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 Computational Methods and Techniques Across Acoustics
Grant C. Eastland
   Sound in the World
Throughout human history, people and cultures have cre- ated sound for more than simple communication. For example, early humans likely made music using primitive flutes (Atema, 2014) and considered sound integral in the design of cities (e.g., Kolar, 2018). Furthermore, the Mayans designed structures at the ruins at Chichen Itza in Mexico that used sound for worship (Declercq et. al., 2004). Specifically, clapping in front of the stairs of the El Castillo pyramid creates a sound resembling a highly revered bird by way of a series of reflections up the stairs (available at
In addition to an interest in making sound, sound and vibration have also been thoroughly investigated by either empirical methods or philosophical arguments since as far back as Pythagoras (550 BCE), who applied his discoveries in mathematics to the harmonic ratios in music. He dis- covered that stringed instruments could be tuned, using small integer ratios of string length, so that they would consistently produce layered consonant musical intervals.
The interest and desire to study our acoustic environ- ment continues to this day, but the methods we use have changed dramatically, and continue to change as new technologies emerge. Beginning in the seventeenth cen- tury with Robert Boyle, empirical investigation showed that sound is a vibration of conceptualized fluid particles transmitting energy from one place to another. Theoreti- cal and empirical investigations are essential but more often require additional help to solve the problems at hand. Indeed, applying sophisticated computational methods, the basis of this article, provides a valuable tool in understanding and analyzing acoustics phenomena.
The Need for Computational Acoustics
The need for computational acoustics shows itself in the difficulty in most real-world physical investigations in
acoustics, often requiring solving the acoustic wave equa- tion. Indeed, there is potential for advancement in new areas of research not contained in the traditional areas by employing computational acoustics. This is already seen from the great developments and advancements in all areas of acoustics over several decades where the com- plexity has required extensive use of numerical methods, optimization, computational modeling, and simulation.
Like the relationships of computational physics to math- ematics and computer science, the relationship between acoustics, mathematics, and computer science define computational acoustics as described by the Venn-type diagram shown in Figure 1.
The Wave Equation Explained
The wave equation enables the expression of motion in a wave, and it shows itself in every area of physics includ- ing acoustics, electromagnetism, quantum mechanics, and optics, to name a few. The equation provides the
  10 Acoustics Today • Spring 2021 | Volume 17, issue 1
Figure 1. Venn diagram showing the concept relationship of computational acoustics, indicating how it connects traditional acoustics with mathematics and computer science.

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