Equations For Sound Propagation Research Articles

Phase-preserving narrow- and wide-angle parabolic equations for sound propagation in moving media

Parabolic equations are among the most popular numerical techniques in many fields of physics. This article considers extra-wide-angle parabolic equations, wide-angle parabolic equations, and narrow-angle parabolic equations (EWAPEs, WAPEs, and NAPEs, respectively) for sound propagation in moving inhomogeneous media with arbitrarily large variations in the sound speed and Mach number of the (subsonic) wind speed. Within their ranges of applicability, these parabolic equations exactly describe the phase of the sound waves and are, thus, termed the phase-preserving EWAPE, WAPE, and NAPE. Although variations in the sound speed and Mach number are often relatively small, omitting the second-order terms pertinent to these quantities can result in large cumulative phase errors for long propagation ranges. Therefore, the phase-preserving EWAPE, WAPE, and NAPE can be preferable in applications. Numerical implementation of the latter two equations can be performed with minimal modifications to existing codes and is computationally efficient. Numerical results demonstrate that the phase-preserving WAPE and NAPE provide more accurate results than the WAPE and NAPE based on the effective sound speed approximation.

An Acoustic Simulation Method of the Japanese Vowels /i/ and /u/ by Using the Boundary Element Method

This study aimed to establish and verify the validity of an acoustic simulation method during sustained phonation of the Japanese vowels /i/ and /u/. The study participants were six healthy adults. First, vocal tract models were constructed based on computed tomography (CT) data, such as the range from the frontal sinus to the glottis, during sustained phonation of /i/ and /u/. To imitate the trachea, after being virtually extended by 12 cm, cylindrical shapes were then added to the vocal tract models between the tracheal bifurcation and the lower part of the glottis. Next, the boundary element method and the Kirchhoff–Helmholtz integral equation were used for discretization and to represent the wave equation for sound propagation, respectively. As a result, the relative discrimination thresholds of the vowel formant frequencies for /i/ and /u/ against actual voice were 1.1–10.2% and 0.4–9.3% for the first formant and 3.9–7.5% and 5.0–12.5% for the second formant, respectively. In the vocal tract model with nasal coupling, a pole–zero pair was observed at around 500 Hz, and for both /i/ and /u/, a pole–zero pair was observed at around 1000 Hz regardless of the presence or absence of nasal coupling. Therefore, the boundary element method, which produces solutions by analysis of boundary problems rather than three-dimensional aspects, was thought to be effective for simulating the Japanese vowels /i/ and /u/ with high validity for the vocal tract models encompassing a wide range, from the frontal sinuses to the trachea, constructed from CT data obtained during sustained phonation.

SOUND PROPAGATION THROUGH STRUCTURAL COMPONENTS UNDER CONDITIONS OF NON-RIGID CONTACT AT THE BOUNDARIES BETWEEN THEM

The report considers the problem statement, derivation and solution of the dispersion equation for sound propagation in a layered inhomogeneous medium with oriented fracturing, simulated by the presence of boundary conditions in the "linear slip" approximation. Numerical solutions are obtained and analyzed for the frequency range and values of the parameters of contact breaking, which is relevant in the problems of ultrasonic measurements

Wave and extra-wide-angle parabolic equations for sound propagation in a moving atmosphere.

The narrow-angle parabolic equation (NAPE) with the effective sound speed approximation (ESSA) is widely used for sound and infrasound propagation in a moving medium such as the atmosphere. However, it is valid only for angles less than 20° with respect to the nominal propagation direction. In this paper, the wave equation and extra-wide-angle parabolic equation (EWAPE) for high-frequency (short-wavelength) sound waves in a moving medium with arbitrary Mach numbers are derived without the ESSA. For relatively smooth variations in the medium velocity, the EWAPE is valid for propagation angles up to 90°. Using the Padé (n,n) series expansion and narrow-angle approximation, the EWAPE is reduced to the wide-angle parabolic equation (WAPE) and NAPE. Versions of these equations are then formulated for low Mach numbers, which is the case that is usually considered in the literature. The phase errors pertinent to the equations considered are studied. It is shown that the equations for low Mach numbers and the WAPE with the ESSA are applicable only under rather restrictive conditions on the medium velocity. An effective numerical implementation of the WAPE for arbitrary Mach numbers in the Padé (1,1) approximation is developed and applied to sound propagation in the atmosphere.

