A Fresnel Zone Approach to the Prediction of Sound Propagation Above a Multi-Impedance Plane

Eilicient and accurate methods exist for the calculation of the sound eld produced by a point source above 'a plane boundary ofuniform surface impedance. For boundaries comprising two regions of di 'crent surface impedance, with a straight discontinuity perpendicular to the direction from source to receiver, several solutions have beenpresented. En o & En o 1 have derived an exact solution which is very di icult to evaluate for practical situations. De long 2 developed a useful semi empirical approximate solution based on far-eld diffraction theory which is easy to evaluate. The method can be applied to multiple discontinuities and is not restricted to a particular orientation of the discontinuities in the boundary. Approximate numerical methods have also been developed based on the Kirchhoff di i'action formula in which the propagating wavefront is discretised above the discontinuity 3 and the boundary element approach where the discretisation is applied is the boundary 4. The boundary element method is potentially the most versatile and accurate but is very costly in computing resources. In this paper, an approximate formulation is developed, based on the concept of the Fresnel zone, to predict propagation over a mum-impedance plane. Predictions using the method are compared with experimental model results, PREDICTION MODELConsider a monochromatic point source of saund, S and a receiver. R above an in nite boundary, shown in section in Figure l. The sound pressure at the receiver results from a combination of the direct wave and the wave re ected from the surface. The pressure of the re ected wave. [1, , can be expressed using the Kirchhoff di raction formula as an integral over the boundary, r. So that _ 1 e h" a 2"" 2"" (3 2" 47 iiiYEiT) T iTii