Sound decay in a rectangular room with impedance walls

The problem of sound decay in a rectangular room is considered for the case of a room with walls the acoustic properties of which are described by the impedance, which implies a dependence of the absorption coefficient on the angle of incidence of sound waves. The ray approximation is used to determine the sound decay laws for different distributions of wall absorption. It is shown that, in a room with impedance walls, the sound decay is slower than in the conventional reverberation model, in which the wall absorption coefficient is independent of the angle of incidence. The problem is also solved in the wave approximation to determine the decay law for a preset frequency band.     

Computer models in room acoustics: The ray tracing method and the auralization algorithms

Computer algorithms are described for constructing virtual acoustic models of various rooms that should satisfy some specific sound quality criteria. The algorithms are based on the ray tracing method, which, in the general case, allows calculation of the amplitude of an acoustic ray that survived multiple reflections from arbitrary curved surfaces. As a result, calculations of room acoustics are reduced to tracing the trajectories of all the acoustic rays in the course of their propagation with multiple reflections from reflecting surfaces to the point of their complete decay. For this approach to be used, the following physical properties of a room should be known: the geometry of the reflecting surfaces, the absorption and diffusion coefficients on each of these surfaces, and the decay law for rays propagating in air. The proposed models allow for the solution of the important problem of architectural acoustics called the auralization problem, i.e., to predict how any given audio segment will sound in any given hall on the basis of computer simulation alone, without any full-scale testing in specific halls.     

Application of Hamiltonian of ray motion to room acoustics

Based on a standard Hamiltonian of acoustic ray, it is shown that a ray motion in a finite region can be treated as a particle motion inside a potential well. The boundary reflections of ray can be described by introducing a so-called confining potential to confine a ray motion in a closed domain. It is shown that the square well potential model for the ray motion can reproduce the reverberation time in a two-dimensional room with irregular walls which is consistent with the Norris-Eyring law. It is also shown that the sound reverberation relates the ray chaos of the billiards in polygons with smooth convex walls.     

Relativistic spin selection rules obtained by SL(3, R) symmetry

All irreducible (unitary or not) ray representations of SL(3, R) obeying the Δj = 2 selection rule imposed by Regge trajectories are constructed. They provide irreducible ray representations of $\text{SL(4,}\text{R}\text{) · T}{}^4$ which restricted to the Poincaré subgroup yield unitary representation of real mass and of spin spectrum which statisfies the Δj = 2 selection rule.     

The possibility of using a vertical array for estimating the delays of sound pulses at multimegameter ranges

The majority of schemes used for acoustic monitoring of temperature fields in the ocean are based on measuring the variations of the so-called ray arrival times, i.e., the travel times of sound pulses along different ray trajectories connecting a source and a receiver. The solution of the inverse problem is considerably hindered by the fact that, in the case of signal detection by a point receiver, it is possible to resolve only the sound pulses propagating along steep rays. To a large extent, this is caused by the phenomenon of ray chaos, which is fully developed at distances of about one thousand of kilometers. The present study shows that the use of a vertical receiving array provides an opportunity to loosen this restriction. An appropriate space-time processing procedure is proposed. The procedure is based on the characteristics of ray arrival distribution in the time-depth plane that remain stable even under the conditions of ray chaos.     

Decay rates and wall absorption at low frequencies

This paper is concerned with evaluating the error of conventional estimates of the boundary absorption of rectangular enclosures, with particular reference to reverberation room sound power measurements. The reverberation process is examined theoretically; the relative contributions to the decay rate from different modes in a rectangular room are calculated from an ensemble average over rooms with nearly the same dimensions. It is shown that the traditional method of determining the absorption of the walls of reverberation rooms systematically underestimates the absorption at low frequencies; the error is computed from the ensemble average. Finally, an unbiased estimate of the sound power radiated by a source in a reverberation room is derived. This estimate involves measurement of the initial decay rates of the room and is, unlike the usual reverberation room sound power estimate, neither based on statistical diffuse field considerations nor on the normal mode theory.     

On measuring the scattering coefficient in a nondiffuse sound field

The laws of sound decay in a cubic room, one wall of which is absorbing and the other scattering, are obtained. It is shown that under certain conditions, sound decay in a room occurs nonexponentially and the shape of the decay curve depends on the scattering coefficient of the walls. This makes it possible to suggest a method for measuring the scattering coefficient by the analysis the decay curve when the walls have sound-scattering materials and structures. Expressions are obtained for approximating the measured decay curve, and the boundaries of the method’s applicability are determined.     

