On the Reflection of a Spherical Sound Wave from an Infinite Plane

The reflection of a spherical sound wave from a wall with the boundary conditions expressed in terms of a normal impedance independent of the angle of incidence is treated. It is shown that the integral for the reflected wave can be evaluated exactly in closed form under certain conditions. The solution given for an arbitrary normal impedance involves a slight approximation of the integral. The reflected wave is brought into a form such that it can be considered originating from an “image source” having a certain amplitude and phase. Graphs for determining this amplitude and phase are given in terms of a “numerical distance,” which depends on the normal impedance and the position of the field point. Pressure distributions around point sources for different wall impedances are shown. The limitations in simulating plane wave conditions at a boundary and the corresponding effect on free field methods of measuring acoustic impedance are discussed.