A Simple Calculation Approach for the Second－Harmonic Sound Beam Generated by an Arbitrary Distribution Source

We present a simple calculation approach for the fundamental and second-harmonic sound beams with an arbitrary distribution source in the quasilinear approximation. The analysis is based on the assumption that the source function with an arbitrary geometry and distribution is expanded into the sum of a set of two-dimensional Gaussian functions. The two- and five-dimensional integral solutions for the fundamental and second-harmonic fields are, respectively, reduced in terms of Gaussian functions and simple one-dimensional integrals. The numerical evaluation of field distributions is then greatly simplified.     

Recovery of the free field in noisy environment by using the spherical wave superposition method

To remove the scattering effect of the disturbing sound on the target source when implementing nearfield acoustic holography in a non-free field, a free field recovery technique based on the spherical wave superposition method is proposed. In the method, the sound field separation technique based on the spherical wave superposition method is first used to separate the incoming and outgoing fields, and a further step for separating the radiated and scattered fields is performed by utilizing the surface admittance of the target source as the boundary condition. The technique makes it possible to correctly identify noise sources in a non-free sound field. The basic principle of the technique is described firstly, a method for choosing the optimal number of spherical wave expansion terms is given, and two numerical simulations are used to demonstrate the validity of this technique. It is shown that, for the lower frequency, the scattering effect can be neglected, and the radiated field of the target source can be obtained by the sound field separation technique, however, as the increasing of the frequency, the scattering effect cannot be neglected, and the free field recovery technique has to be used to obtain the radiated field of the target source.     

Axial distribution of Gaussian beam limited by a hard-edged aperture

In this letter, the axial distribution of Gaussian beam limited by a hard-edged aperture is studied. We theoretically analyze the axial diffraction of Gaussian beam limited by a hard-edged aperture, and give the simpler formulas of the axial diffraction intensities of Gaussian beam in Fresnel diffraction field and Fraun-hofer diffraction field. The corresponding numerical calculation of axial diffraction intensity distribution of Gaussian beam with different wave waist is provided and the evolution of the diffraction distribution with the wave waist of Gaussian beam is explained. As the especial cases of the truncated Gaussian beam, the Gaussian beam in free space and the parallel light limited by the aperture are discussed too, and the system parameters of the truncated Gaussian beam which can cause it to equal to these cases are given. The theoretical results conform to the numerical analysis.     

A Novel Algorithm for the Sound Field of Elliptically Shaped Transducers

An alternative extension to the Gaussian-beam expansion technique is presented for efficient computation of the Fresnel field integral for elliptically symmetric sources. With a known result that the circ function is approximately decomposed into a sum of Gaussian functions, the cosine function is similarly expanded by the Bessel-Fourier transform. Two expansions are together inserted into this integral, it is then expressible in terms of the simple algebraic functions. The numerical examples for the elliptical and uniform piston transducers are presented, in good agreement with the results given by other methods. The approach is applicable to treat the field radiation problem for a large and important group of piston sources in acoustics.     

Calculation of three-dimensional acoustic scattering from Gaussian rough under-ice surface using the Kirchhoff approximation method with modified reflection coefficient

The Kirchhoff approximation with a modified reflection coefficient is used to calculate the three-dimensional acoustic scattering of a Gaussian rough under-ice surface.The concept of a local statistical average reflection coefficient of an under-ice surface is proposed in the calculation model.The scattered sound field of a two-dimensional Gaussian rough under-ice surface is divided into coherent scattering and incoherent scattering.A formula is derived for the scattering coefficient of each scattering component,and the three-dimensional scattering intensity is obtained.The relationships between the scattering intensity and(ⅰ) the root-meansquare height of the Gaussian rough under-ice surface,(ⅱ) the angle of incidence,and(ⅲ) the sound frequency are analyzed.The scattering intensity of a Gaussian rough under-ice surface is measured in a laboratory water tank,and the calculation results of the theoretical model are verified.The experimental results are compared with those of the theoretical model using(ⅰ) the present local statistical average reflection coefficient of an under-ice surface and(ⅱ) the mirror reflection coefficient of an under-ice surface from the literature.The calculation results of the model using the local statistical average reflection coefficient agree well with the experimental results.     

Sound field separation technique with double holographic planes and its applications in acoustic holography

Sound field separation technique with double holographic planes is proposed, which overcomes the limitation on applications of near-field acoustic holography (NAH) and broadband acoustic holography from intensity measurement (BAHIM). The limitation is that sound field on one side of holographic plane must be free, that is to say, all the sound sources must be confined to the other side; but it is not easy to achieve for industrial measurements. The technique builds the sound field separation formula in wave number domain according to the wave field extrapolation theorem, and the sound pressure caused by sources on one side of holographic plane can be obtained as expected by taking two-dimensional Fourier transform of the formula. The derivation of the principle verifies the technique theoretically. The numerical simulations demonstrate its feasibility and effectiveness.     

