Spherical Wave Diffraction by a Slit in an Impedance Screen

An exact solution is developed for the problem of diffraction of an E-polarized and an H-polarized spherical waves by a slit in an impedance screen. This consideration is important in the sense that point sources are regarded as better substitutes for real sources than line sources/plane waves. The two independent problems are solved using the Fourier transform, the Wiener-Hopf technique and asymptotic approximations.     

Directional properties of an array of sound receivers positioned in an impedance screen recess

Expressions for calculating the directional characteristics of an array of sound receivers positioned in a waveguide with impedance walls are obtained from the solution to the problem on the diffraction of a plane sound wave by the waveguide open end with impedance flanges. The waveguide can be of a finite length, and, in this case, it can be considered as an open cavity in an impedance screen. The solution of the integral equation for the sound pressure distribution over the opening area is reduced to the solution of an infinite system of algebraic equations for the coefficients of the field expansion in normal waveguide waves. Examples of calculated directional characteristics are presented for arrays with receivers positioned at different distances from the opening and for different values of the impedances of the waveguide walls and flanges.     

Effect of wall aperture on sound propagation within a tube

I.IntroductionInmanycasesthecontinuityofsoundpropagationwithinatubeisbrokenbyaperturesonthetubewallsuchastoneholesonthemainboreofwoodwindmusicalinstruments,rectangularsound-windowofChineseinstrumentshengetc.Thediscontinuityhaseffectonwavccncoun-tCringit.Keefestudicdasing1etoneholeofwoodwindinstrumentandrepresenteditbyaT-sectionequiva1entcirc.it[11.Inthispaper,theapertureontubewa1lisstudiedfromdifferentpointofview,a1thoughtheGreen'sfunctionmethodisalsousedinthetheoreticalana1ysis.Moresimp1er…     

Diffraction of an ultrashort pulse by an aperture

The scalar problem of diffraction of an infinitely short pulse by a plane screen is solved within Kirchhoff’s approximation. The response of an infinitely small aperture is calculated, and the explicit solution is found for the case of a circular aperture.     

Beugung elektromagnetischer Wellen in Braunbekscher Näherung. I

An approximation method proposed by Braunbek for the diffraction of scalar waves by plane obstacles, or apertures in a plane screen, is extended to the diffraction of electromagnetic waves. As an example, the diffraction of a linearly polarized plane electromagnetic wave normally incident on a circular aperture in a perfectly conducting plane screen and on a perfectly conducting plane circular disk is considered in detail. The results are compared with those obtained from the exact solution ofMeixner andAndrejewski and with the results ofKirchhoff's approximations. It is shown that, in contrast to theKirchhoff approximations,Braunbek's method leads in all cases to the correct ‘optical’ limits and represents a good approximation even for wavelengths comparable with the size of the obstacle. After a general formulation ofBraunbek's method in the electromagnetic diffraction problem, we calculate in the present paper the far field of the circular aperture and the transmission coefficient by means of the cross section theorem. The near field of the circular aperture and the circular disk will be considered in a subsequent paper.     

Suppression of the sound field produced behind an aperture in a screen by an extraneous source

The three-dimensional problem of the active suppression of sound behind an aperture in a perfectly rigid screen is formulated and solved.     

Toward an estimation of the clarinet reed pulse from instrument performance

In this work, a technique is presented for estimating the reed pulse from the pressure signal recorded at the bell of a clarinet during performance. The reed pulse is a term given to the typically periodic sequence of bore input pressure pulses, a signal related to the volume flow through a vibrating reed by the characteristic impedance of the aperture to the bore. The problem is similar to extracting glottal pulse sequence from recorded speech; however, because the glottis and instrument reeds have very different masses and opening areas, the source-filter model used in speech processing is not applicable. Here, the reed instrument is modeled as a pressure-controlled valve coupled to a bi-directional waveguide, with the output pressure approximated as a linear time invariant transformation of the product of reed volume flow and the characteristic impedance of the bore. By noting that pressure waves will make two round trips from the mouthpiece to the bell and back for each reed pulse, yielding a distinct positive and negative lobe in the running autocorrelation period of the recorded signal, the round-trip attenuation experienced by pressure waves in the instrument is estimated and used to invert the implied waveguide, producing reed pulse estimates.     

A theory of the diffraction of an electromagnetic wave by a plane screen

The problem of the diffraction of an arbitrarily polarized electromagnetic plane wave by a perfectly conducting plane screen of infinitesimal thickness is reduced to scalar problems by the method known from earlier papers. The wave field diffracted either by a screen of infinite extent which is perforated by an aperture of arbitrary size and shape or by a complementary screen is then described by means of the bra-vectors, ket-vectors and linear operators introduced by the present author in one of his preceding papers.     

Propagation of sound over grassland and over an earth barrier

A model for the calculation of effects of ground and a screen or a wedge shaped barrier on the transmission of sound has been tested by comparing calculated transmission losses with losses measured in real situations. With the model presented in this paper, the effect of a homogeneous ground with a finite or an infinite impedance, the effect of diffraction at a discontinuity in the impedance of the ground (e.g., the transition between road surface and adjacent grassland), and the combined effect of ground surface and a barrier with a finite or an infinite surface impedance can be handled. The incorporation of the effects of a discontinuity in the impedance of the ground and of the finiteness of the height of a barrier led to an additional improvement of the agreement between calculated and measured transmission losses.     

