147th ASA Meeting, New York, NY

Jos Snchez-Dehesa- jsdehesa@upvnet.upv.es
Andreas Hkansson, Francisco Cervera
Nanophotonics Technology Center
Univ. Polytechnic of Valencia
E-46022 Valencia, Spain
F. Meseguer
(Unidad Asociada CSIC-UPV, Valencia, Spain)
B. Manzanares-Martnez, F. Ramos-Mendieta
(CIFUS, Univ. of Sonora, Hermosillo, Mexico)

Popular version of paper 5aAA8
Presented Friday morning, May 28, 2004
147th ASA Meeting, New York, NY

The Maya is the most notable of the classical civilizations in Mesoamerica. Calendrical documents have demonstrated that mathematics and astronomy are among the intellectual hallmarks of the Maya. They also made fundamental achievements in monumental architecture; the Maya built magnificent ceremonial buildings, such as pyramidal temples as well as palaces and observatories. Recent research has uncovered equally remarkable acoustic properties associated with Mayan architecture. For example, there are ball courts that are characterized by the fact that a whisper at one end can be heard clearly at the other more than 500 feet away. Another example is the Kukulkan temple at Chichen Itza in Yucatan (Mxico): a handclap made in front of one of the stairs stimulates two chirped echoes that are similar to the Quetzal bird chirps. The connection between the pyramid of Kukulkan and the Queztal bird is supported by a Mayan glyph from the Dresden Codex.

The Totonac were contemporary with the Maya and shared a similar culture. The Totonac also configured their architecture in such a way that time and space were integrated. They also constructed  magnificent buildings. The most known are located at El Tajin in the state of Veracruz (Mxico). Here, we report studies made at the ceremonial site of Cempoala, located near the city Veracruz. The architecture in this site is characterized by the crenellations of the buildings.  A sonic effect similar to the one reported in the pyramid at Chichen Itza also was recorded by us in front of the pyramid called The Chimneys. Here, we report our acoustical study of the larger round structure (see Figs. 1-2). According to the booklet provided to the visitors this structure is "associated with gladiator worship of Mexica (Aztec) origin, although it may have served as an intake for rainwater." This monument was made by walls of rolling stones and clay with stuccowork. The stucco has completely disappeared (see Fig. 2). Nevertheless, a singular sonic effect is detectable by one's own ears in spite of the poor state of conservation of the walls.

Figure 1. The so called "gladiator circle"	Figure 2. A closer view of the circle

 The Acoustical Phenomenon

     Mr. Bernardo Mendoza, a volunteer guide at the site, claims to be the first person who observed the sonic effect reported here. He made us the following demonstration. First, he

Fig. 3  Mr. Mendoza doing the demonstration

placed us at one selected point inside the circle. This point was placed along the diameter that coincides with the East-West direction and separated about two meters from the center. Then, he went to the border of the circle and walked towards us, speaking at the same time. When he arrived at about the same distance from the center in front of us, we suddenly noticed reinforcement of Mr. Mendoza's voice that seemed to come from all directions. This effect puzzled us so much that we came back after few months to characterize it. Our basic equipment was a loudspeaker, several microphones and a laptop for sound generation, data recording and analyzing. The experimental set-up is described schematically in Figure 4. In brief, the sound emitter (E), which is placed at one predetermined position on the East-West direction, emits a 5 ms pulse consisting in a 440 Hz sinusoidal signal. A microphone receiver (R) connected to the laptop records both the direct and the reflected/diffracted sound by the round wall. Figure 5 represents the data recorded at R for several positions along the E-W direction. The time origin is chosen when the signal is emitted at E. Different sound signals can be distinguished on the plots shown in Fig. 5: 1) ballistic (highlighted in yellow), it is the first arriving at R; 2) 1^st echo (highlighted in green), which arrives at R after one reflection by the round wall; and 3) 2^nd echo (highlighted in blue), which corresponds to the sound that arriving after two reflections at the wall. The time signals in Figure 5 show that when the microphone is at around 1.65 m (position F in Figure 4) the first echo  becomes comparable in magnitude to the ballistic sound. This fact characterizes the phenomenon that is noticed by one's own ears. A series of experiments were performed to confirm the phenomenon and they demonstrated that the phenomenon is very robust; it holds even at heights as larger as 3 meters above the ground. Therefore, it can be concluded that the circle acoustically behaves as an ellipse since two singular points inside the circle, E and F, behave as the foci of an elliptical cavity. It is clear that this anomalous phenomenon comes out from the sound scattering by the round crenellated wall. A theoretical treatment of the exact  problem is a cumbersome task. Nevertheless, an empirical model can be worked out  in order to obtain a physical insight of this phenomenon. Thus, on an existing flat crenellated wall we established as a function of the angle impinging the wall the points at which the sound could be considered as effectively reflected by a rigid wall. We concluded that the circle can be replaced by a rigid wall whose shape can be approximated by the low eccentric ellipse that is represented by a red line in Figure 4; it looks like a "flattened circle." The foci of this ellipse are in agreement with the positions at which the acoustical phenomenon was measured.

 

Figure 4. Scheme of the circle and possible paths for sound propagation inside the circle	Figure 5. Pulse propagation measurements

The Circle of Venus

Contrary to the information provided to the visitors, we speculate that this monument could be devoted to the god of wind (Ehcatl). Effectively, round structures found in Mesoamerica were devoted to this god since it was told that "the god of wind hates the angles that break the flux of air." Also, we believe that this monument and the full ceremonial site was probably dedicated to Quetzacatl, the "sovereign plumed serpent," the main deity of the pre-Colombian religion in Mesoamerica. In this light, the crenellated walls would represent the undulations of the "sacred serpent". Moreover, we propose that the Totonac encoded in this round structure their knowledge about the movement of Venus. For example, we have found that when the more important

Figure 6. The Calendrical stone Nahoui  Ollin inscribed in the circle of Venus

Calendrical stone Nahui Ollin of Malinalco is inscribed into the circle (see Figure 6), a series of coincidences accurs, the more remarkable being that the internal circle of the Nahui Ollin, which might represent the orbit of earth, coincides with the circle passing trough the acoustical foci. Since the center of the Nahui Ollin is believed to define the position of the sun, the external circle could be referred to the orbit of Venus. The most remarkable fact is that, acoustically, the orbit of Venus appeared as a "flattened circle." But, when one studies the flattened circles of the Mesoamerican art, one always observes that the ratio between the larger diameter to the shorter gives a number between 1.05 and 1.07. The "flattened circle" acoustically determined in this round structure gives 1.05. The question is, was all this accidental or by design? We hope that this work stimulates further studies about the possible link between acoustics, architecture and astronomy in the classical Mesoamerican cultures.

Acknowledgements. Work financially supported by Universidad Autnoma of Madrid and Banco  Santander-Central-Hispano of Spain. We also thank to CONALCULTA-INAH-MEX that provided us with technical support and permissions.