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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.