Verification of mathematical formulae applied to overhead stage canopy design

Abstract

Abstract This paper presents a comparison of the experimental research concerning overhead stage canopies with a numerical approach based on selected mathematical models. The numerical predictions are made using the simplified asymptotic curves suggested by Rindel and modified by Skalevik. For singular cases a prediction with detailed calculations based on the Fresnel–Kirchhoff approximation is also given. The aim of the work is to verify proposed algorithms for designing reflective panels as well as to determine the conditions of conducting such procedures. It is shown that based on Rindel’s approximation one may determine some substantial information about sound reflection from the panels i.e. the value of upper limit frequency as well as the relative sound reflection level. On the other hand, the lower cut-off frequency should be calculated using Skalevik’s model as the value obtained from Rindel’s formula is undervalued. Such an approach could be applied to design reflective structures. However, it has some limitations for example for arrays of perturbed symmetry or sparse arrays as well as in the case of non-perpendicular angles of sound wave incidence. Then it may be necessary to apply more accurate numerical models.