Slow Sound Propagation Research Articles

Ultrathin acoustic metamaterial as super absorber for broadband low-frequency underwater sound

In this work, an ultrathin acoustic metamaterial formed by space-coiled water channels with a rubber coating is proposed for underwater sound absorption. The proposed metamaterial achieves perfect sound absorption (alpha > 0.99) at 181 Hz, which has a deep subwavelength thickness (lambda {/}162). The theoretical prediction is consistent with the numerical simulation, which demonstrate the broadband low-frequency sound absorption performance of the proposed super absorber. The introduction of rubber coating leads to a significant decrease of the effective sound speed in the water channel, resulting in the phenomenon of slow-sound propagation. From the perspective of numerical simulations and acoustic impedance analysis, it is proved that the rubber coating on the channel boundary causes slow-sound propagation with inherent dissipation, which is the key to meet the impedance matching condition and achieve perfect low-frequency sound absorption. Parametric studies are also carried out to investigate the effect of specific structural and material parameters on sound absorption. By tailoring key geometric parameters, an ultra-broadband underwater sound absorber is constructed, with a perfect absorption range of 365–900 Hz and a deep subwavelength thickness of 33 mm. This work paves a new way for designing underwater acoustic metamaterials and controlling underwater acoustic waves.

Secret Key Generation From Route Propagation Delays for Underwater Acoustic Networks

With the growing use of underwater acoustic communications and the recent adoption of standards in this field, it is becoming increasingly important to secure messages against eavesdroppers. In this paper, we focus on a physical-layer security solution to generate sequences of random bits (keys) between two devices (Alice and Bob) belonging to an underwater acoustic network (UWAN); the key must remain secret to a passive eavesdropper (Eve) not belonging to the UWAN. Our method is based on measuring the propagation delay of the underwater acoustic channel over multiple hops of the UWAN: this harvests the randomness in the UWAN topology and turns the slow sound propagation in water into an advantage against eavesdropping. Our key generation protocol includes a route discovery handshake, whereby all UWAN devices at intermediate hops accumulate their message processing delays. This enables Alice and Bob to compute the actual propagation delays along each route and to map such information to a sequence of bits. Finally, from these bit sequences, Alice and Bob obtain a secret key. We analyze the performance of the protocol theoretically and assess it via extensive simulations and field experiments.

Low-frequency underwater sound absorption of hybrid metamaterials using dissipative slow-sound

In this work, a hybrid metamaterial is proposed as a new type of underwater absorber, which is composed of carefully designed periodically arranged units. Each unit consists of a perforated panel, a water chamber and a coiled water channel coated with rubber on the channel walls. The coiled channel is designed to reduce the thickness of the structure. The introduction of the rubber coating changes the boundary condition of the coiled channel from rigid to non-rigid, resulting in dissipative slow-sound propagation in the coiled channel. The slow-sound propagation leads to the decrease of resonant frequency, and its inherent dissipation can consume sound energy, resulting in perfect low-frequency sound absorption at subwavelength thickness. Theoretical and numerical results show that the proposed hybrid metamaterial exhibits more than 99% sound energy absorption at 155 Hz, and the thickness of the structure is only 1/456 of the wavelength of sound wave. This work paves the way for the design of ultrathin underwater low-frequency absorbers.

Slow-Sound-Based Delay-Line Acoustic Metamaterial

Periodic structures composed of quarter-wavelength or Helmholtz resonators have been widely used in the design of acoustic metamaterials. An interesting phenomenon achievable through hybridization in such structures is the slow sound, which results from the strong dispersion produced by the local resonances. It gives rise to many applications such as deep subwavelength sound absorbers or metadiffusers. All the applications proposed so far have been analyzed only in the frequency domain (steady state). In this work, we propose a passive treatment that can be used in room acoustics, which requires considering the time domain and all multiple reflections. We analytically design a delay line from a metasurface made of Helmholtz resonators, using slow-sound propagation. We prove numerically and experimentally that such structures can delay a pulse and thus reproduce the sound perception of a propagation over a given distance, larger than the actual size of the treatment. The limitations of real-time pulse propagation, dispersion, and losses on audio fidelity are discussed.

