Colombian physicists have reproduced the unusual acoustic effect observed at the Temple of Kukulcan, located on the Yucatan Peninsula in Mexico. The echo of hand clapping at the base of the pyramid resembles the chirping or chirping of a bird. Simulations showed that this effect occurs due to the addition of many waves reflected from the steps of the staircase leading to the top of the pyramid. The study was published in Physics Education.
Architectural acoustics became a separate science in the 19th century. Its tasks include the design of buildings and premises with certain acoustic properties. First of all, we are talking about the design of concert halls, theaters and cinemas, although the tasks of soundproofing houses and spaces are also relevant for it. You can read more about the fight against noise in the material “You drive more quietly.”
However, ancient architects had previously used the laws of acoustics to achieve the desired sound effects. Quite often their task was to enhance the religious experience when visiting places of worship, which was achieved through interesting resonance effects. For example, the whispering galleries of St Paul's Cathedral in London are a ring resonator in which the sound wave interferes with itself, propagating along the walls. Today, the term “whispering gallery resonator” has migrated to other branches of physics that deal with waves.
Another example of acoustics in the service of worship is the Temple of Kukulcan, erected by the ancient Mayans a thousand years ago. The temple is a pyramid 24 meters high and with sides equal to 55 meters. The pyramid is formed by nine square terraces, and on each of its sides there are steep staircases with 91 steps. The structure is crowned by a small temple for sacrifices, six meters high. The structure of the temple produces an interesting effect: if you clap your hands near its base, the echo that returns will resemble the chirping of the quetzal bird, sacred to the Mayans (the effect can be clearly heard in the video attached below). Its quantitative understanding requires knowledge of the laws of propagation and addition of sound waves.
Two Colombian physicists succeeded in reproducing the tweeting of the Kukulkan pyramid: Diego Fabian Vizcaino Arevalo from the Universidad Antonio Nariño and Olga Lucia Castiblanco Abril from the Universidad Distrital Francisco José de Caldas. To do this, they used one of the many amateur videos of the effect. The authors digitized the sound from the clap and processed it in such a way as to obtain the effect of reflection from all steps of the staircase. The spectrum of the simulated echo was a frequency comb, which is also present in the real echo.
The unusual phenomenon owes its existence to multiple reflections of sound from the steps of the stairs. Each subsequent stage sends back the same, but slightly delayed audio signal. Physicists estimate that this delay averages two milliseconds. If the original clap was “white”, that is, it contained a continuous frequency spectrum, then the result of the addition of many waves that differ from each other by a small phase delay will be a frequency comb, that is, a signal whose spectrum will consist of alternating dips and peaks.
To reproduce this effect, the authors extracted an audio track from one of the Youtube videos in which a man reproduces the chirping effect. Using Audacity, they calculated the delay between the clap and the echo, which turned out to be 115 milliseconds. This let physicists know that the man was standing 19.7 meters from the base of the pyramid. They took this into account when they modeled the time delays from each stage.
Next, scientists were convinced that cotton actually has a continuous spectrum in the range from 2 to 15 kilohertz. To simulate the echo, they needed to add this signal 91 times, but due to the limitations of the program, which only allowed 30 additions, the procedure had to be broken down into parts. However, the spectrum resulting from the procedure did contain a frequency comb. The peaks it contained were responsible for the chirping effect. The researchers also plotted the spectrum of echoes extracted from the video. It was noisier and quieter, but from it it was also possible to isolate a set of several frequencies whose amplitude was above the limit of audibility.
The effect studied by physicists is a bit like the effect of acoustic dispersion. There, too, the addition of waves arriving with different delays occurs, only they differ in frequency. Acoustic dispersion is responsible for the sound of a Star Wars blaster.