a challenge that offers to unlock the flexibility in wave transport required for efficient energy harvesting and vibration mitigation devices. We design elastic metasurfaces, consisting of a graded array of rod resonators attached to an elastic substrate that, together with critical insight from Umklapp scattering in phonon-electron systems, allow us to leverage the transfer of crystal momentum; we mode-convert Rayleigh surface waves into bulk waves that form tunable beams. Experiments, theory and simulation verify that these tailored Umklapp mechanisms play a key role in coupling surface Rayleigh waves to reversed bulk shear and compressional waves independently, thereby creating passive self-phased arrays allowing for tunable redirection and wave focusing within the bulk medium.

Umklapp scattering, an effect that has been conventionally studied in phonon systems in quantum transport, is studied here in an elastic system. The authors demonstrate mode conversion from surface Rayleigh waves into bulk waves that have uniquely tunable properties.

Compact broadband acoustic sink with coherently coupled weak resonances

Broadband sound sink/absorber via a structure with deep sub-wavelength thickness is of great and continuing interest in physics and engineering communities. An intuitive technique extensively used is to combine components (resonators) with quasi-perfect absorption to piece together a broad absorbing band, but the requirement of quasi-perfect absorption substantially places a very strict restriction on the impedance and thickness of the components. Here, we theoretically and experimentally demonstrate that a compact broadband acoustic sink that quasi-perfectly absorbs broadband arriving sound waves can be achieved with coherently coupled "weak resonances" (resonant sound absorbing systems with low absorption peaks). Although each component exhibits rather low absorption peak alone, via manipulating the coherent coupling effect among the components, they collectively provide a remarkably improved performance over a wide frequency range with a significantly compressed thickness. To illustrate the design principle, a hybrid metasurface utilizing the coaction of parallel and cascade couplings is presented, which possesses an average absorption coefficient of 0.957 in the quasi-perfect band (α>0.9) from 870 to 3224 Hz with a thickness of only 3.9 cm. Our results open new avenues for the development of novel and highly efficient acoustic absorbers against low frequency noise, and more essentially, suggest an efficient approach towards on-demand acoustic impedance engineering in broadband.

Sound Absorption and Diffusion by 2D Arrays of Helmholtz Resonators

We report a theoretical and experimental study of an array of Helmholtz resonators optimized to achieve both efficient sound absorption and diffusion. The analysis starts with a simplified 1D model where the plane wave approximation is used to design an array of resonators showing perfect absorption for a targeted range of frequencies. The absorption is optimized by tuning the geometry of the resonators, i.e., by tuning the viscothermal losses of each element. Experiments with the 1D array were performed in an impedance tube. The designed system is extended to 2D by periodically replicating the 1D array. The 2D system has been numerically modeled and experimentally tested in an anechoic chamber. It preserves the absorption properties of the 1D system and introduces efficient diffusion at higher frequencies due to the joint effect of resonances and multiple scattering inside the discrete 2D structure. The combined effect of sound absorption at low frequencies and sound diffusion at higher frequencies, may play a relevant role in the design of noise reduction systems for different applications.

Mimicking the active cochlea with a fluid-coupled array of subwavelength Hopf resonators

We present a design for an acoustic metamaterial that mimics the behaviour of the active cochlea. This material is composed of a size-graded array of cylindrical subwavelength resonators, has similar dimensions to the cochlea and is able to per- form frequency separation of audible frequencies. Nonlinear amplification is introduced to the model in order to replicate the behaviour of the cochlear amplifier. This formulation takes the form of a fluid-coupled array of Hopf resonators. We seek solutions in the form of a modal decomposition, so as to retain the physically derived coupling between resonators.

Low-frequency wave-energy amplification in graded two-dimensional resonator arrays

Energy amplification in square-lattice arrays of C-shaped low-frequency resonators, where the resonator radii are graded with distance, is investigated in the two-dimensional linear acoustics setting for both infinite (in one dimension) and finite arrays. Large amplifications of the incident energy are shown in certain array locations. The phenomenon is analysed using: (i) band diagrams for doubly-periodic arrays; (ii) numerical simulations for infinite and finite arrays; and (iii) eigenvalue analysis of transfer matrices operating over individual columns of the array. It is shown that the locations of the large amplifications are predicted by propagation cut-offs in the modes associated with the transfer-matrix eigenvalues. For the infinite array, the eigenvalues form a countable set, and for the low frequencies considered, only a single propagating mode exists for a given incident wave, which cuts off within the array, leading to predictive capabilities for the amplification location. For the finite array, it is shown that (in addition to a continuous spectrum of modes) multiple discrete propagating modes can be excited, with the grading generating new modes, as well as cutting others off, leading to complicated amplification patterns. The numerical simulations reveal that the largest amplifications are achieved for a single row array, with amplifications an order of magnitude smaller for the corresponding infinite array. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.

Low-frequency perfect sound absorption achieved by a modulus-near-zero metamaterial

We have analytically proposed a mechanism for achieving a perfect absorber by a modulus-near-zero (MNZ) metamaterial with a properly decorated imaginary part, in which the perfect absorption (PA) is derived from the proved destructive interference. Based on the analysis, an ultrathin acoustic metamaterial supporting monopolar resonance at 157 Hz (with a wavelength about 28 times of the metamaterial thickness) has been devised to construct an absorber for low-frequency sound. The imaginary part of its effective modulus can be easily tuned by attentively controlling the dissipative loss to achieve PA. Moreover, we have also conducted the experimental measurement in impedance tube, and the result is of great consistency with that of analytical and simulated ones. Our work provides a feasible approach to realize PA (>99%) at low frequency with a deep-wavelength dimension which may promote acoustic metamaterials to practical engineering applications in noise control.

Damped resonance for broadband acoustic absorption in one-port and two-port systems

We demonstrate broadband perfect acoustic absorption by damped resonances through inclusion of lossy porous media. By minimally placing the lossy materials around the necks of single-resonance Helmholtz resonators, where acoustic energy is concentrated, we show an increase in absorption bandwidths (>100% of the resonance frequency). Using the damped resonance, we demonstrate three types of broadband acoustic absorbers in one-port and two-port systems: broadband absorbers (one-port), broadband sparse absorbers (two-port), and broadband duct absorbers (two-port). Our approach for broadband absorption allows to minimize the number of resonances for compact absorbers, while it is beneficial for practical applications owing to the minimum use of porous materials.

A fully coupled subwavelength resonance approach to filtering auditory signals

The aim of this paper is to understand the behaviour of a large number of coupled subwavelength resonators. We use layer potential techniques in combination with numerical computations to study an acoustic pressure wave scattered by a graded array of subwavelength resonators. Using this approach, the spatial frequency separation properties of such an array can be understood. Our set-up is inspired by the graded structure of cochlear hair cells on the surface of the basilar membrane. We compute the resonant modes of the system and explore the model's ability to decompose incoming signals. We propose a mathematical explanation for phenomena identified with the cochlea's ‘travelling wave’ behaviour and tonotopic frequency map.