GREENS-FUNCTIONS FOR WAVE-PROPAGATION ABOVE AN IMPEDANCE GROUND

In this paper, a new method is introduced for attacking the problem of sound propagation above an impedance ground. This new method is based on a technique in which the solution of the Helmholtz equation is expressed as a onefold integral with an integrand that is identified as the solution of the heat conduction equation for an auxiliary problem. The heat conduction equation is solved via the inverse Laplace transform and its solution is substituted back into the original onefold integral. Finally, the new integral solution of the Helmholtz equation is approximated by the modified stationary phase method. Solutions of the Helmholtz equation are given for point and line sources above an impedance ground. The results obtained from these new solutions are compared with results from direct numerical integration of the exact solution. The agreement is excellent.