ABSTRACT
The constants CI.2 in the function h(a, z) can be obtained by making use of the boundary condition at z = O. The function h satisfies the same boundary condition as the function P (see equation (4.5)). Let us find the boundary condition for p. To do this consider the known boundary condition for the sound pressure p of a plane wave incident obliquely on an impedance surface located at z = 0:
(4.49)
Here, ko = w/co, Co = c(z = 0) and !3 is the admittance of the surface, determined by the ratio of the characteristic impedance of the medium in which the sound propagates and the impedance of the surface. Moreover, in equation (4.49), V is the plane wave reflection coefficient of the impedance surface, depending on the angle of incidence and hence on a. For an acoustically hard surface V = 1 and !3 = 0, while for an acoustically soft surface V = -1 and !3 = 00. The admittance !3 does not depend on a for a locally reacting surface. Note that in many cases the ground can be considered as a locally reacting surface [51, 217].
