On the Reflection of a Spherical Sound Wave from a Finite Size Surface

Room acoustics computer models based on geometrical acoustics usually handle the sound reflections by the assumption of plane waves. However, if the sound source is a point source, which is usually the case, the spherical wave reflection would be more correct. An approximate model for the spherical wave reflection is presented, starting with the assumption of an infinite plane. It was found that the errors caused due to the simplified plane wave assumption can be significant, especially for hard surfaces and near grazing incidence. As something new, the gradual transition from a spherical wave to a plane wave approximation was addressed. For sound propagation exceeding 50 times the wavelength, the plane wave approximation was found to be fully justified, but for shorter distances the spherical wave reflection model should be applied. In contrast to previous work on spherical wave reflection, the reflection from a finite-sized surface was studied. For the first time, the spherical wave reflection model was combined with the complex radiation impedance of a finite-sized surface. One interesting application example of the spherical reflection model is the attenuation of sound propagation above the audience area in a performance space. Finally, the extension of the spherical wave reflection model to higher order reflections was addressed.