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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Mersenne's laws ： ウィキペディア英語版 Mersenne's laws Mersenne's laws are laws describing the frequency of oscillation of a stretched string.〔Jeans, James H. (1968). ''Science and Music'', . Dover, ISBN 978-0486619644. Cited in "(Mersenne's Laws )", ''Wolfram.com''.〕 The equation was first proposed by French mathematician and music theorist Marin Mersenne in his 1637 work ''Traité de l'harmonie universelle''.〔Mersenne, Marin (1637). ''Traité de l'harmonie universelle'', . via the Bavarian State Library. Cited in "(Mersenne's Laws )", ''Wolfram.com''.〕 Mersenne's laws govern the construction and operation of string instruments, pianos, harps, which must accommodate the total tension force required to keep the strings at the proper pitch. Lower strings are thicker, thus having a greater mass per unit length. They typically have lower tension. Higher-pitched strings typically are thinner, have higher tension, and may be shorter. ==Equations== The fundamental frequency is: *a) Inversely proportional to the length of the string, *b) Proportional to the square root of the stretching force, and *c) Inversely proportional to the square root of the mass per unit length. :$f\_1\; \backslash propto\; \backslash tfrac.$ (equation 26) :$f\_1\; \backslash propto\; \backslash sqrt.$ (equation 27) :$f\_1\; \backslash propto\; \backslash frac\; =\; \backslash frac\backslash sqrt\}.$ The formula for the fundamental frequency is: :$f\_0=\backslash frac\backslash sqrt\},$ where ''f'' is the frequency, ''L'' is the length, ''F'' is the force and ''μ'' is the mass per unit length. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Mersenne's laws」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.