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Bulk Acoustic Waves in Solids
Published in J. David, N. Cheeke, Fundamentals and Applications of Ultrasonic Waves, 2017
For order of magnitude purposes, let us take a typical solid as having a density of 5000 kg·m−3 and a longitudinal velocity of 5000 m·s−1, giving a longitudinal acoustic impedance of 25 MRayls where the Rayl (after Lord Rayleigh) is the MKS unit of acoustic impedance. Referring to Table 5.1, it is seen that the range for typical solids is 10–15 MRayls, with some high-density, high-velocity materials such as tungsten going up to 100 MRayls. By comparison, plastics and rubbers are in the range 1–5 MRayls, water 1.5 MRayls, and air is orders of magnitude less at 400 Rayls. This is why, for off-the-cuff calculations, a solid–air or liquid–air interface can be taken to first order as totally reflecting. In some cases, the required range of sound velocities or densities of a material is fixed by other considerations (e.g., focusing properties of acoustic lenses), in which case Figures 5.2 and 5.3 are useful for showing at a glance the possible choices of common materials in a given acoustic impedance range.
Seeing with Sound: Diagnostic Ultrasound Imaging
Published in Suzanne Amador Kane, Boris A. Gelman, Introduction to Physics in Modern Medicine, 2020
Suzanne Amador Kane, Boris A. Gelman
Acoustic impedance is measured in units of kg/(m2-sec) (also called a rayl). Table 4.2 shows values for the acoustic impedance for a variety of body tissues. Note the similarity of acoustic impedance values of all soft tissues, such as fat, water, and muscle, when compared with air and bone. Thus, the quantity that determines whether a sound wave is reflected depends upon both the speed of sound and the density of the medium; this is unlike the case of light waves, where the reflected fraction depended only on the refractive indices (and therefore only on the values of the speed of light) of the mediums in which the incident and transmitted light travel (e.g., see problem P2.9).
Basics of Acoustics
Published in Randall F. Barron, Industrial Noise Control and Acoustics, 2002
The characteristic acoustic impedance is Zo = 409.8 rayl from Appendix B. The wave number is: k=2πfc=(2π)(125)(346.1)=2.269m−1
Multi-factor joint return period of rainstorms and its agricultural risk analysis in Liaoning Province, China
Published in Geomatics, Natural Hazards and Risk, 2019
Yu Feng, Ying Li, Zhiru Zhang, Shiyu Gong, Meijiao Liu, Fei Peng
The premise of constructing a Copula function is to determine the marginal distribution function of each single factor. The maximum likelihood method is used to fit the marginal function of the rainstorm elements (Park et al. 2015). This study uses seven kinds of marginal functions that are commonly adopted in hydrology and meteorology to perform marginal fitting on rainstorm elements. They are the Generalised Extreme Value Distribution (GEV), Extreme Value Distribution (EV), Exponential Distribution (Exp), Poisson Distribution (Poisson), Normal Distribution (Norm), Gamma Distribution (Gam), and Rayleigh Distribution (Rayl), and they are served to determine the best fitting marginal function of each rainstorm element.
An enhanced data-driven polynomial chaos method for uncertainty propagation
Published in Engineering Optimization, 2018
Fenggang Wang, Fenfen Xiong, Huan Jiang, Jianmei Song
In this section, the enhanced DD-PCE method is applied to UP to calculate the first four moments and probability of failure (Pf). The results are compared with those of the well-recognized gPCE method as well as the GS-PCE method that can address arbitrary random distributions to demonstrate the effectiveness and relative merits of the enhanced DD-PCE method. To comprehensively compare the three PCE approaches, four cases are respectively tested on four mathematical functions with varying nonlinearity and dimension, shown in Table 2, in which N, U, Exp, Wbl, Rayl, Logn denote normal, uniform, exponential, Weibull, Rayleigh, lognormal distribution, respectively. Pf is defined as . The PCE order is set as H = 5 for all the functions for comparison, which means that 0 through 9th moments of the random inputs should be matched to construct the one-dimensional orthogonal polynomials for DD-PCE. The technique introduced in Section 4 is used to obtain the Gaussian quadrature nodes and weights for DD-PCE. For the first and second functions, FFNI-based Galerkin projection is used to calculate the PCE coefficients, while for the latter two, the sparse grid-based method with accuracy level k = 4 is used, since the dimension is higher (marked with * in the tables below). The results of MCS with 107 runs is used to benchmark the effectiveness of the three methods.