Whispering galleries modeling Didier Cassereau 1 , Vincent Gibiat 2 and Pierre de Guibert 2 1 Laboratoire d’Imagerie Biom´ edicale, 15 rue de l’Ecole de M´ edecine, 75006 Paris, France 2 Laboratoire PHASE, Universit´ e Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex 9, France Abstract The whispering galleries phenomenon can be observed at various locations in the world, like the main dom of the St-Paul cathedral in London. Various physical interpre- tations of this phenomenon have been suggested by Lord Airy and Lord Rayleigh in the XIXth century, based on either multiple reflections of a wave in air or on surface waves that travel along the solid interface of the dom. In this work, we present various numerical simulations that can help understanding the propagation of a surface wave inside the solid layer that surrounds the volume of the dom. In particular we can observe how the incident energy is mainly trapped inside the solid shell. Measure- ments have been realised with a semi-closed cavity made of a 5cm-thick curved plasterboard, with microphones lo- cated at different positions near the wall. We present comparisons between experimental and nu- merical results, helpful to better understand the com- plexity of the measured signals. Introduction The whispering galleries phenomenon is a quite surpris- ing acoustic phenomenon that can be observed at var- ious locations in the world, like the main dome of the St-Paul cathedral in London: walking just under the dome, it is possible to whisper near the wall ; another visitor, located at a completely different location under the dome, can under some circumstances hear what we have whispered, although the large distance (40-50m) be- tween the two persons. Here we can mention some other famous locations in the world, where this kind of phe- nomenon can be observed: the Tabernacle in Salt Lake City (Mormon monument), the Galerie des Cariatides at the Louvre museum in Paris, or the Chaise-Dieu Abbey (Auvergne, France). A similar acoustic phenomenon can also be observed in some metro stations. A common feature of these various locations is that we consider an acoustic source located inside a reflecting and concave cavity. In this paper, we propose a numerical modelling of this phenomenon, with experimental measurements realised at a reduced scale. This allows to illustrate the existence of surface waves that travel along the wall. These surface waves can permanently radiate in direction of the inside of the cavity, and can consequently explain the whisper- ing galleries phenomenon. A few historical reminders The whispering galleries phenomenon has been observed at the end of the XIX th century under the dome of the St-Paul cathedral in London: • 1871 : Lord Airy, Astronomer Royal of the Great Britain Court (1835-1881), provides a physical inter- pretation in terms of geometrical acoustics, includ- ing multiple reflections of the signal on the walls of the concave cavity, • 1896 : Lord Rayleigh disputes Airy’s interpretation and gives his own explanation in terms of modal propagation inside the volume, associated with sur- face waves that propagate along the wall, • 1904, 1910 : Rayleigh realizes an experimental mea- surement at a reduced scale in his laboratory, • 1922 : Raman and Sutherland confirm Rayleigh’s in- terpretation. One of the fundamental questions that arises from this work is the following: what can we really measure in an experiment like Rayleigh’s experiment? Nowadays, the available experimental equipments are significantly more efficient than at the beginning of the XX th century. We now also have the possibility to run numerical simulations to try to understand the phenomenon. Rayleigh’s experiment The Rayleigh’s experiment, at the beginning of the XX th century, is illustrated by Figure 1. It uses a thin cylin- drical metallic plate of diameter 2m. The source is a bird call (B) that mainly behaves as a small organ pipe, with a frequency near 4kHz, and a sensitive flame (F) is used as detector. As a preliminary step for this experiment, it has been verified that no direct sound, from the source to the detector, could be detected by the sensitive flame. A first measurement is done using a free metallic plate: the sensitive flame flickers, revealing the existence of a vibration in air. Then, a second measurement is done by adding an obturating screen (W) on the metallic plate: the sensitive flame does not show any movement. The interpretation given by Rayleigh to these observa- tions is based on a surface wave that propagates along the metallic plate and permanently radiates back in air. In the presence of the obturating screen, this surface wave cannot reach the sensitive flame, therefore resulting in the absence of any movement. It results therefore that this experiment, realized at a reduced scale, a priori con- DAGA 2016 Aachen 264