Mersenne’s laws

physics

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June 30, 2026

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Mersenne's laws describe how the fundamental frequency of a stretched string is determined by its length, tension, and mass per unit length. Specifically:1
* Frequency is inversely proportional to length.
* Frequency is directly proportional to the square root of tension.
* Frequency is inversely proportional to the square root of mass per unit length.1

These principles are crucial for understanding the construction and sound production of string instruments like guitars and violins. Marin Mersenne, a French mathematician, also explored numbers of the form 2ⁿ - 1, known as Mersenne numbers, some of which are prime numbers (Mersenne primes).123

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Mersenne’s laws
From equation (22) can be derived three “laws” detailing how the fundamental frequency of a stretched string depends on the length, tension, and mass per unit length of the string. Known as Mersenne’s laws, these can be written as follows:
Read More
From equation (22) can be derived three “laws” detailing how the fundamental frequency of a stretched string depends on the length, tension, and mass per unit length of the string. Known as Mersenne’s laws, these can be written as follows:
Read More