This work has been initiated at LAUM to study the propagation of low frequency acoustic waves in the cities. The geometry of a street can be modeled by a canyon opened on the roof. Then, it appears that the acoustic waves are guided by the facades of the street but also are attenuated by the leaks in the canyon due to the open roof. A multimodal approach is used to describe the acoustic field in a street where the transverse modes (difficult to determine analytically) are calculated using a Finite Element method (FE). Let’s note that the geometry of the transverse section can include geometrical complexity (balcony or changes of section shape) and different impedance conditions at the wall since the resolution uses Finite Elements method. This approach is also completed by a method using the parabolic approximation in the wave guides. As illustrated in the figure, resonance phenomena in urban courtyards have been highlighted using the multimodal method with good agreement with experimental results.
Acoustics field in a street with a courtyard
Acoustics field in a street
Moreover, this method allows to study the acoustic propagation in an urban environment described by a network of street (see figure). In the spectral domain, it has been showed the existence of band gaps in the case of periodic arrangement of urban canyons. We have also developed a method in the temporal domain to model the propagation of acoustic waves in a network of waveguides. This method is based on a previous characterization in the frequency domain of each of the elements forming the network (waveguides and junctions). This characterization is performed using a mode matching technique and the information obtained is traduced to the time domain using Fourier analysis. A good agreement between experience and theory is obtint by comparison of snapshots of a pulse propagation in a network of open waveguide.
Experimental setup for urban acoustics