معادلة موجية: الفرق بين النسختين

 

وتاريخيا فكان الصوت هو أول ما درسه العلماء في اهتزاز الأوتار في مختلف [[آلة موسيقية|الآلات الموسيقية]] . واهتم بتلك الدراسا العلماء "جين دي لامبرت" و "ليونهارد أويلار " و "دانيل بيرنولي" و [[جوزيف لوي لاغرانج|جوزيف لاغرانج]] .<ref>[http://homes.chass.utoronto.ca/~cfraser/vibration.pdf {{cite journal|الأخير1= Cannon |الأول1=John T.|الأخير2=Dostrovsky|الأول2=Sigalia|العنوان=The evolution of dynamics, vibration theory from 1687 to 1742|السنة=1981|volume= 6|series=Studies in the History of Mathematics and Physical Sciences|ISBN= 0-3879-0626-6|الناشر=Springer-Verlag|المكان=New York|الصفحات=ix + 184 pp.}}] {{cite journal|الأخير= GRAY|الأول=JW|العنوان=BOOK REVIEWS |journal=BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY |السنة=1983|الشهر=July |volume= 9| issue = 1}} (retrieved 13 Nov 2012). {{Webarchive|url=https://web.archive.org/web/20161229061211/http://homes.chass.utoronto.ca/~cfraser/vibration.pdf |date=29 ديسمبر 2016}}</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. {{Webarchive|url=https://web.archive.org/web/20160305003539/https://www.scribd.com/doc/32298888/The-Vibrating-String-Controversy-Am-J-Phys-1987-v55-n1-p33-37 |date=05 مارس 2016}}</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. {{Webarchive|url=https://web.archive.org/web/20200209023122/http://www.lynge.com/item.php?bookid=38975&s_currency=EUR&c_sourcepage= |date=9 فبراير 2020}}</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) {{Webarchive|url=https://web.archive.org/web/20141222032839/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 |date=22 ديسمبر 2014}}</ref>