ACOUSTICS OF PLANE WAVES IN WIND TUNNEL NOZZLES

The problem of propagating plane waves in a subsonic wind tunnel nozzle is considered. The contour of the nozzle is formed by the Witoszynski formula. In the case in which the gas is at rest, a conformal transformation is used to solve the wave equation that leads the system to a cylindrical geometry. This allows using the results of sound emission from a semi-infinite tube to determine the reflection coefficient from the nozzle edge. It is shown that in the conformal coordinates the equations are similar to the equation of sound propagation in thin tubes. In this case, the solutions to both equations give close results. In view of this, the problem is solved within the framework of the thin tube equation. Numerical results show that there are no resonances in the wind tunnel nozzle.

Using the Sonification for Hardly Detectable Details in Medical Images

The inverse sonification problem is investigated in this article in order to detect hardly capturing details in a medical image. The direct problem consists in converting the image data into sound signals by a transformation which involves three steps - data, acoustics parameters and sound representations. The inverse problem is reversing back the sound signals into image data. By using the known sonification operator, the inverse approach does not bring any gain in the sonified medical imaging. The replication of the image already known does not help the diagnosis and surgical operation. In order to bring gains in the medical imaging, a new sonification operator is advanced in this paper, by using the Burgers equation of sound propagation. The sonified medical imaging is useful in interpreting the medical imaging that, however powerful they may be, are never good enough to aid tumour surgery. The inverse approach is exercised on several medical images used to surgical operations.

On the sonification technique

An introduction of the sonification theory and its applications to the medical imaging is presented in this paper. The sonification theory is known in the literature as the transformation of the image into sound by means of a linear operator based on the linear theory of sound propagation. By reversing back to image, an inverse problem has to be solved in order to find if the sound discovers or not new details in the original image. When the classical sonification operator is applied in the inverse problem, no image enhancement is achieved and no details are discovered. This is probably because the classical operator is based on the linear theory of sound propagation. In this paper a new sonification algorithm is advanced based on the Burgers equation of sound propagation. The new algorithm is able to bring improvements in the medical image by inversion. It earns gains in improvement of the medical image by capturing hardly detectable details in the unclear original images. The approach is exercised on fictive ultrasound images of human and rat livers.

Measuring the Impulse Response of an Acoustic MLS Signal in a Moving Medium

The paper presents the results of an experiment that uses the MLS technique to measure the impulse response when a signal passes through an air jet. The data are compared with the numerical simulation results obtained by solving the equation for sound propagation in a steady flow using a finite-difference method. It is shown that the longitudinal component of the flow causes drift and focusing of the signal.

Guided wave propagation in cylindrical ducts with elastic walls enclosing a fluid moving with a uniform velocity

Theoretical models for elastic wave propagation in fluid filled ducts normally neglects mean fluid flow. However, in many engineering applications the velocity of the fluid may influence the modal characteristics of the duct, for example in gas pipelines, turbomachinery applications and ventilation systems. Accordingly, the influence of a mean uniform fluid flow on acoustically driven duct wall vibration is analysed here for a cylindrical geometry. The semi-analytic finite element method is used to couple the elastodynamic wave equation for the duct wall to the convected wave equation for sound propagation in a uniform fluid flow. A one dimensional finite element approach is described and this is used to find the coupled eigenmodes for the duct. Under certain conditions, a uniform mean flow is seen to significantly affect the phase speed for different eigenmodes, and it is shown that this may cause energy to transfer from the fluid to the surrounding wall at frequencies much lower than those seen without mean flow. This behaviour has the potential to increase sound radiation from ducts at lower frequencies when mean flow is present.

Acoustic radiation of rotating and non-rotating finite length cylinders

In this paper, a semi-analytical solution is presented for the problem of modal acoustic radiation efficiency of a finite-length rotating cylinder. The cylinder is immersed in an irrotational inviscid compressible fluid. Assuming the cylinder to vibrate sinusoidally in transverse direction and rotate at constant angular velocity, the scalar equation of sound propagation is decomposed into a coupled set of time independent equations. Using Galerkin method and employing spherical eigen-functions as a complete set of solution, modal acoustic pressure and acoustic radiation efficiency of the cylinder are calculated. Numerical solutions are presented to discuss modal radiation efficiency corresponding to forward and backward circumferential waves.