Slow-sound propagation in aerogel-inspired hybrid structure with backbone and dangling branch

Slow-sound propagation in aerogel-inspired hybrid structure with backbone and dangling branch

Experimental validation of deep-subwavelength diffusion by acoustic metadiffusers

An acoustic metadiffuser is a subwavelength locally resonant surface relying on slow sound propagation. Its design consists of rigidly backed slotted panels, with each slit being loaded by an array of Helmholtz resonators. Due to the slow sound properties, the effective thickness of the panel can therefore be dramatically reduced when compared to traditional diffusers made of quarter-wavelength resonators. The aim of this work is to experimentally validate the concept of metadiffusers from the scattering measurements of a specific metadiffuser design, i.e., a quadratic residue metadiffuser. The experimental results reported herein are in close agreement with analytical and numerical predictions, therefore showing the potential of metadiffusers for controlling sound diffusion at very low frequencies.

Multimode acoustic transparency and slow sound effects in hybrid subwavelength resonators

In this paper, we demonstrate that a series of hybrid Helmholtz resonators, which introduce “acoustic transparent atoms”, “acoustic nontransparent atoms”, and “acoustic quasitransparent atoms” simultaneously, can generate multimode acoustic transparency and the slow sound effect. Dual-mode acoustic transparency can be achieved by employing a waveguide incorporating three different Helmholtz resonators. Additional modes are introduced by adding further acoustic quasitransparent atoms. This can be explained by the destructive interference among different resonators. Furthermore, slow sound propagation is demonstrated in our multimode acoustic transparency systems by employing time-domain simulations. Our results may have potential applications for sound control in one-dimensional waveguides.

Ultra-thin metamaterial for perfect and quasi-omnidirectional sound absorption

Using the concepts of slow sound and critical coupling, an ultra-thin acoustic metamaterial panel for perfect and quasi-omnidirectional absorption is theoretically and experimentally conceived in this work. The system is made of a rigid panel with a periodic distribution of thin closed slits, the upper wall of which is loaded by Helmholtz Resonators (HRs). The presence of resonators produces a slow sound propagation shifting the resonance frequency of the slit to the deep sub-wavelength regime (λ/88). By controlling the geometry of the slit and the HRs, the intrinsic visco-thermal losses can be tuned in order to exactly compensate the energy leakage of the system and fulfill the critical coupling condition to create the perfect absorption of sound in a large range of incidence angles due to the deep subwavelength behavior.

The use of slow waves to design simple sound absorbing materials

We demonstrate that the phenomenon of slow sound propagation associated with its inherent dissipation (dispersion + attenuation) can be efficiently used to design sound absorbing metamaterials. The dispersion relation of the wave propagating in narrow waveguides on one side of which quarter-wavelength resonators are plugged with a square lattice, whose periodicity is smaller than the wavelength, is analyzed. The thermal and viscous losses are accounted for in the modeling. We show that this structure slows down the sound below the bandgap associated with the resonance of quarter-wavelength resonators and dissipates energy. After deriving the effective parameters of both such a narrow waveguide and a periodic arrangement of them, we show that the combination of slow sound together with the dissipation can be efficiently used to design a sound absorbing metamaterial which totally absorbs sound for wavelength much larger than four times the thickness structure. This last claim is supported by experimental results.

Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures

We investigate sound propagation in lossy, locally resonant periodic structures by studying an air-filled tube periodically loaded with Helmholtz resonators and taking into account the intrinsic viscothermal losses. In particular, by tuning the resonator with the Bragg gap in this prototypical locally resonant structure, we study the limits and various characteristics of slow sound propagation. While in the lossless case the overlapping of the gaps results in slow-sound-induced transparency of a narrow frequency band surrounded by a strong and broadband gap, the inclusion of the unavoidable losses imposes limits to the slowdown factor and the maximum transmission. Experiments, theory, and finite element simulations have been used for the characterization of acoustic wave propagation by tuning the Helmholtz/Bragg frequencies and the total amount of loss both for infinite and finite lattices. This study contributes to the field of locally resonant acoustic metamaterials and slow sound applications.

Demonstration of slow sound propagation and acoustic transparency with a series of detuned resonators

We present experimental results demonstrating the phenomenon of acoustic transparency with a significant slowdown of sound propagation realized with a series of paired detuned acoustic resonators (DAR) side-attached to a waveguide. The phenomenon mimics the electromagnetically induced transparency in atomic physics. By arranging four identical DAR pairs along the waveguide with an equal subwavelength separation between adjacent pairs, we show that this arrangement features unique properties of narrow-band transmission and strong dispersion. In particular, we demonstrate side-lobe suppression of more than 20 dB on both sides of the transparency window, and we quantify directly (using a pulse propagation) the acoustic slowdown effect, resulting in the sound group velocity of \ensuremath{\sim}9.8 m/s (i.e. in the group refractive index of 35). We find very similar values of the group refractive index by using measurements of the phase of the transmitted wave. It is also shown that a direct coupling exists between the DAR in each pair, which cannot be explained by the interference of waves radiated from those resonators. This detrimental coupling becomes noticeable for small values of detuning and also if the cross-sectional area of the neck of the resonators is increased.

Self-collimated slow sound in sonic crystals

Self-collimated slow-sound propagation in a two-dimensional rectangular sonic crystal composed of elliptical scatterers in air is numerically demonstrated. The group velocity at the centre and the edges of the fourth acoustic band is reduced to 45 m s−1 and 30 m s−1, corresponding to 1/8 and 1/12 of the speed of sound in air, respectively. Elimination of omni-directional reflections encountered in linear waveguides and the reduction of group-velocity dispersion at the mid-band frequencies lead to preservation of pulse shape and amplitude upon traversal of the sonic crystal. Wave transmission is increased from approximately −20 to −2.5 dB, with almost an order of magnitude enhancement, via injector layers optimized through a pattern search algorithm. Self-collimating performance of the system is not degraded under oblique incidence, except for pulse broadening due to increased effective source width.

Slow sound propagation in a sonic crystal linear waveguide

A linear waveguide along the [11] direction of a triangular sonic crystal, composed of aluminum cylinders in air is shown both experimentally and numerically to facilitate slow sound propagation. Supercell-based calculations through the finite element method reveal a band centered at approximately 16.0 kHz with 255 Hz span, exhibiting linear variation away from band edges, for the lattice constant and cylinder radii of 21.7 mm and 10.0 mm, respectively. The experimental setup is based on monitoring the propagation of a Gaussian-enveloped sinusoidal pulse at 16.0 kHz inside the waveguide. Numerical behavior of the Gaussian pulse is investigated by time-dependent finite-element computations. The experimental and numerical group velocities are found to be 26.7 m/s and 22.6 m/s, respectively. Being congruous with the experimental findings, numerical transient study of the system reveals significant longitudinal compression commensurate with the calculated group index.

Acoustic transparency and slow sound using detuned acoustic resonators

We demonstrate that the phenomenon of acoustic transparency and slow sound propagation can be realized with detuned acoustic resonators (DAR), mimicking thereby the effect of electromagnetically induced transparency (EIT) in atomic physics. Sound propagation in a pipe with a series of side-attached DAR, with adjacent DAR units spaced by a distance much smaller than the wavelength, is analyzed. We show that such a chain of DAR units forms an analog of one-dimensional (1D) metamaterial with unique properties of dispersion and transmission, revealing the possibility of slowing sound (at 2 kHz) down by \ensuremath{\sim}100 times within the 40-Hz-broad transparency window. Preliminary experiments with two resonators detuned from the central frequency of 1.2 kHz verify the occurrence of the transparency effect.