Ray and wave chaos in problems of sound propagation in the ocean

In the 1990s, a new area of research appeared in underwater acoustics: the investigation of the chaotic behavior of ray trajectories in inhomogeneous waveguides. It was found that, at distances on the order of 1000 km, the ray chaos already is fully developed, and this phenomenon should be taken into account in describing long-range sound propagation in the ocean. The present review, using specific examples, describes the methods of theoretical studies of both the ray chaos and its manifestations at a finite wavelength, as well as the results obtained in this area of research.     

The effect of multiple branches on sound propagation in long enclosures

Since the classical room acoustics can not be used for long enclosures due to the inhomogeneous sound field, much work has been carried out recently to investigate the sound propagation in long enclosures, which are helpful to the acoustic design of practical long enclosures, such as the high-speed railway tunnels. However, most of these works focuses on the straight long enclosures without branches or with one branch. In this paper, the effects of the multiple branches on sound propagation of long enclosures are studied. The sound pressure level (SPL) attenuation, early decay time (EDT), and reverberation time (T30) of long enclosures with multiple branches have been investigated by physical scale models based acoustic experiments. Several interesting results have been obtained concerning the sound propagation of long enclosures with multiple branches. It shows that the sound field of long enclosures with multiple branches is more complex and inhomogeneous than that of the long enclosures without branches or with one branch.     

Variations of mode amplitudes in a range-dependent waveguide

The ray method of calculating the mode amplitudes is used to analyze the sound fields in deep-water acoustic waveguides with two types of inhomogeneities of the refractive index: (i) weak inhomogeneities that cause small perturbations of ray trajectories and (ii) strong inhomogeneities with large spatial scales. Simple analytical relations are derived for describing the variations of the mode structure of the sound field in the presence of the aforementioned inhomogeneities. A new criterion defining the validity of the adiabatic approximation is formulated. To illustrate and test the results obtained, a numerical simulation of the sound fields is performed on the basis of the parabolic equation method.

     

两端开口空间的声场研究

研究了两端开口空间中声压分布同封闭空间和长空间中的不同,比较传统赛宾公式、改进赛宾公式和声线法对这种空间的估计准确度,同时对其中出现非指数衰变曲线进行讨论,分析其产生的原因、影响因素和规律。文中使用声线法进行数值计算,并且通过实验来和数值结果比较,验证结论。研究表明:两端开口空间中的稳态声压分布与封闭空间和长空间明显不同,混响时间的计算不能再使用传统赛宾公式,声线追踪法无法完全准确地估计稳态声压;其中出现非指数衰变曲线的原因经分析为空间内各不同活跃度的小区域之间的声能量耦合造成,而能否被观察到取决于能否满足耦合空间理论中对于双斜率衰变曲线出现的要求,直观上只要观察点和声源距离相差不远,并且不都在空间中央便可观察到明显的双斜率衰变曲线。      

Observation of Stable Sound Field Components in Lake Ladoga

The paper presents the results of processing measurement data on the spatiotemporal structures of sound fields in Lake Ladoga. Measurements were taken with an extended vertical receiver array. The aim of processing was to isolate the field components that were stable with respect to small variations in the waveguide parameters. Since a model of the medium is inevitably inaccurate, such components can be predicted with greater accuracy than the total field. In terms of the ray approach, a stable component is generated by a beam of rays propagating over close trajectories. The discussed experiment analyzed sound fields excited by a point source that emitted wideband pulses, as well as the fields of wave beams excited by the emitting vertical array at fixed frequencies. In both cases, the processing results showed that the isolated stable components, as expected, coincide substantially better with the prediction of theoretical calculation (by the wide angle parabolic equation method) than with the total wave field.     

Phosphorescence of pi-conjugated oligomers and polymers

We observed phosphorescence from a ladder-type poly-(para-phenylene) and an analogous oligomer containing five phenylene rings. The spectra are similar to the intrinsic fluorescence spectra and bear out a singlet-triplet splitting of 5000 cm(-1) (polymer) and 6800 cm(-1) (oligomer). Phosphorescence decay of the polymer occurs on a 10-100-micros scale obeying a power law and suggestive of nonradiative quenching, while that of the oligomer is asymptotically exponential with an intrinsic decay time of approximately 250 ms. The polymer also exhibits delayed fluorescence. It originates from delayed recombination of geminate electron-hole pairs rather than from triplet-triplet annihilation.     