Time-domain propagation in porous media using the auxiliary differential equation method: Application for outdoor acoustics

Time-domain sound propagation equations in porous media usually involve convolutions, which can be computationally cumbersome. Indeed, a naïve approach would require to store the acoustic variables at every time-step, which would lead to an unacceptable memory space for long range propagation. To reduce the computational burden associated to convolutions, an efficient numerical method, referred to as the auxiliary differential equation (ADE) method, originated from the computational electromagnetic community and presented in Dragna et al. [J. Acoust. Soc. Am. 138, 1030–1042 (2015)] is proposed. The idea behind is to approximate the relaxation functions, which depend on the porous media properties, by rational functions in the frequency-domain. The time variation of the convolution is thus given by first-order differential equations which can be solved using standard time-marching schemes. The accuracy of the method is investigated and compared to that of recursive convolution methods. The ADE method is then applied for outdoor sound propagation using the time-domain rigid-frame model proposed by Wilson et al. [Appl. Acoust. 68, 173–200 (2007)] in the ground. Results obtained with Wilson's model are compared at long range to those obtained with Zwikker and Kosten's equations and with an equivalent impedance surface for different flow resistivities.

Coupled Modeling of Hydrodynamics and Sound in Coastal Ocean for Renewable Ocean Energy Development

AbstractThe rapid growth of renewable offshore energy development has raised concerns that underwater noise from construction and operation of offshore devices may interfere with communication of marine animals. An underwater sound model was developed to simulate sound propagation from marine and hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite difference methods were developed to solve the 3-D Helmholtz equation for sound propagation in the coastal environment. A 3-D sparse matrix solver with complex coefficients was formed for solving the resulting acoustic pressure field. The complex shifted Laplacian preconditioner (CSLP) method was applied to solve the matrix system iteratively with Message Passing Interface (MPI) parallelization using a high-performance cluster. The sound model was then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities, such as construction of OSW turbines or tidal stream turbine operations, in a range-dependent setting. As a proof of concept, the validation of the solver is tested with an ideal case against two other methods, and its application is then presented for two coastal wedge problems. This sound model can be useful for evaluating impacts on marine mammals due to deployment of MHK devices and OSW energy platforms.

Modeling of sound in coastal oceans with a finite volume method

In this research, the finite volume method is employed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. The grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3D sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The recent CSLP and ADEF1 preconditioning methods are applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. This model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound generated by offshore wind energy platform constructions in a range-dependent setting. Details of the development and initial validation will be presented. Keywords: Sound, Coastal Ocean, Finite Volume, Offshore Wind, Coupling, CSLP, ADEF1, Helmholtz equation.

A generalized recursive convolution method for time-domain propagation in porous media.

An efficient numerical method, referred to as the auxiliary differential equation (ADE) method, is proposed to compute convolutions between relaxation functions and acoustic variables arising in sound propagation equations in porous media. For this purpose, the relaxation functions are approximated in the frequency domain by rational functions. The time variation of the convolution is thus governed by first-order differential equations which can be straightforwardly solved. The accuracy of the method is first investigated and compared to that of recursive convolution methods. It is shown that, while recursive convolution methods are first or second-order accurate in time, the ADE method does not introduce any additional error. The ADE method is then applied for outdoor sound propagation using the equations proposed by Wilson et al. in the ground [(2007). Appl. Acoust. 68, 173-200]. A first one-dimensional case is performed showing that only five poles are necessary to accurately approximate the relaxation functions for typical applications. Finally, the ADE method is used to compute sound propagation in a three-dimensional geometry over an absorbing ground. Results obtained with Wilson's equations are compared to those obtained with Zwikker and Kosten's equations and with an impedance surface for different flow resistivities.

Efficient Outdoor Sound Propagation Modeling with the Finite-Difference Time-Domain (FDTD) Method: A Review

The finite-difference time-domain (FDTD) method, solving the inhomogeneous, moving medium sound propagation equations, also referred to as the Linearized Euler(ian) Equations (LEE), has become a mature reference outdoor sound propagation model during the last two decades. It combines the ability to account for complex wave effects like reflection, scattering and diffraction near arbitrary objects, and complex medium effects like convection, refraction and (turbulent) scattering. In addition, it has the general advantages of a time-domain method. It is indicated that the numerical discretisation scheme should be chosen depending on the flow speed of the background medium. Perfectly matched layers, applicable to cases in presence of (non-)uniform flow, are state-of-the-art perfectly absorbing boundary conditions that are key in outdoor sound propagation applications, where only a small part of the unbounded atmosphere can be numerically described. Various ways to include outdoor soils are summarized, like time-domain impedance plane boundary conditions and explicitly including the upper part of the soil in the simulation domain. Approaches for long-distance sound propagation, including moving calculation frames and hybrid modeling are discussed. This review deals with linear sound propagation only.