Impacts of uniaxial elongation on the bandstructures of two-dimensional sonic crystals and associated applications

Influences of uniaxial elongation along the [11] direction of triangular and [10] direction of square sonic crystals under the constraint of conserved unit cell area are investigated by examining band structures and equi-frequency contours. Lowest-lying band gap of the triangular lattice observed at high filling fractions diminishes for negative elongation (compression), whereas another band gap develops at lower frequencies whose width reaches appreciable values for moderate elongation. The band gap of the square lattice, which appears at high filling fractions, is modified slightly with elongation. Frequency ranges of the bands, and thus the group velocities along the high-symmetry directions, vary with elongation which may be useful in applications like slow sound propagation. Elongation is observed to modify the equi-frequency contours significantly through reducing the lattice symmetry. The most prominent impact is the transformation of closed contours into open ones, whereas the rest are stretched either along or normal to the elongation axis of the 1st Brillouin Zone. This observation is utilized to implement wide-band all-angle self-collimation and superprism effect, which are demonstrated through Finite-Element computations.

Anisotropy-induced polarization mixture of surface acoustic waves inGaN∕c-sapphire heterostructures

The characteristics of surface acoustic waves (SAWs) in GaN layers grown on $c$-plane sapphire are investigated. Besides Rayleigh mode, Sezawa and Love modes, which are confined in the nitride layers, arise because of the slow sound propagation in GaN compared with the substrate. In addition, pseudo-SAWs leaking into the bulk are observed. The trigonal crystal symmetry of sapphire not only leads to an anisotropic propagation of the SAWs in the heterostructures, despite the isotropic elastic properties in the $c$-plane GaN, but also mixes their polarization even for the propagation along high-crystal-symmetry directions. Love modes, which are normally piezoelectrically inactive, can be excited by interdigital transducers through this polarization mixture. The nonzero value of the elastic coefficient ${c}_{14}$ of sapphire is indicated to be the origin of the coupling of sagittal and shear horizontal displacements.

Eigenvalue tests and distributions for small sample order determination for complex Wishart matrices

This is a theoretical thesis. The goal is to determine how many signal sources exist in the medium when constrained to using only a few samples. The need to make decisions based on only a few samples is motivated by the slow sound propagation speed and the time urgency to make decisions. This research treats the problem from the point of view of classical hypothesis testing assuming complex multivariate Gaussian random variables. This is the small sample complex principal components analysis problem. The critical issue is the derivation of probability density functions of appropriate test statistics. The goal has been partially achieved. The probability density functions for several important distributions have been derived. In particular, these include the distribution for the set of eigenvalues satisfying the generalized eigenvalue problem of two complex Wishart matrices, the matrix complex Gaussian distribution, a joint distribution needed to derive the density for the sphericity test statistic, the density function for the ratio of averages of disjoint sums of sequential eigenvalues of a complex Wishart matrix, and several tests based on the ratio of an arbitrary eigenvalue to the maximum, minimum, average, or sum of all the eigenvalues for a special case of the complex Wishart matrix. This thesis includes a derivation completely in the context of complex variables of the density function of the complex Wishart distribution and the distribution of its eigenvalues. It also includes a few minor results regarding zonal polynomials of complex matrix argument. A comprehensive development of the tools of statistics of complex variables for engineers and physicists is provided. This includes a study of complex matrix derivatives, changes of complex variables, and properties of the characteristic function of a complex multivariate random variable. A derivation of the complex Hotelling's T$\sp2$ test statistic and distribution useful for tests on means is given. A tutorial on Kiefer and Wolfowitz' application of the Lebesgue-Radon-Nikodym theorem for the estimation approach is provided.