There is substantial interest in the analytical and numerical modeling of low-frequency, long-range atmospheric acoustic propagation. Ray-based models, because of their frequency limitations, do not always give an adequate prediction of quantities such as sound-pressure or intensity levels. However, the parabolic approximation method, widely used in ocean acoustics and often more accurate than ray models for frequencies of interest, can be applied to this type of acoustic propagation in the atmosphere. Modifications of an existing implicit finite-difference implementation for computing solutions to the parabolic approximation are discussed. A locally reacting ground surface is used with one- and two-parameter impedance models, while a nonreflecting boundary condition is used to handle the upper boundary. Relative sound-pressure level calculations are performed for a number of flow resistivity values in both homogeneous and nonhomogeneous atmospheres. Comparisons to experimental data are made which suggest this modeling approach can be useful in the study of these types of propagation problems.
appropriate formulas are included and many examples are given. It should therefore be of interest to practicing acoustical engineers and, for selective readings, to teachers of courses in engineering acoustics. This book is another in the series of classic texts in acoustics that the Acoustical Society of America has rescued from out-of-print status. The series is a valuable resource to a new generation of students, engineers, and scientists in acoustics.Springer, New York, 1987. xiv -/-710pp. Price $49.00.The Institute for Naval Oceanography (INO), located at NTSL, Mississippi, is a new agency focusing its energies principally on modeling and predicting ocean circulation. With the advent of this organization, the vision of ocean "weather" forecasting 1'2 moves even closer to becoming reality. Published objectives of INO with particular relevance to acousticians are twofold: first, the harmonious cooperation among ocean prediction systems and acoustic models, and, second, the exploitation of ocean acoustic tomography. Both of these concerns underscore the importance of the sometimes subtle interplay between ocean dynamic processes and underwater acoustic propagation. On the one hand, the mechanisms through which sound transmissions are affected by ocean environmental phenomena can be critically important in many applications. Numerous studies emphasizing this point have been published in The Journal of the Acoustical
The effect of currents on the acoustic pressure field in an underwater sound channel is investigated. Based on fundamental fluid equations, model equations are formulated for sound pressure while including nonuniform currents in the source–receiver plane. Application of parabolic-type approximations yields a collection of parabolic equations. Each of these is valid in a different domain determined by the magnitudes of current speed, current shear, and depth variation of sound speed. Under certain conditions, it is possible to interpret current effects in terms of an effective sound speed. Using this effective sound speed in an existing numerical code, we examine sound speed in a shallow water isospeed channel with a simple shear flow and a lossy bottom. It is found that even small currents can induce very substantial variations in relative intensity. The degree of variation depends upon current speed, source and receiver geometry, and acoustic frequency. Particular emphasis is placed on intensity-difference predictions in reciprocal sound transmissions in the presence of an ocean current.
The calculation of the Fibonacci sequence using recursion gives rise to an interesting question: How many times does a recursive function call itself? This paper presents one way to examine this question using difference equations with initial conditions, or discrete dynamical systems (DDS). We show that there is a linear relationship between the Fibonacci numbers themselves and the number of recursive calls. This relationship generalizes to any type of DDS of second-order, and DDS of higher-order.
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