Incoherent Line Source Research Articles

A VARIATIONAL APPROACH FOR THE STUDY OF OUTDOOR SOUND PROPAGATION AND APPLICATION TO RAILWAY NOISE

A boundary element program for the study of 2D acoustical problems is presented. It uses a variational approach leading to symmetric matrices after discretization. Numerical optimization enables the study of complex situations, such as screens placed near trains, for the full frequency range of interest, at reasonable cost. The ground effect is included in the Green function. Post-treatments offer means of introducing point or incoherent line sources. Several applications to the cases of screens placed near trains are given.

A study of 2D and 3D barrier insertion loss using improved diffraction-based methods

Lam recently introduced an improved diffraction-based method for calculating the insertion loss of a single, finite length, three-dimensional barrier ( Applied Acoustics, 42, 29–40). Comparisons of this new method with experimental scale modeling and the wave-based boundary element method showed good agreements over a broad frequency range. This preliminary work of Lam is extended in this paper to include the modeling of two dimensional geometries, the comparison of two- and three-dimensional modeling, the consideration of parallel barriers, modeling the effect of finite ground impedance and the consideration of three-dimensional coherent and incoherent line sources. Results of these developed modeling methods compare well with both boundary element and finite element modeling.

Line spread function formulation proposed by W H Steel: a revision

A revised formulation of the image light distribution of an incoherent line source proposed by Steel [Rev. Opt. 31, 334-340 (1952)] is presented. Analytical and numerical results based on this new representation are given. We explicitly show that a major error in Steel's final expression generates singularities, thereby preventing convenient numerical computation.

EFFICIENT CALCULATION OF THE THREE-DIMENSIONAL SOUND PRESSURE FIELD AROUND A NOISE BARRIER

A numerical method is presented for calculating the sound pressure around a noise barrier of constant but arbitrary cross-section. To obtain the exact solution of this problem, the Helmholtz equation must be solved in the three-dimensional domain outside the barrier. It is shown in this article how to calculate this 3-D sound pressure from solutions of simpler problems defined on the two-dimensional domain outside a cross-section of the barrier. The numerical solution of a large three-dimensional problem is thus avoided and the efficiency of the calculation is considerably improved especially when a whole frequency spectrum is needed. By using the boundary element method to calculate the numerical solutions in the two-dimensional domains, examples are given of determinations of sound pressure fields created by a point source and by an incoherent line source. In this way the efficiency of barriers of different cross-sections can be compared by using the real sound pressure around them. From the frequency spectrum at a point, one can then calculate by Fourier transform the temporal variations of the sound pressure created by a noise source moving in a direction parallel to the barrier.

Propagation of the mutual coherence function in inhomogeneous turbulent media

An inhomogeneous turbulent medium is characterized by a refractive index spectrum that varies from point to point. The mutual coherence function (MCF) is used to analyze the distortion that electromagnetic waves suffer when they propagate through such a medium. In this paper, we analyze the MCF in two dimensions for an incoherent line source. We show that the MCF consists of delta and non-delta components and derive the differential equations that each component must satisfy. Finally, we present results obtained by a numerical solution of these differential equations.

Temperature Profiles Induced by Recrystallization of Silicon-on-Insulator with Scanning Incoherent Light Line Source

Temperature Profiles Induced by Recrystallization of Silicon-on-Insulator with Scanning Incoherent Light Line Source

Reconstruction of the Mutual Coherence Function for a Moving Source

The acoustic radiation of a randomly fluctuating source in motion is characterized analytically to determine the mutual coherence function (MCF). A far-field relation is derived via a series of invertible transformations, and a higher-dimension Radon transformation is performed to reconstruct the MCF; explicit formulas for computing the MCF from the transformed radiation data are provided. The technique is applied to the cases of an axisymmetric line source of finite extent moving at constant velocity along a line and a spatially incoherent line source. Applications to X-ray tomography and analysis of the noise emitted by a moving jet aircraft are suggested.

Noise reduction by barriers on finite impedance ground

The sound field due to a point source behind a barrier on ground of finite impedance has been calculated from five theories that differ mainly in their theoretical approach to diffraction and the model for ground impedance. These predicted values for the sound field have been compared with results measured outdoors using plywood barriers on different combinations of hard and soft ground. Each of these theories allows for interference due to differences between several paths of propagation, determined by the geometry of the source, receiver, barrier, and ground. One of these theories that shows good agreement with measurements, has been extended to calculate the sound spectrum level behind a barrier due to an incoherent line source, and further, to calculate the overall or A-weighted sound level for a known source spectrum. Results suggest that there is a significant effect, due to the presence of the ground, that is much greater than that due to absorptive properties of the barrier. Results also predict sound level reductions that differ from predictions using well-known barrier theories (most noticeably a smaller insertion loss): these differences can be of the order of 10 dB(A) depending on geometry, source spectrum, and acoustical condition of the ground.

