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en>Dicklyon
Reverted 1 edit by Drew776 (talk): Unexplained removal of relevant link. (TW)
 
en>Olli Niemitalo
Add units. "frequency" --> "center frequency".
 
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'''Mersenne's laws''' are [[Scientific law|laws]] describing the [[frequency]] of [[oscillation]] of a stretched [[Strings (music)|string]].<ref name="jeans">Jeans, James H. (1968). ''Science and Music'', {{page missing|date=October 2013}}. Dover, ISBN 978-0486619644.</ref> The equation was first proposed by French mathematician and music theorist [[Marin Mersenne]] in his 1637 work ''[[Traité de l'harmonie universelle]]''.<ref name="mersenne">Mersenne, Marin (1637). ''Traité de l'harmonie universelle'', {{page missing|date=October 2013}}. via the [[Bavarian State Library]].</ref> Mersenne's laws govern the construction and operation of [[string instruments]], [[piano]]s, [[harp]]s, 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 and have higher tension.


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==Equations==
The [[fundamental frequency]] is:


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*a) Inversely [[Proportionality (mathematics)|proportion]]al 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.


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:<math> f_1 \propto \tfrac{1}{L}.</math> (equation 26)


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:<math> f_1 \propto \sqrt{F}.</math> (equation 27)


  ghd lisseur cheeux Plus otre franchise la r��duire otre prime mensuelle de la couerture d'assurance. assurance sant�� ghd straighener est cher, il n'y a pas d'acqu��rir �� ce sujet - mais pour ceux qui consacrent un peu de temps sur Internet et renseigner certaines requ��tes difficiles de soi-m��me, ��pistage d'appareils transportables n'est pas effectu�� mon beaucoup de nos concurrents, n��anmoins il est un ��l��ment important de nos serices et r����le notre engagement �� offrir un grand serices de r��paration excellents.
:<math> f_1 \propto \frac{1}{\sqrt{\mu}}.</math> (equation 28)


Vos d��frisants peuent ��tre retourn��s beaucoup plus rapide que plusieurs heures, alors que m��me si elle est plus proche de heures, je suis garanti que ous coniendrez qu'il est n��anmoins un des serices rapides.<br><br>
These laws are derived from Mersenne's equation 22:<ref name="Steinhaus">Steinhaus, Hugo (1999). ''Mathematical Snapshots'', {{page missing|date=October 2013}}. Dover, ISBN 9780486409146.</ref>
:<math> f_1 = \frac{\nu}{\lambda} = \sqrt{\frac{F}{\mu}}.</math>


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The [[formula]] for the [[fundamental frequency]] is:
:<math> f=\frac{1}{2L}\sqrt{\frac{F}{\mu}}, </math>
 
where ''f'' is the frequency, ''L'' is the length, ''F'' is the force and ''&mu;'' is the mass per unit length.
 
==See also==
*[[Musical tuning]]
 
==References==
{{reflist}}
 
==External links==
*[http://scienceworld.wolfram.com/physics/MersennesLaws.html Mersenne's Laws] via [[Wolfram Research]]
 
{{Acoustics}}
[[Category:Musical tuning]]
[[Category:Empirical laws]]
 
{{music-stub}}

Latest revision as of 22:59, 1 November 2013

Mersenne's laws are laws describing the frequency of oscillation of a stretched string.[1] The equation was first proposed by French mathematician and music theorist Marin Mersenne in his 1637 work Traité de l'harmonie universelle.[2] 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 and have higher tension.

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.
(equation 26)
(equation 27)
(equation 28)

These laws are derived from Mersenne's equation 22:[3]

The formula for the fundamental frequency is:

where f is the frequency, L is the length, F is the force and μ is the mass per unit length.

See also

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

Template:Acoustics

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  1. Jeans, James H. (1968). Science and Music, Template:Page missing. Dover, ISBN 978-0486619644.
  2. Mersenne, Marin (1637). Traité de l'harmonie universelle, Template:Page missing. via the Bavarian State Library.
  3. Steinhaus, Hugo (1999). Mathematical Snapshots, Template:Page missing. Dover, ISBN 9780486409146.