On the approximation of total absorption of the street open ceiling at low frequencies

This work deals with numerical modeling of sound propagation in street canyons with flat building facades. The street is seen as an open waveguide and two 3D wave models are used: a parabolic equation model and a modal expansion model. The comparison between the models shows a very good agreement. Then, the study focuses on the radiation condition at the opening of the street. In usual energetic approaches as ray tracing, the opening is assumed to be perfectly absorbing. This assumption is realistic at high frequencies, however the reflection phenomenon caused by the geometric discontinuity at the opening is still an open question at low frequencies. This possible reflection is investigated through three parametric studies of the acoustic longitudinal energy flux decay along the street. The first study shows that the approximation of total absorption at the street open ceiling is no longer valid when the ratio η between the street width and the wavelength is small. The second study shows that the effect of source height is weak except under restrictive conditions: when η is small and when the source height is not small compared to the wavelength, the approximation of total absorption is acceptable for an elevated source. At least, the results of the last study show that the error made by assuming a perfectly absorbing ceiling is not negligible compared to the error made by considering perfectly reflecting walls.