Multiple reflection of traffic noise in the city area

In Tokyo, it is very difficult to get the space for road construction. Twelve-million people are concentrated in a limited area. Many houses and buildings are arranged closely on both sides of the street, and city freeways are built frequently above the main street by overhead elevated constuction. In such cases the noise radiated from vehicles is reflected between houses, buildings, the bottom of the elevated road, and the lower street surface, and consequently the sound level observed along the street is higher than that in the case of open area. The effect of the buildup of sound level caused by multiple reflection in city area was studied by means of 1/40 scale model experiments and field measurements. Scale model experiments were carried out concerning various conditions of reflection by using an incoherent line source, and spacial distribution of SPL surrounding the road and the street was observed. Results of the scale model experiments showed similar tendency to that of field measurements. Relations between the buildup of SPL and various factors of sound reflection, for instance, the width of street, the height of buildings, houses, and elevated road and so on, were discussed. The results of this study will be applicable in the road traffic noise prediction at the point located in the roadside.

Noise prediction in the city area

The distribution of houses plays an important role to the noise propagation in the city area. The purpose of this study is to make clear the tendency of road traffic noise propagation into the city area, and it is carried out by means of scale model and field measurements. In model experiments, an incoherent line source (jet noise type) is used as road traffic noise. Houses are defined to be only one or two story houses and are distributed in random order. In this model of the residential area, the spacial distribution of sound pressure levels at the specified distance from the road are observed. From the experimental results, we can derive an empirical equation which gives the excess attenuation caused by houses as a correction term. This correction is given as a function of the density of houses, the source height and the distance from the road. Predicted sound level obtained by using the correction term agrees well with the result of the field measurements.

Noise Reduction by Acoustic Barriers for Incoherent Line Source

Noise Reduction by Acoustic Barriers for Incoherent Line Source

Scale model experiments on noise reduction by acoustic barrier of a straight line source

Noise reduction by an acoustic barrier of a straight line source is examined with the aid of scale model experiments. The line source used in these experiments is an incoherent line source mechanically radiating broad band noise. From the experimental results a curve can be deduced which shows a relation between sound attenuation and Fresnel number N. This curve shows values lower than those of Maekawa's data by 3 ∼ 5 dB, which are presented for a point source. On the other hand, it agrees fairly well with Rathe's experimental results, measured near the tracks of a railway line, and also shows a similar tendency to the curve calculated by Kurze and Anderson for an incoherent line source.

Sound attenuation by barriers

Experimental data on sound attenuation by barriers and an engineering prediction scheme recently proposed by Rathe 6 are compared with results of the geometrical theory of diffraction. A simple analytic expression is proposed for the calculation of the excess attenuation due to diffraction around a barrier of sound rays emanating from a point source; this analysis takes into account oblique sound incidence at the barrier and also includes the transition region from the bright zone to the shadow zone behind the barrier. The excess attenuation by a barrier parallel to an incoherent line source is shown to be calculable from the excess attenuation of sound emanating from a few points on the line source. Engineering estimates for the required length of an efficient barrier parallel to a line source yield an aspect angle for the barrier equal to 95% of the aspect angle of the line source. The sound transmission through a barrier is found to be negligible for a typical automotive traffic noise spectrum if the mass per unit area of the barrier exceeds 4 lb/ft 2.

Prediction of Sound Attenuation by Barriers

A simple analytical approximation for the sound attenuation by barriers is derived on the basis of prior theoretical and experimental results. The approximation takes into account oblique sound incidence at the barrier and also applies for the transition region between the “bright” zone and the shadow zone behind the barrier. Results for a point source are compared with those for a line source parallel to the edge of the barrier. Engineering estimates are given for the aspect angle of an incoherent line source, for which the barrier attenuation can be calculated by considering only a single diffracted ray. Predictions of the sound attenuation by a barrier parallel to a number of incoherent line sources agree well with experimental results reported for an acoustical model of a multilane highway. The length of a barrier along a highway required for efficient sound attenuation is calculated in terms of the angle at the observer that encompasses the barrier. [These studies were carried out in part under Contr. No. DOT-OS-A9-018, under subcontract with Serendipity, Inc., Arlington, Virginia.]

Measurement of the Total Illuminance in a Diffraction Image Part II Line Sources

A method of measuring the total illuminance of the diffracted image of an incoherent line source is described. Measurements on a 6-in. focal length objective are reported. Experimental measurements of this kind give a quantitative measure of lens system performance in terms of total illuminance of the diffracted image of a line source. The results of theoretical diffraction calculations based upon lens design data were compared with experimental values and showed good correlation.