Decay of a Linear Pendulum in a Free-Molecular Gas and in a Special Lorentz Gas

A circular disk without thickness is placed in a gas, and an external force, obeying Hooke’s law, is acting perpendicularly on the disk. If the disk is displaced perpendicularly from its equilibrium position and released, then it starts an oscillatory or non-oscillatory unsteady motion, which decays as time goes on because of the drag exerted by the gas molecules. This unsteady motion, i.e., the decay of this linear pendulum, is investigated numerically, under the diffuse reflection condition on the surface of the disk, with special interest in the manner of its decay, for two kinds of gases: one is a collisionless gas (or Knudsen gas) and the other is a special Lorentz gas interacting with a background. It is shown that the decay of the displacement of the disk is slow and is in proportion to an inverse power of time for the collisionless gas. The result complements the existing mathematical study of a similar problem (Caprino et al. in Math. Models Methods Appl. Sci. 17:1369–1403, 2007) in the case of non-oscillatory decay. It is also shown that the manner of the decay changes significantly for the special Lorentz gas.     

Simple Proof for Global Existence of Bohmian Trajectories

We address the question whether Bohmian trajectories exist for all times. Bohmian trajectories are solutions of an ordinary differential equation involving a wavefunction obeying either the Schrödinger or the Dirac equation. Some trajectories may end in finite time, for example by running into a node of the wavefunction, where the law of motion is ill-defined. The aim is to show, under suitable assumptions on the initial wavefunction and the potential, global existence of almost all solutions. We provide an alternative proof of the known global existence result for spinless Schrödinger particles and extend the result to particles with spin, to the presence of magnetic fields, and to Dirac wavefunctions. Our main new result is conditions on the current vector field on configuration-space-time which are sufficient for almost-sure global existence.     

Modelling the interior sound field of a railway vehicle using statistical energy analysis

The sound field in train compartments, treated as a series of connected air cavities, is modelled using statistical energy analysis, SEA. For the case under study, with five cavities in series and the source in the second cavity, a closed-form solution is obtained. An adjusted SEA model is used to predict the rate of spatial decay within a cavity. The SEA model is validated using results from a ray tracing method and from scale model measurements. For the octave bands 500–4000 Hz, good agreement is shown between the results from measurements, the ray tracing and the SEA model, for the two saloons closest to the source cavity (a vestibule). The SEA model was shown to slightly underestimate the rate of spatial decay within a cavity. It is concluded that a reasonable cause is the additional diffusion due to the seating.     

Estimating the mixing time of concert halls using the eXtensible Fourier Transform

In room acoustics, we measure room impulse responses (RIRs) in order to fully describe the hall. RIRs are composed of a succession of arrivals (i.e., some sound rays which have undergone one or more reflections on their way from the source to the receiver). We propose the eXtensible Fourier Transform (XFT) in order to investigate the time evolution of spectral components of RIRs. The phase evolution versus time allows to estimate the mixing time, which is defined as the time it takes for initially adjacent sound rays to spread uniformly across the room. After presenting some properties of the XFT, we show why one must compensate the natural energy decay of the RIR in order to obtain stationary signals. We estimate mixing times for a set of experimental RIRs and several that are synthesized using a stochastic model. Then, we estimate the dependance of mixing time upon the source/receiver distance in all these RIRs. Results are consistent up to the lack of reproducibility of the sound sources, but are strongly dependent on some parameters used for computing the XFT. We finally discuss the relevance of the name mixing time with respect to the theory and in regard to the time we estimate, that we propose to call cross-over time.     

Replica Symmetry Breaking in Critical Phenomena in Long-Range Disordered Ferromagnets

The replica symmetry breaking (RSB) is investigated in m-component ferromagnetic spin systems with a long-range disorder, with a correlation function obeying a power law ~s^-a. The Landau-Ginzburg Hamiltonjan with an RSB quartic interaction term is studied, with the renormalization-group expansion in ε = 4-D and δ = 4-a, where D is the spatial dimension. It is shown that the long-range disorder fixed point found previously is unstable under the perturbation of RSB for m<4 and stable for m≥4. The RSB fixed points are calculated and there is no physical stable fixed point for m<4.