An Impedance Model for Angle-Dependent Sound Reflection and Absorption with Diffraction Effects

Traditionally, an open window is considered a kind of reference for perfect sound absorption. The sound reflection and absorption of an aperture is analyzed by means of an impedance model representing a rectangular absorbing surface surrounded by a thin, infinite rigid baffle. The most important part of the model is the complex radiation impedance. It is shown that the sound absorption coefficient of the open window is not exactly 1, but it is angle-dependent and decreases towards low frequencies. Two diffraction effects are identified: the refraction that appears when a wave passes through an aperture, and the scattering of waves from the edges of the aperture. A revised model for sound absorption is presented, taking these diffraction effects into account. It is shown that the refraction effect is the reason for measured absorption coefficients greater than 1, whereas the scattering effect can explain the typical decrease in absorption towards lower frequencies. The revised model is validated against examples of measured sound absorption. Finally, it is discussed how room acoustic calculation models can handle realistic absorption data.