Source-observer Distance Research Articles

SEL for electrically hauled trains

The aim of this work is the search of an easy method to estimate the Sound Exposure Level (SEL), referring to noise emitted by trains. The theoretical model is based considering the train as a directional linear noise source, providing the SEL value in function of both source-observer distance and train speed. Experimental data obtained from electrically hauled trains and theoretical model results are compared in order to study the correlation between them.

Use of ray theory to calculate high-frequency radiation from earthquake sources having spatially variable rupture velocity and stress drop

AbstractWe analyze the problem of calculating high-frequency ground motions (>1 Hz) caused by earthquakes having arbitrary spatial variations of rupture velocity and slip velocity (or stress drop) over the fault. We approximate the elastic wave Green's functions by far-field body waves, which we calculate using geometric ray theory. However, we do not make the traditional Fraunhofer approximation, so our method may be used close to large faults. The method is confined to high frequencies (greater than about 1 Hz) due to the omisson of near-field terms, and must be used at source-observer distances less than a few source depths, due to the omission of surface waves. It is easily used in laterally varying velocity structures. Assuming a simple parameterization of the slip function, the computational problem collapses to the evaluation of a series of line integrals over the fault, with one line integral per each time ti in the observer seismogram. The path of integration corresponding to observation time ti consists of only those points on the fault which radiate body waves arriving at the observer at exactly time ti. This path is an isochron of the arrival time function. An isochron velocity may be defined that depends on rupture velocity and resembles the usual directivity function. Observed ground motions are directly dependent upon this isochron velocity. Ground velocity is proportional to isochron velocity and ground acceleration is proportional to isochron acceleration in dislocation models of rupture. Ground acceleration may also be related to spatial variations of slip velocity on the fault, using the square of isochron velocity as a constant of proportionality. We show two rupture models, one with variable slip velocity and the other with variable rupture velocity, that cause the same ground acceleration at a single observer. The computational method is shown to produce reasonably accurate synthetic seismograms, compared to a method using complete Green's functions, and requires about 0.5 per cent of the computer time. It may be very effective in calculating ground motions in the frequency band 1 to 10 Hz at observers within a few source depths of large earthquakes, where most of the high-frequency motions may be caused by direct P and S waves. We suggest a possible method for inverting ground motions for both slip velocity and rupture velocity over the fault.

Far-Field Condition in Jet Noise Experiments

The far-field condition is considered that has to be fulfilled when jet noise radiation data are compared. It becomes critical particularly when the jet flow is radiating as one coherent source extending over many jet diameters D in the axial and radial directions. To illustrate this, the jet is modeled by a distribution of 160 discrete, fixed point sources. The jet turbulence is simulated by a convected Gaussian turbulence. The deviation of the acoustical pressure field at a finite distance from the nozzle from the ideal far field at an infinite distance is studied numerically. The geometrical near-field effect is studied by assuming the point sources to be incoherent. It is strongest for small Strouhal numbers and far-field points near the jet axis. The interference effects which come into play if the sources are coherent are generally strongest for small Strouhal numbers in the direction of maximum jet noise radiation. Whereas the geometric near-field effect depends on Strouhal number, the interference near-field effect depends in addition strongly on the Mach number. For the error due to a finite source-observer distance to be less than 1 dB at the Strouhal number 5f = 0.1, the measuring distance from the jet nozzle should be at least 120 jet diameters for an incoherent source and even longer for a coherent jet.

Computer Simulations of Highway Traffic and Associated Noise Levels

A set of computer programs has been developed that provides the capability to simulate highway traffic and to calculate the associated noise levels. Extensive measurements of vehicular noise have been classified and averaged to produce characteristic spectra for passenger cars, heavy trucks, motorcycles, and other classes of vehicles. These spectra are used to represent the contribution of individual sources along a roadway. Sources are arrayed across multiple lanes to satisfy a stated proportion of cars, trucks, and other types of vehicles, as well as specified vehicle flow and speed. The individual contributions are adjusted for the effects of source—observer distance, air attenuation, vehicle speed, etc., and summed to produce a sample spectrum. Sets of these sample spectra can then be processed by computer to yield dBA values and statistical summaries of these values, or they can be utilized in the same fashion as measured data to determine noise levels adjacent to a highway. [Work performed as a part of Highway Research Board Project NCHRP 3–7.]