A Fast Field Scheme for the Parametric Sound Radiation from Rectangular Aperture Source

A virtual complex source approach has been developed to calculate numerically the ultrasound field generated by a rectangular planar source with high efficiency. The sound field can be treated as the resultant sound pressure from a set of complex virtual sources located at a complex distance, and then by exploiting the integrability of Gaussian function, a substantial analytical reduction to single integral is derived for the second-order field of the sum-, difference-frequency and second harmonic components. The validity of this fast field scheme is confirmed by comparison of numerical results and the experimental data published previously.     

Linear superposition solutions to nonlinear wave equations

The solutions to a linear wave equation can satisfy the principle of superposition,i.e.,the linear superposition of two or more known solutions is still a solution of the linear wave equation.We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic,triangle,and exponential functions,and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics.The linear superposition solutions to the generalized KdV equation K(2,2,1),the Oliver water wave equation,and the k(n,n) equation are given.The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed,and the reason why the solutions with the forms of hyperbolic,triangle,and exponential functions can form the linear superposition solutions is also discussed.     

Reconstruction and prediction of coherent acoustic field with the combined wave superposition approach

The routine wave superposition approach cannot be used in reconstruction and prediction of a coherent acoustic field, because it is impossible to separate the pressures generated by individual sources. According to the superposition theory of the coherent acoustic field , a novel method based on the combined wave superposition approach is developed to reconstruct and predict the coherent acoustic field by building the combined pressure matching matrixes between the hologram surfaces and the sources. The method can reconstruct the acoustic information on surfaces of the individual sources, and it is possible to predict the acoustic field radiated from every source and the total coherent acoustic field can also be calculated spontaneously. The experimental and numerical simulation results show that this method can effectively solve the holographic reconstruction and prediction of the coherent acoustic field and it can also be used as a coherent acoustic field separation technique. The study on this novel method extends the application scope of the acoustic holography technique.     

Theory of sound field in a room—re-examination

The theory of steady-state sound field in a room is re-examined. It is shown that the normal-mode solution of the wave equation is not the exact solution, and the derivation is incorrect... The exact solution of the wave equation in a reflective room should contain both the free space solution (direct sound field) and the standing wave solution (reverberant sound field), the latter is formed by all the reflected waves to a group of allowed wave types (the normal modes of vibration ).     

A Simple and Accurate Method for Calculating the Gaussian Beam Expansion Coefficients

The calculation of the diffraction field radiated from the ultrasonic transducer can be simplified by using the Gaussian beam expansion technique. The key problem of this technique is how to determine the coefficients of Gaussian functions. We present a simple and accurate optimization method to calculate the Gaussian beam expansion coefficients, Half of the coefficients are obtained by solving linear equations. The other half are derived from the Fourier series expansion. Wave field simulation results demonstrate the validity of the new method.     

Fluctuations of optical phase of diffracted light for Raman–Nath diffraction in acousto–optic effect

The Raman–Nath diffraction in acousto–optic effect was studied theoretically and experimentally in the paper.Up to now,each order of diffracted light in Raman–Nath diffraction was still considered simply to be just frequency-shifted and to be a plane wave.However,we find that the phase and frequency shifts occur simultaneously and individually in Raman–Nath diffraction.The findings demonstrate that,in addition to the frequency shift,the optical phase of each order of diffracted light is also shifted by the sound wave and fluctuates with the sound wave and is related to the location in the acoustic field from which the diffracted light originates.As a result,the wavefront of each order of diffracted light is modulated to fluctuate spatially and temporally with the sound wave.Obviously,these findings are significant for applications of Raman–Nath diffraction in acousto–optic effect because the optical phase plays an important role in optical coherence technology.     

Research and experiments of mutual radiation impedance effect on array directivity

The mutual radiation impedance ignored in conventional array directivity formula is introduced into the calculation of array radiation sound field,and a modified array directivity formula considering the mutual radiation impedance is gained according to the superposition principle.Results of computer simulation and experiments for a uniform linear array and a uniform planar array show superior performance on the present of the practical directivity pattern of the modified formula in this paper in comparison to the conventional one.     

A three-dimensional sound ray tracing method by deploying regular tetrahedrons

A sound ray tracing algorithm is presented, which helps to rapidly find the sound ray trajectories in three-dimensional (3-D) space. At each step of ray tracing, a small regular tetrahedron is made in front of a ray, so that the sound speed field inside may be approximately regarded as linear. Since a ray trajectory in the linear sound speed field is always on a plane, it may be obtained by the two-dimensional (2-D) sound ray tracing method by deploying triangles. The theoretical derivation is given and a numerical model is discussed. It shows that the algorithm is fast and precise. It is also more concise and reliable than the traditional 3-D algorithms, and may be used to avoid the damage to the precision by the acoustic refraction in the 3-D ultrasound computerized tomography.     

Patch nearfield acoustic holography combined with sound field separation technique applied to a non-free field

The conventional nearfield acoustic holography(NAH) is usually based on the assumption of free-field conditions, and it also requires that the measurement aperture should be larger than the actual source. This paper is to focus on the problem that neither of the above-mentioned requirements can be met, and to examine the feasibility of reconstructing the sound field radiated by partial source, based on double-layer pressure measurements made in a non-free field by using patch NAH combined with sound field separation technique. And also, the sensitivity of the reconstructed result to the measurement error is analyzed in detail. Two experiments involving two speakers in an exterior space and one speaker inside a car cabin are presented. The experimental results demonstrate that the patch NAH based on single-layer pressure measurement cannot obtain a satisfied result due to the influences of disturbing sources and reflections, while the patch NAH based on double-layer pressure measurements can successfully remove these influences and reconstruct the patch sound field effectively.     

Simulation research on effect of magnetic nanoparticles on physical process of magneto–acoustic tomography with magnetic induction

Magneto–acoustic tomography with magnetic induction(MAT-MI) is a multiphysics coupled imaging technique that is combined with electrical impedance tomography and ultrasound imaging. In order to study the influence of adding magnetic nanoparticles as a contrast agent for MAT-MI on its physical process, firstly, we analyze and compare the electromagnetic and acoustical properties of MAT-MI theoretically before and after adding magnetic nanoparticles, and then construct a two-dimensional(2 D) planar model. Under the guidance of space-time separation theory, we determine the reasonable simulation conditions and solve the electromagnetic field and sound field physical processes in the two modes by using the finite element method. The magnetic flux density, sound pressure distribution, and related one-dimensional(1 D), 2 D, and three-dimensional(3 D) images are obtained. Finally, we make a qualitative and quantitative analysis based on the theoretical and simulation results. The research results show that the peak time of the time item separated from the sound source has a corresponding relationship with the peak time of the sound pressure signal. At this moment, MAMPTMI produces larger sound pressure signals, and the sound pressure distribution of the MAMPT-MI is more uniform, which facilitates the detection and completion of sound source reconstruction. The research results may lay the foundation for the MAT-MI of magnetically responsive nanoparticle in subsequent experiments and even clinical applications.     

Visual-Width of an Ultrasonic Gaussian Beam on the Schlieren Photograph and Explanation to the Nonspecularly Reflected Sound Field

On the Schlieren photograph,a continuous ultrasonic Gaussian beam and its nonspecularly reflected beams [Chin.Phys.Lett.16 (1999)819] always have limited visual-width,although the theoretical spatial distribution of the sound field is a continuous function.To study this problem,the first step is to investigate the visual-width of the beam on the photograph related to the sound pressure at the centre of the beam by the threshold of the optical system caused by the refraction of light;the second step is to explain the visual-width of nonspecularly reflected field.By applying a relevant threshold,checked by the visual width of the incident beam,to cut the theoretical curves of the reflected sound field,one can find the visual-width of the two reflected beams and the gap between them correspond to that on the Schlieren photograph.     

A numerical study of sound field radiated by the flow around a circular cylinder

The Von-Karman vortex street flow behind a circular cylinder issuccessfully solved at R_e=100 for incompressible N-S equations in theform of stream function and vorticity.The method adopted here involvesADI-BGE schemes,a recent treatment of body boundary conditions anda new acceptable perturbation model.The solutions of the flow fieldobtained here are better than previous numerical ones and agree with theexperimental data closer.Therefore,it can be used to study sound fieldnumerically.The Curle equation is directly and numerically solved to ana-lyze the distribution of sound sources and the characteristics of their radi-ated sound field at R_e=100 and to compare with the solution fromthe theory of vortex sound.It is shown that this method is successful.     

Singularities of noncompact charged objects

We formulate a model of noncompact spherical charged objects in the framework of noncommutative field theory. The Einstein-Maxwell field equations are solved with charged anisotropic fluid. We choose matter and charge densities as functions of two parameters instead of defining these quantities in terms of Gaussian distribution function. It is found that the corresponding densities and the Ricci scalar are singular at origin, whereas the metric is nonsingular, indicating a spacelike singularity. The numerical solution of the horizon equation implies that there are two or one or no horizon(s) depending on the mass. We also evaluate the Hawking temperature, and find that a black hole with two horizons is evaporated to an extremal black hole with one horizon.