Metasurfaces formed by monopole and dipole resonators are studied theoretically. The monopole resonators are Helmholtz resonators or membranes vibrating on the first eigenfrequency; the dipole ones are spheres on springs or membranes vibrating on the second eigenfrequency. It is shown that acoustic properties of the metasurface formed by the built-in monopole resonators can be described by an equivalent impedance, which characterizes a normal forcing to the surface, whereas this impedance is not suitable for the metasurface formed by the dipole resonators, because motion of the metasurface is excited by a forcing tangential to the surface. For such boundaries, a new characteristic named “tangential impedance” is proposed. This is a ratio of the second derivative of the sound pressure along a coordinate tangential to the boundary to the normal velocity of the boundary. The dipole metasurface can be described by the equivalent tangential impedance. Reflection and absorption coefficients of the surface with the tangential impedance are found for a harmonic plane wave in dependance of an incidence angle. It is found that the angular dependences of the coefficients are very different for the monopole and dipole metasurfaces.
Resonant vessels in ancient and medieval buildings are the subject of some historical and acoustic research today. There have been a number of detailed surveys of European churches, where acoustic pots remain in the buildings. Despite the fact that in medieval Russia the use of built-in vessels was very common in the construction of churches, they have been hardly considered in recent publications. Therefore, the first goal of this paper is to give a brief overview of the Russian experience. Some of the most interesting examples of Russian churches are presented, and among them there may be a world record for the number of the vessels in a single room. The Church of St. Nicholas in Pskov has about 300 pots inserted into the walls, apse and pendentives. The second goal is to study the efficiency of acoustic vessels in an ordinary room. Acoustic measurements were carried out in the Rachmaninov Hall, which is part of the Moscow Conservatory. This chamber concert hall built over 100 years ago has 29 vessels. The first conclusion is that the vessels behave like resonators, their natural frequencies have been identified. The second conclusion is that we found no considerable changes of the acoustics due to the vessels.
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