檢視波动方程式的原始碼

'''波动方程'''或称'''波方程'''（{{lang-en|'''wave equation'''}}）是一种重要的[[偏微分方程]]，主要描述[[自然界]]中的各种的[[波动]]现象，包括横波和纵波，例如[[声音|声]]波、[[光]]波、[[无线电波]]和[[水]]波。波动方程抽象自[[声学]]、[[物理光学]]、[[电磁学]]、[[电动力学]]、[[流体力学]]等领域。

历史上许多科学家，如[[达朗贝尔]]、[[欧拉]]、[[丹尼尔·伯努利]]和[[拉格朗日]]等在研究[[乐器]]等物体中的弦振动问题时，都对波动方程理论作出过重要贡献。<ref>[http://homes.chass.utoronto.ca/~cfraser/vibration.pdf {{cite journal|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|ISBN= 0-3879-0626-6|publisher=Springer-Verlag|location=New York|pages=ix + 184 pp.}}] {{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. [http://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, Leonhard Euler, Daniel Bernoulli. - the controversy about vibrating strings] (retrieved 13 Nov 2012). Herman HJ Lynge and Son.</ref><ref>For de Lagrange's contributions to the acoustic wave equation, can consult [http://books.google.co.uk/books?id=D8GqhULfKfAC&pg=PA18&lpg=PA18&dq=lagrange+paper+on+the+wave+equation&source=bl&ots=E-RPop_GGD&sig=aJ41g1nlDTDKUqvw9OAXFjjutV4&hl=en&sa=X&ei=KCPEUMaOCI2V0QXz5YC4DQ&ved=0CDQQ6AEwAQ#v=onepage&q=lagrange%20paper%20on%20the%20wave%20equation&f=false Acoustics: An Introduction to Its Physical Principles and Applications] Allan D. Pierce, Acoustical Soc of America, 1989; page 18.(retrieved 9 Dec 2012)</ref>  1746年，达朗贝尔发现了一维波动方程，欧拉在其后10年之内发现了三维波动方程。<ref name=Speiser>Speiser, David.  ''[http://books.google.com/books?id=9uf97reZZCUC&pg=PA191 Discovering the Principles of Mechanics 1600-1800]'', p. 191 (Basel: Birkhäuser, 2008).</ref>