NONLINEAR PROPAGATION OF SOUND EMITTED BY HIGH SPEED WAVE PACKETS

Jet's sound-field emitted by a large scale source modeled as a wave packet is considered. Attention is given to nonlinear propagation effects caused by the source's supersonic Mach number and high amplitude. The approach of the Westervelt equation is adapted to derive a new set of weakly nonlinear sound propagation equations. An optimized Lax–Wendorff scheme is proposed for the newly derived equations. It is shown that these equations can be simulated using a time step close to the CFL limit even for high amplitudes unlike the conventional finite-difference simulation approach of the Westervelt equation. Two- and three-dimensional sound propagations were simulated for symmetric and asymmetric supersonic wave packets. It is seen that nonlinearity in the sound field is affected by the wave packet form, an effect that cannot be captured by a 1D propagation equation. High skewness in the pressure fluctuation and its time derivative were found near the Mach direction, showing crackle-like features. Pressure time history and frequency spectra are also investigated.

Determination of elastic, piezoelectric, and dielectric constants of an R:BaTiO3 single crystal by Brillouin scattering

From the sound velocity measured using the Brillouin scattering technique, the elastic, piezoelectric, and dielectric constants of a high-quality monodomain tetragonal Rh:BaTiO3 single crystal are determined at room temperature. The elastic constants are in fairly good agreement with those of the BaTiO3 single crystal, measured previously by Brillouin scattering and the low-frequency equivalent circuit methods. However, their electromechanical properties are significantly different. Based on the sound propagation equations and these results, the directional dependence of the compressional modulus and the shear modulus of Rh:BaTiO3 in the (010) plane is investigated. Some properties of sound propagation and electromechanical coupling in the crystal are discussed.

The study of sono-elasticity of floating bodies in the acoustical environment of shallow sea

A concept combining sono-elasticity research field with oceanic sound propagation research field in developed in this paper. The paper formulates in details about how to transfer the sono-elasticity dynamic equations together with oceanic sound propagation equations in theoretical model into related numerical program by using the PEKERIS neritic acoustic environment as an example. The further verification of this approach and related computing program, and analyses on characteristics of the structural vibration and acoustic radiation in neritic acoustic environment are also provided in the paper by analyzing the problem of a elastic spherical shell as an example. Keywords:Sono-elasticity; Sound propagation; Shallow sea; Spherical shell.

Finite Element Solutions of a Wave Equation for Sound Propagation in Sheared Flows

Aweakdiscretization in the frequency domain of theLilley–Goldstein acoustic analogy equation is presented. This equation is cast into a linear system of two equations that are successively arranged in a convenient form for a Galerkin projection. The method is applied to compute the sound generated by Dirac ring sources of different azimuthal order and radius and propagated through an axisymmetric parallel jet. The effects due to the jet temperature and velocity profile combined with the effects due to the source frequency, radius, and azimuthal order are illustrated through extensive parametric results. It is shown that three-dimensional Green’s functions can be reconstructed by superposition of few axisymmetric solutions of low azimuthal order when the sources are located inside the jet. Finally, tones from annular sources located in the potential core of amixing jet are propagated through the jet shear layer and compared with the tones computed in uniform flow conditions. It is shown that, for conditions that are representative of a propeller rig located in the potential core of a wind-tunnel jet, the shear-layer refraction effects can be corrected by using a thin-layer approximation.

Brillouin scattering study on elastic and piezoelectric properties of laser irradiated ZnO single crystals

Brillouin light scattering technique can be successfully used to determine the whole set of elastic and piezoelectric constants of a ZnO single crystal irradiated by different laser energy densities, into a micron range (radiation layer thickness). It is found that the scattering intensity, the linewidth and the Brillouin scattering shift of acoustic phonons are all strongly dependent on laser energy density. Based on the sound propagation equations and these results, the directional dependences of the compressional and shear moduli of the irradiated ZnO sample in the (001) plane are investigated. It is found that under an appropriate laser condition, 248 nm KrF excimer laser irradiation can significantly improve the surface quality and increase the elastic properties of ZnO single crystal. This procedure has potential applications in the fabrication of ZnO-based surface acoustic wave and optic-electronic devices.