Editing Acoustics (section)

=== Early research in acoustics ===
[[Image:Harmonic partials on strings.svg|thumb|The [[Fundamental frequency|fundamental]] and the first 6 [[overtone]]s of a vibrating string. The earliest records of the study of this phenomenon are attributed to the philosopher [[Pythagoras]] in the 6th century BC.]]

In the 6th century BC, the ancient Greek philosopher [[Pythagoras]] wanted to know why some [[Interval (music)|combinations of musical sounds]] seemed more beautiful than others, and he found answers in terms of numerical ratios representing the [[harmonic]] [[overtone series]] on a string. He is reputed to have observed that when the lengths of vibrating strings are expressible as ratios of integers (e.g. 2 to 3, 3 to 4), the tones produced will be harmonious, and the smaller the integers the more harmonious the sounds. For example, a string of a certain length would sound particularly harmonious with a string of twice the length (other factors being equal). In modern parlance, if a string sounds the note C when plucked, a string twice as long will sound a C an octave lower.  In one system of [[musical tuning]], the tones in between are then given by 16:9 for D, 8:5 for E, 3:2 for F, 4:3 for G, 6:5 for A, and 16:15 for B, in ascending order.<ref>C. Boyer and [[Uta Merzbach|U. Merzbach]]. ''A History of Mathematics.'' Wiley 1991, p. 55.</ref>

[[Aristotle]] (384–322 BC) understood that sound consisted of compressions and rarefactions of air which "falls upon and strikes the air which is next to it...",<ref>{{cite web|title=How Sound Propagates|url=http://press.princeton.edu/chapters/s9912.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://press.princeton.edu/chapters/s9912.pdf |archive-date=2022-10-09 |url-status=live|publisher=Princeton University Press|access-date=9 February 2016}} (quoting from Aristotle's ''Treatise on Sound and Hearing'')</ref><ref>{{Cite book|last=Whewell, William, 1794–1866.|title=History of the inductive sciences : from the earliest to the present times. Volume 2|isbn=978-0-511-73434-2|location=Cambridge|oclc=889953932|page=295}}</ref> a very good expression of the nature of [[wave]] motion. ''[[On Things Heard]]'', generally ascribed to [[Strato of Lampsacus]], states that the pitch is related to the frequency of vibrations of the air and to the speed of sound.<ref>{{Cite book|title=Greek musical writings|date=2004|publisher=Cambridge University Press|others=Barker, Andrew|isbn=0-521-38911-9|edition=1st pbk.|location=Cambridge|oclc=63122899|page=98}}</ref>

In about 20 BC, the Roman architect and engineer [[Vitruvius]] wrote a treatise on the acoustic properties of theaters including discussion of interference, echoes, and reverberation—the beginnings of [[architectural acoustics]].<ref>ACOUSTICS, Bruce Lindsay, Dowden&nbsp;– Hutchingon Books Publishers, Chapter 3</ref> In Book V of his {{lang|la|[[De architectura]]}} (''The Ten Books of Architecture'') Vitruvius describes sound as a wave comparable to a water wave extended to three dimensions, which, when interrupted by obstructions, would flow back and break up following waves. He described the ascending seats in ancient theaters as designed to prevent this deterioration of sound and also recommended bronze vessels (echea) of appropriate sizes be placed in theaters to resonate with the fourth, fifth and so on, up to the double octave, in order to resonate with the more desirable, harmonious notes.<ref>Vitruvius Pollio, [https://archive.org/details/vitruviustenbook00vitr_0 ''Vitruvius, the Ten Books on Architecture''] (1914) Tr. Morris Hickey Morgan BookV, Sec.6–8</ref><ref>[[wikiquote:Vitruvius#Book V|Vitruvius]] article @Wikiquote</ref><ref>Ernst Mach, Introduction to ''The Science of Mechanics: A Critical and Historical Account of its Development'' (1893, 1960) Tr. Thomas J. McCormack</ref>

During the [[Islamic Golden Age|Islamic golden age]], Abū Rayhān al-Bīrūnī (973–1048) is believed to have postulated that the speed of sound was much slower than the speed of light.<ref>{{cite journal|arxiv = 1312.7288|title = The Science of Al-Biruni|first = Amelia Carolina|last = Sparavigna|s2cid = 119230163|doi = 10.18483/ijSci.364|volume = 2|issue = 12|date = December 2013|journal = International Journal of Sciences|pages = 52–60|url = https://www.ijsciences.com/pub/pdf/V220131220.pdf|bibcode = 2013arXiv1312.7288S|access-date = 2018-11-04|archive-date = 2018-07-21|archive-url = https://web.archive.org/web/20180721215451/https://www.ijsciences.com/pub/pdf/V220131220.pdf|url-status = live}}</ref><ref>{{cite web|url = http://www-groups.dcs.st-and.ac.uk/history/Biographies/Al-Biruni.html|title = Abu Arrayhan Muhammad ibn Ahmad al-Biruni|publisher = School of Mathematics and Statistics, University of St. Andrews, Scotland|date = November 1999|access-date = 2018-08-20|archive-url = https://web.archive.org/web/20161121101131/http://www-groups.dcs.st-and.ac.uk/history/Biographies/Al-Biruni.html|archive-date = 2016-11-21|url-status = dead}}</ref>

[[File:Amman Roman theatre.jpg|thumb|left|Principles of acoustics have been applied since ancient times: a [[Roman theatre (structure)|Roman theatre]] in the city of [[Amman]]]]

The physical understanding of acoustical processes advanced rapidly during and after the [[Scientific Revolution]]. Mainly [[Galileo Galilei]] (1564–1642) but also [[Marin Mersenne]] (1588–1648), independently, discovered the complete [[Mersenne's laws|laws of vibrating strings]] (completing what Pythagoras and Pythagoreans had started 2000 years earlier).  Galileo wrote "Waves are produced by the [[vibration]]s of a sonorous body, which spread through the air, bringing to the tympanum of the [[ear]] a stimulus which the mind interprets as sound", a remarkable statement that points to the beginnings of physiological and psychological acoustics. Experimental measurements of the [[speed of sound]] in air were carried out successfully between 1630 and 1680 by a number of investigators, prominently Mersenne. Inspired by Mersenne's ''Harmonie universelle'' (''Universal Harmony'') or 1634, the Rome-based Jesuit scholar [[Athanasius Kircher]] undertook research in acoustics.<ref>P. Findlen, ''Athanasius Kircher: The Last Man who Knew Everything'', Routledge, 2004, p. 8 and p. 23.</ref> Kircher published two major books on acoustics: the ''[[Musurgia Universalis|Musurgia universalis]]'' (''Universal Music-Making'') in 1650<ref>Athanasius Kircher, ''Musurgia universalis sive Ars magna consoni et dissoni'', Romae, typis Ludovici Grignani, 1650</ref> and the ''[[Phonurgia Nova|Phonurgia nova]]'' (''New Sound-Making'') in 1673.<ref>Athanasius Kircher, ''Phonurgia nova, sive conjugium mechanico-physicum artis & natvrae paranympha phonosophia concinnatum'', Campidonae: Rudolphum Dreherr, 1673.</ref> Meanwhile, [[Isaac Newton|Newton]] (1642–1727) derived the relationship for wave velocity in solids, a cornerstone of [[physical acoustics]] ([[Philosophiæ Naturalis Principia Mathematica|Principia]], 1687).