Mersenne’s laws of vibrating strings

E609411

acoustics law physical law wave theory principle

Mersenne’s laws of vibrating strings are early 17th-century mathematical relations that quantify how a string’s frequency depends on its length, tension, and mass per unit length, forming a foundation of musical acoustics and wave theory.

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All labels observed (3)

Label	Occurrences
Mersenne’s laws of acoustics	1
Mersenne’s laws of vibrating strings canonical	1
Mersenne’s laws relating frequency, length, and tension of a string	1

How this entity was disambiguated

This entity first appeared as the object of triple T6642033 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Mersenne’s laws of vibrating strings
Context triple: [Marin Mersenne, knownFor, Mersenne’s laws of vibrating strings]

A. The Theory of Sound
The Theory of Sound is Lord Rayleigh’s landmark two-volume treatise that systematically established the mathematical and experimental foundations of acoustics.
B. The Dynamical Theory of Sound
The Dynamical Theory of Sound is a foundational treatise by mathematician and physicist Horace Lamb that rigorously develops the mathematical principles underlying acoustics and wave propagation.
C. The Science of Musical Sound
The Science of Musical Sound is a book by engineer and acoustics researcher John R. Pierce that explains the physical and perceptual principles underlying how music and sound are produced, transmitted, and heard.
D. The Physics of Music
The Physics of Music is a foundational text that explains how physical principles such as vibration, resonance, and wave behavior give rise to musical sounds and acoustical phenomena.
E. Pythagorean harmony of the spheres
The Pythagorean harmony of the spheres is an ancient philosophical and cosmological concept proposing that the movements of celestial bodies produce a hidden, mathematically ordered music reflecting the harmony of the universe.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Mersenne’s laws of vibrating strings
Target entity description: Mersenne’s laws of vibrating strings are early 17th-century mathematical relations that quantify how a string’s frequency depends on its length, tension, and mass per unit length, forming a foundation of musical acoustics and wave theory.

A. The Theory of Sound
The Theory of Sound is Lord Rayleigh’s landmark two-volume treatise that systematically established the mathematical and experimental foundations of acoustics.
B. The Dynamical Theory of Sound
The Dynamical Theory of Sound is a foundational treatise by mathematician and physicist Horace Lamb that rigorously develops the mathematical principles underlying acoustics and wave propagation.
C. The Science of Musical Sound
The Science of Musical Sound is a book by engineer and acoustics researcher John R. Pierce that explains the physical and perceptual principles underlying how music and sound are produced, transmitted, and heard.
D. The Physics of Music
The Physics of Music is a foundational text that explains how physical principles such as vibration, resonance, and wave behavior give rise to musical sounds and acoustical phenomena.
E. Pythagorean harmony of the spheres
The Pythagorean harmony of the spheres is an ancient philosophical and cosmological concept proposing that the movements of celestial bodies produce a hidden, mathematically ordered music reflecting the harmony of the universe.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	acoustics law ⓘ physical law ⓘ wave theory principle ⓘ
appliesTo	ideal stretched string ⓘ
appliesToInstrument	guitar ⓘ harp ⓘ piano ⓘ violin ⓘ
assumes	constant tension ⓘ perfect flexibility of the string ