Theory of sound field in a room

In the normal-mode theory of Morse, it gives a series of normal modes as the solution of forced vibration in a room. But actually there is always the direct radiation besides the normal modes which represent the reverbrant sound field only. The reason is that the normal modes were assumed only in the source, and naturally normal modes only are obtained in the solution. A theory of double source is proposed, that the sound source is both the source of the direct radiation as if in free space before the boundary surfaces were reached by the direct radiation, and after the first reflection from the boundary surfaces, the source of the reflected wavelets, randomly distributed both in space an in time on the boundary surfaces that build up the normal modes after further reflections. The wave equation is formed accordingly, and the solution of the wave equation, the sound field in a room, contains explicitly both the direct radiation and the reverberant sound formed of normal modes. The approximate mean square sound pressure is found to be the dircet sound determined by the sound power of the source,and reverberant sound determined by the sound power reduced by a factor of π/2, different slightly from the result obtained from energy consideration, if the source is pure tone. There is essentially no difference for a source of band noise.     

Steady-state sound field in enclosures

The classical normal-mode theory expresses the steady-state soundfield in an enclosure produced by a sound source as a series of normal modes ofvibration.Experimental facts are not often explained by this theory,and it wasconjectured that the normal-mode expression is not the complete solution ofthe wave equation in the enclosure,but only the reverberant part of it,and thereshould be an additional term representing the direct spherical radiation to makethe solution complete.The problem is examined by critically reviewing the de-rivation of the normal-mode expression,and by theoretical analysis of thesteady-state sound field in the room and experimental measurements therein.The conjecture is thus confirmed,and it is definitely shown that the sound fieldshould contain the direct wave as well as the standing waves(normal modes)formed by the confinement of the boundary surfaces.Relevant mathematicalexpressions are derived.     

POWER EMISSION OF A MONOPOLE IN REVERBERATION CHAMBERS

An exact sound power emission formula of a simple source in a reverberation chamber is derived fromnormal mode theory as a function of its position in the room,and important properties of the emission arefound from simple analyses.For example,the average emission of the source in the room is not equal to thefree space emission but greater,on the contrary to the common notion.A smooth statistical formula is alsoderived for the variation of average sound power in an axial direction,which holds even at low frequency atwhich the wave length approaches the mean free path in the room.The sound power is found to havenumerous peaks in the room forming a three-dimensional lattice structure with high power barriers aroundthe boundary walls.The space factor in an axial direction is essentially exact,but the general formula of poweremission formed with the product of space factors in three axial directions might have some error.Numericalexamples are presented to check this.The variability of sound power emission in     

An Approach for Solving Short-Wave Models for Camassa-Holm Equation and Degasperis-Procesi Equation

In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived. We investigate the short wave model for the Camassa-Holm equation and the Degasperis-Procesi equation respectively. One-cusp soliton solution of the Camassa-Flolm equation is obtained. One-loop soliton solution of the Degasperis- Procesi equation is also obtained, the approximation of which in a closed form can be obtained firstly by the Adomian decomposition method. The obtained results in a parametric form coincide perfectly with those given in the present reference. This illustrates the efficiency and reliability of our approach.     

Solitonic Information Transmission in General Relativity

An exact solution of the vacuum Einstein＇s field equations is presented, in which there exists a congruence of null geodesics whose shear behaves like a travelling wave of the KdV equation. On the basis of this exact solution, the feasibility of solitonic information transmission by exploiting the nonlinearity intrinsic to the Einstein field equations is discussed.     

Gravitational Wave in Lorentz Violating Gravity

By making use of the weak gravitational field approximation, we obtain a linearized solution of the gravitational vacuum field equation in an anisotropic spacetime. The plane-wave solution and dispersion relation of gravitationaJ wave is presented explicitly. There is possibility that the speed of gravitational wave is larger than the speed of light and the easuality still holds. We show that the energy-momentum of gravitational wave in the ansiotropic spacetime is still well defined and conserved.     

Charged Particle Motion in Temporal Chaotic and Spatiotemporal Chaotic Fields

We investigate charged particle motion in temporal chaotic and spatiotemporal chaotic fields.In its steady wave frame a few key modes of the solution of the driven/damped nonlinear wave equation are used as the field.It is found that in the spatiotemporal chaotic field the particle drifts relative to the steady wave,in contrast to that in the temporal chaotic field where the particle motion is localized in a trough of the wave field.The result is of significance for understanding stochastic acceleration of particles.     

Study on an extended Boussinesq equation

An extended Boussinesq equation that models weakly nonlinear and weakly dispersive waves on a uniform layer of water is studied in this paper. The results show that the equation is not Painlev\'e-integrable in general. Some particular exact travelling wave solutions are obtained by using a function expansion method. An approximate solitary wave solution with physical significance is obtained by using a perturbation method. We find that the extended Boussinesq equation with a depth parameter of $1/\sqrt 2$ is able to match the Laitone's (1960) second order solitary wave solution of the Euler equations.     

Sensitivity correction of co-vibrating vector hydrophone in standing wave tube by numerical calculation

When the sensitivity of a large-size vector hydrophone is calibrated in a standing wave tube, the distribution of the calibration sound field will be uneven, resulting in a large error in the calibration results. In the case that the accurate analytical expression of the calibration sound field cannot be obtained, the sound field simulation analysis model is established based on the actual standing wave tube calibration device. The sound pressure and acceleration values of vector hydrophone and ...     

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.     

Supersonic Shock Wave with Landau Quantization in a Relativistic Degenerate Plasma

A three-dimensional(3D)BurgersJ equation adopting perturbative methodology is derived to study the evolution of a shock wave with Landau quantized magnetic field in relativistic quantum plasma.The characteristics of a shock wave in such a plasma under the influence of magnetic quantization,relativistic parameter and degenerate electron density are studied with assistance of steady state solution.The magnetic field has a noteworthy control,especially on the shock wave's amplitude in the lower range of the electron density,whereas the amplitude in the higher range of the electron density reduces remarkably.The rate of increase of shock wave potential is much higher(lower)with a magnetic Held in the lower(higher)range of electron density.With the relativistic factor,the shock wave's amplitude increases significantly and the rate of increase is higher(lower)for lower(higher)electron density.The combined effect of the increase of relativistic factor and the magnetic field on the strength of the shock wave,results in the highest value of the wave potential in the lower range of the degenerate electron density.     

SCATTERING NEAR FIELD OF A RECTANGULAR COMPOSITE PLATE IMMERSED IN WATER

According to the extensive theory of flexural vibration of elastic-viscoelastic composite platesystem in a previous paper,the vibration and scattering sound near field of an immersed rectangularelastic-viscoelastic composite plate in an underwater sound are studied.The solution for deflectionof the composite plate is expanded into a series in terms of normal mode,whatever plate is vibratingin water under the influence of incident sound wave.The interaction between normal modes owingto sound field coupling is taken into consideration.As a function of(kl_1,r;m,n;p,q),the couplingcoefficients between(m,n);(p,q)modes of vibration are calculated numerically.Whith these coef-ficients,the vibration of composite plate and the sound irradiation from which may be characterized(where k is wave number,l_1,is length of one parallel edges,r=1_2/l_1 is parametric variable,l_2 is lengthof another parallel edges).And then,the complex values of amplitude of normal modes for flexuralmotion of a Steel-Rubber bilaminar plate     

Influence of Intrinsic Decoherence on Nonclassical Effects of System of a Three-Level Atom in Ξ Configuration

With the help of an SU(3) dynamical algebraic structure, we find an exact solution of the Milburn equation for the system of a three-level atom in the Ξ configuration interacting with one quantized field mode with arbitrary detuning. The exact solution is then used to discuss the influence of the intrinsic decoherence on the nonclassical properties of the system, such as collapes and revivals of the atomic populations, oscillations of the photon number distribution, and squeezing of the radiation field.     

Improved Speed and Shape of Ion-Acoustic Waves in a Warm Plasma

The basic set of fluid equations can be reduced to the nonlinear Kortewege-de Vries(KdV)and nonlinear Schro¨dinger(NLS)equations.The rational solutions for the two equations has been obtained.The exact amplitude of the nonlinear ion-acoustic solitary wave can be obtained directly without resorting to any successive approximation techniques by a direct analysis of the given field equations.The Sagdeev’s potential is obtained in terms of ion acoustic velocity by simply solving an algebraic equation.The soliton and double layer solutions are obtained as a small amplitude approximation.A comparison between the exact soliton solution and that obtained from the reductive perturbation theory are also discussed.     

Small amplitude approximation and stabilities for dislocation motion in a superlattice

Starting from the traveling wave solution, in small amplitude approximation, the Sine-Gordon equation can be re- duced to a generalized Duffing equation to describe the dislocation motion in a superlattice, and the phase plane properties of the system phase plane are described in the absence of an applied field. The stabilities are also discussed in the presence of an applied field. It is pointed out that the separatrix orbit describing the dislocation motion as the kink wave may transfer the energy along the dislocation line, keep its form unchanged, and reveal the soliton wave properties of the dislocation motion. It is stressed that the dislocation motion process is the energy transfer and release process, and the system is stable when its energy is minimum.     

Prediction of underwater target strength

1 IntroductionTarget Strength of underwater objects is an importallt parameter of the sonar equations.A method for the calculation of target strength using Lighthill's acoustic analogy approach ispresellted. Farassat's solution to the FW-H equation for the calculation of discrete noise ofsubsonic propeller in the free field is used. For a rigid bodys the suxface sound pressure inducedby incident sound wave could be obtained by united aerodynamics and aeroacoustics approach,which have been su…     

REFLECTION AND REFRACTION OF PLANE SOUND WAVES IN MOVING STRATIFIED MEDIA

This paper deals with the fundamental problems concerning the propagation of plane soundwaves in moving stratified media.Starting from the wave equation in moving media,we haveaccomplished a systematic study of reflection and refraction of the waves at the interface between twomoving homogeneous media under the assumption that the Mach numbers of the motion are smallcompared with unity.The coefficients of reflection and transmission as well as the equation for thetotal reflection cone are obtained. Similar treatment is extended to a slowly varying stratified moving medium,and the W.K.B.solu-tion and the successive modifications to the sound field are worked out.Following the approachdeveloped by Gans,we have investigated the field within the total reflection zone where the geometricalacoustics is no longer valid,and obtained an appropriate solution which can be connected with thegeometrical acoustics solution at the boundaries of that zone.     

Travelling Wave Solutions for Konopelchenko-Dubrovsky Equation Using an Extended sinh-Gordon Equation Expansion Method

The sinh-Gordon equation expansion method is further extended by generMizing the sinh-Gordon equation and constructing new ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Konopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtained including solitary wave solutions, trigonometric function solutions and Jacobi elliptic doubly periodic function solutions, some of which are new exact solutions that we have never seen before within our knowledge. The method can be applied to other nonlinear evolution equations in mathematical physics.