Zur Theorie einer Klasse von Beugungsproblemen mittels singulärer Integralgleichungen. IV Hochfrequente Schallbeugung an der Kreisblende: numerische Ergebnisse

The six-term developments of the far-field amplitude and the transmission coefficient formerly given for the high-frequency diffraction of a plane sound wave by a circular aperture in an infinite plane sound-soft screen at normal incidence are corrected and numerically evaluated.     

Efficiency of sound field focusing in an oceanic waveguide with background internal waves

The efficiency of focusing a reversed wave and the possibility of scanning the focal point in a shallow sea in the presence of an anisotropic field of background internal waves are theoretically considered. The localized fields are controlled by varying the transmission frequency without a change in the distribution of the reversed field over the array aperture. The effect of the periodically repeated focal spots is analyzed. Numerical calculations are performed for the longitudinal and transverse orientations of acoustic path relative to the propagation direction of internal waves.     

Diffraction of a sound wave by the open end of a flanged waveguide with impedance walls

Diffraction of a plane sound wave by the open end of an impedance-wall waveguide connected to an opening in an impedance screen is considered. The plane wave is incident on the waveguide from a free half-space. Two versions of the problem are considered: for a semi-infinite waveguide and for a finite-length waveguide with a specified bottom impedance; the impedances of the walls, screen, and waveguide bottom can be different. The finite-length waveguide can be treated as an open cavity in the impedance screen. For the cavity of zero length, the problem is reduced to the diffraction by an impedance insert in the impedance screen. The solution in the external region determines the scattered field; the solution in the internal region allows one to determine the directional pattern of an array of receivers located in the cavity. The problem is solved using the integral Helmholtz equation with a specially selected Green’s function that provides the fulfillment of the boundary conditions. Formally, the problem is reduced to an infinite system of algebraic equations. The computational results obtained for bistatic and monostatic scattering patterns are presented.     

Zur Theorie einer Klasse von Beugungsproblemen mittels singulärer Integralgleichungen. V Hochfrequenz-Beugung ebener elektromagnetischer Wellen an einer ideal leitenden Kreisblende

The high-frequency diffraction of a plane electromagnetic wave by a circular aperture in a infinite plane conducting screen is considered at normal incidence. The asymptotic solution of the singular integral equation for the Fourier-transform of the current density on the screen is found by means of elementary function-theoretic methods. Five terms of the high-frequency development of the transmission coefficient are given.     

Piston acoustic radiator in an impedance screen of a Pekeris waveguide

A model problem of seismic hydroacoustics is studied for a piston radiator inserted in an impedance screen that coincides with the lower boundary of a Pekeris waveguide. The radiation resistance of the piston is numerically calculated as a function of the screen type and parameters of the radiator and the waveguide.     

The scattering of the field of a point source by an axisymmetric screen with a variable impedance

The method of continued boundary conditions is used to solve the acoustic diffraction problem for the case of a field generated by a point source and diffracted by an axisymmetric screen, with generalized impedance boundary conditions being satisfied at the screen surface. Two types of impedance boundary conditions are considered, which differ; at zero impedance one of them takes the form of the Dirichlet boundary condition, while the other the takes the form of the Neumann boundary condition. Both stationary and non-stationary diffraction problems are investigated. Numerical results are obtained for screens with parabolic and spherical shapes.     

Scattering from loaded grooves

Electromagnetic scattering from a two-dimensional groove recessed in an arbitrarily thick conducting screen is studied. The groove may be empty or loaded with a lossy material which may or may not completely fill the cavity. For the partially loaded groove, the filling material is assumed electrically dense so that the standard impedance boundary condition is applicable at the top surface of the material. Employing a full-wave analysis, integral equations are derived for the tangential components of the electric field over the aperture. It is shown that the equations are identical for both partially loaded and completely loaded (or empty) cases provided that the aperture admittance of the groove is treated as the equivalent admittance of the internal medium looking into the aperture, thus simplifying the integral equations.When the groove is completely filled by a dense material, the formulation reduces to that corresponding to a direct application of the impedance boundary condition over the aperture.     

Reflection of an acoustic line source by an impedance surface with uniform flow

An exact analytic solution is derived for the 2D acoustic pressure field generated by a time-harmonic line mass source located above an impedance surface with uniform grazing flow. Closed-form asymptotic solutions in the far field are also provided. The analysis is valid for both locally-reacting and nonlocally-reacting impedances, as is demonstrated by analyzing a nonlocally reacting effective impedance representing the presence of a thin boundary layer over the surface. The analytic solution may be written in a form suggesting a generalization of the method of images to account for the impedance surface. The line source is found to excite surface waves on the impedance surface, some of which may be leaky waves which contradict the assumption of decay away from the surface predicted in previous analyses of surface waves with flow. The surface waves may be treated either (correctly) as unstable waves or (artificially) as stable waves, enabling comparison with previous numerical or mathematical studies which make either of these assumptions.     

A hybrid Maliuzhinets/PO method for diffraction problems by impedance wedges

The solution of Maliuzhinets of the diffraction problem of waves by an impedance wedge is transformed into a physical optics integral. The resultant expression is suitable for the investigation of various diffraction problems having impedance wedges. The method is applied to the scattering of waves by an impedance spherical reflector with wedge structure at its discontinuity. The results are examined numerically.     

On the application of symmetrization to the transmission of electromagnetic waves through small convex apertures of arbitrary shape

The transmission of an electromagnetic wave through a small aperture in a perfectly conducting screen is examined from the viewpoint of symmetrization.