Overhead canopies are used in auditoriums to blend the direct and reflected sound and either increase intelligibility or enhance musical clarity and intimacy. Typically canopy arrays are used instead of a solid ceiling, to provide needed early reflections, while maintaining a desired reverberation time. Often, flat panel arrays are used for economy. However, flat panel arrays can potentially provide non-uniform scattered sound, due to the lack of scattering from gaps between the panels. One approach to help reduce this problem is to utilize shaping to provide diffusion. The simplest approach is a single curvature panel called the Monoradial™. The Monoradial™ is typically used to provide longitudinal (front-back) scattering to help minimize the problems from flat panels. RPG offers the Monoradial™ in Class A Glass Reinforced Gypsum and wood.

Problem
The figure shows coverage plot simulations from 4 sources to 16 receivers comparing spaced arrays of flat panels and curved panels. In the upper illustration, typical coverage holes are apparent. These coverage problems, which are due to the spaces between the panels, result when there is no ceiling panel to specularly reflect a source ray to a receiver.

Solution
A simple conventional solution is to curve the panel in one direction forming an arc. In the middle illustration, it is apparent that the curve introduces scattering into non specular directions, partially solving the coverage problem. The level of the reflections is illustrated in the bottom graphic.

Diffusion

In the left illustration, we show an array of flat panels 1m wide and 1.25 m apart, along with the source and the receiver arc. In the middle illustration, we show the far field response along the receiver arc for this flat panel array. Periodicity lobing at +/- 53 degrees at mid frequencies (dark line) is evident. High frequencies (light line) are purely specular and low frequencies (dashed line) are omnidirectional for this panel size. On the right, the response for an array of semicylinders of the same size is shown at mid frequency (light line), illustrating the dispersing effect of the semicylinders. Periodicity lobing, however, is still present. The response of an aperiodic semicylinder array is also shown (dark line) to illustrate the improvement modulation provides.