Reflection of sound from finite-size plane and curved surfaces

The author’s research on reflectors over nearly 25 years is summarized. The influence of curvature was analyzed by a geometrical model in order to quantify the attenuation by a simple expression. Reflection from a finite size plate was studied using the Kirchhoff-Fresnel approximation and the design frequency for a single reflector was derived. Above the design frequency the attenuation due to the finite size can be neglected and the reflection is efficient in the specular direction. The method was extended to the case of a reflector array and it was demonstrated that the performance of a reflector array can improve if the size of the panels is decreased. The same design frequency applies to a single reflector and a reflector array, but with different meaning; in the latter case the design frequency is the upper limit for useful reflections. This design rule was first used in the refurbishment of the concert hall of the Danish Radio in Copenhagen 1989, and later in many other halls. In order to describe the scattering due to edge diffraction the directional characteristic of reflections from a finite-size plate has been studied and a simple approximation valid for octave bands has been derived.