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Acoustic wave equation

About: Acoustic wave equation is a(n) research topic. Over the lifetime, 5382 publication(s) have been published within this topic receiving 93010 citation(s). more

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01 Jan 1950-
Abstract: Fundamentals of Vibration. Transverse Motion: The Vibrating String. Vibrations of Bars. The Two--Dimensional Wave Equation: Vibrations of Membranes and Plates. The Acoustic Wave Equation and Simple Solutions. Reflection and Transmission. Radiation and Reception of Acoustic Waves. Absorption and Attenuation of Sound. Cavities and Waveguides. Pipes, Resonators, and Filters. Noise, Signal Detection, Hearing, and Speech. Architectural Acoustics. Environmental Acoustics. Transduction. Underwater Acoustics. Selected Nonlinear Acoustic Effects. Shock Waves and Explosions. Appendices. Answers to Odd--Numbered Problems. Index. more

4,045 citations

Journal ArticleDOI
Haruichi Washimi1, Tosiya Taniuti1Institutions (1)

1,638 citations

01 Jan 1969-

1,030 citations

Journal ArticleDOI
James C. Phillips1, Leonard Kleinman1Institutions (1)
15 Oct 1959-Physical Review
Abstract: For metals and semiconductors the calculation of crystal wave functions is simplest in a plane wave representation. However, in order to obtain rapid convergence it is necessary that the valence electron wave functions be made orthogonal to the core wave functions. Herring satisfied this requirement by choosing as basis functions "orthogonalized plane waves." It is here shown that advantage can be taken of crystal symmetry to construct wave functions ${\ensuremath{\phi}}_{\ensuremath{\alpha}}$ which are best described as the smooth part of symmetrized Bloch functions. The wave equation satisfied by ${\ensuremath{\phi}}_{\ensuremath{\alpha}}$ contains an additional term of simple character which corresponds to the usual complicated orthogonalization terms and has a simple physical interpretation as an effective repulsive potential. Qualitative estimates of this potential in analytic form are presented. Several examples are worked out which display the cancellation between attractive and repulsive potentials in the core region which is responsible for rapid convergence of orthogonalized plane wave calculations for $s$ states; the slower convergence of $p$ states is also explained. The formalism developed here can also be regarded as a rigorous formulation of the "empirical potential" approach within the one-electron framework; the present results are compared with previous approaches. The method can be applied equally well to the calculation of wave functions in molecules. more

897 citations

Journal ArticleDOI
Steven A. Cummer1, David Schurig1Institutions (1)
Abstract: A complete analysis of coordinate transformations in elastic media by Milton et al has shown that, in general, the equations of motion are not form invariant and thus do not admit transformation-type solutions of the type discovered by Pendry et al for electromagnetics. However, in a two-dimensional (2D) geometry, the acoustic equations in a fluid are identical in form to the single polarization Maxwell equations via a variable exchange that also preserves boundary conditions. We confirm the existence of transformation-type solutions for the 2D acoustic equations with anisotropic mass via time harmonic simulations of acoustic cloaking. We discuss the possibilities of experimentally demonstrating acoustic cloaking and analyse why this special equivalence of acoustics and electromagnetics occurs only in 2D. more

856 citations

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Topic's top 5 most impactful authors

Changsoo Shin

12 papers, 78 citations

Yang Liu

12 papers, 148 citations

Sean Wu

10 papers, 189 citations

Kevin B. Smith

9 papers, 96 citations

Mrinal K. Sen

9 papers, 148 citations