Elementary pulse diffraction problems and the generation of sound by a dipole moving across the edge of a halfplane
Abstract
The exact solution of the linearized wave equation for the diffracted field of a three dimensional sound pulse incident on the sharp edge of a half plane is constructed in closed form using Sommerfeld's method. From this solution the well known two dimensional equivalent is derived by the method of descent. The transient behavior of two dimensional and three dimensional switchon sources, leading to steady incompressible potential flow, is obtained by time integrations of the pulse solutions. The characteristic features are discussed and plots of the flow field are presented. The three dimensional switchon source is the classical result of Cagiard's 1935 paper. The field of a moving source in a branched space is generated by integration of the field of a pulse source. The diffracted field of the moving source can only approximately be obtained and only for relatively low velocity motion. Differentiation of the moving source solution yields the approximation to the field of a moving dipole in a branched space. The pressure (sound) wave generated by a dipole passing near the sharp edge of a half plane is computed as an application of the elementary solutions in a branched space. Spatial plots of the wave profiles and time histories of the pressure are presented. The results are compared with the existing literature and it must be concluded that the above direct approach presents a substantial improvement to the pulse Green's function.
 Publication:

Unknown
 Pub Date:
 November 1990
 Bibcode:
 1990epdp.rept.....S
 Keywords:

 Aerodynamic Noise;
 Dipoles;
 Half Planes;
 Magnetic Dipoles;
 Pulse Diffraction;
 Sound Generators;
 Wave Equations;
 Green'S Functions;
 Integrals;
 Mathematical Models;
 Numerical Integration;
 Partial Differential Equations;
 Quadrupoles;
 Sommerfeld Approximation;
 Weighting Functions;
 Acoustics