What is Wave equation?
{{multiple image | direction = vertical | width = 250 | image1 = Wave equation 1D fixed endpoints.gif | caption1 = A [[pulse (physics)|pulse]] traveling through a string with fixed endpoints as modeled by the wave equation. | image2 = Spherical wave2.gif | caption2 = Spherical waves coming from a point source. }} [[Equation]]s that describe [[wave]]s as they occur in nature are called '''wave equations'''. Waves as they occur in [[river]]s, [[lake]]s, and [[ocean]]s are similar to those of [[sound]] and [[light]]. The problem of having to describe waves arises in fields like [[acoustics]], [[electromagnetism|electromagnetics]], and [[fluid dynamics]]. Historically, the problem of a vibrating string such as that of a [[musical instrument]] was studied by [[Jean le Rond d'Alembert]], [[Leonhard Euler]], [[Daniel Bernoulli]], and [[Joseph-Louis Lagrange]].<ref>{{cite book|last1=Cannon|first1=John T.|last2=Dostrovsky|first2=Sigalia|title=The evolution of dynamics, vibration theory from 1687 to 1742|year=1981|volume=6|series=Studies in the History of Mathematics and Physical Sciences|url=http://homes.chass.utoronto.ca/~cfraser/vibration.pdf|isbn=0-3879-0626-6|publisher=Springer-Verlag|location=New York|pages=ix + 184 pp|access-date=2014-05-17|archive-date=2016-12-29|archive-url=https://web.archive.org/web/20161229061211/http://homes.chass.utoronto.ca/~cfraser/vibration.pdf|url-status=dead}}] {{cite journal|last= GRAY|first=JW|title=BOOK REVIEWS |journal=BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY |date=July 1983 |volume= 9| issue = 1}} (retrieved 13 Nov 2012).</ref><ref>Gerard F Wheeler. [https://www.scribd.com/doc/32298888/The-Vibrating-String-Controversy-Am-J-Phys-1987-v55-n1-p33-37 The Vibrating String Controversy,] (retrieved 13 Nov 2012). Am. J. Phys., 1987, v55, n1, p33-37.</ref><ref>For a special collection of the 9 groundbreaking papers by the three authors, see [http://www.lynge.com/item.php?bookid=38975&s_currency=EUR&c_sourcepage= First Appearance of the wave equation: D'Alembert,