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                  Fig. 5. The theater of Epidaurus in Greece well-known for its wonderful acoustic properties.
that an appropriate periodicity, in combination with properly selected building materials, has a significant influence on the theater’s acoustics, and provides critically important design guidelines to improve the acoustical performance of modern outdoor theatres and sports stadiums. Investigations on the constructive influence of periodic seat rows, and later also on corrugated ceilings32 as band pass filters on the acoustics of rooms and theatres, resulted in a new architectural paradigm that not only changed the way we look at ancient buildings but also how we design new buildings. (see Fig. 5)
Explanation of acoustic marvels at the Pyramid of Chichen Itza in Mexico
As pointed out earlier, perpendicular pulse-echo ultra- sound experiments on corrugated surfaces were used in the 1990’s to determine the corrugation periodicity or to generate surface waves at certain frequencies. More complicated peri- odic structures, such as photonic and phononic crystals, were developed in the late 1990’s and into the 21st century. The first element of added complexity appeared in the 1990’s in experi- ments on oblique pulse-echo ultrasound. These experiments actually illuminated a striking feature of the El Castillo pyra- mid in Chichen Itza, on Mexico’s Yucatan peninsula. There, acoustic waves generated by a handclap were back-reflected by the immense ziggurat causing them to sound not like a hand- clap, but like a chirping Quetzal. This phenomenon has long intrigued not only tourists and archeologists, but also acousti- cians.4–11 Declercq et al.12 were the first to deliver a full explana- tion of this phenomenon based on a theoretical model and subsequent numerical simulations. This study received wide attention because of the widespread interest in this phenome- non in other branches of science and culture and because of the possibility that Mayans actually built pyramids not only as tremendous calendars but also as recordings of the chirp of the holy Quetzal Coatl (Kukulkan).
Another phenomenon, the so called raindrop effect, ear- lier believed to be caused by the partial hollowness of the pyramid, was explained by Cruz and Declercq13 as a natural effect caused by the staircase. (see Fig. 6)
Conclusions and continued research
Without being exhaustive we have tried to give a brief overview of fields in which diffraction of sound by a period- ic structure is of importance and we have to some extent explained our share in this exciting research area. As the fab- rication of new micron and nano materials has become com- mon practice, it is believed that more problems and applica- tions involving sound diffraction will need study the coming years. New results and new physical phenomena related to diffraction of sound are currently under investigation and can be expected as publications in the near future. AT
Research mentioned in this document covers collabora- tive work between Nico F. Declercq and (in alphabetical order) Sarah Benchabane, Mack A. Breazeale, Rudy Briers, Jorge Antonio Cruz Calleja, Joris Degrieck, Cindy S. A. Dekeyser, Katrien Dewijngaert, Roger D. Hasse, Sarah Herbison, Vincent Laude, Oswald Leroy, Jingfei Liu, Michael S. McPherson, Rayisa P. Moiseyenko, Bart Sarens, Alem A. Teklu, Katelijn Vanderhaeghe, John M. Vander Weide, Patricia Verleysen and has been sponsored in one way or another (travel grants, equipment grants, awards, project grants) by the following funding agencies: The French ‘Agence National de la Recherche’ (ANR), the Belgian agency for innovation by science and technology (IWT), the Belgian Fund for Scientific Research (FWO), The North Atlantic Treaty Organization (NATO), The French Conseil Regional de Lorraine (CRL), Georgia Tech, the National Center for Physical Acoustics (NCPA), the French ‘Centre National de la
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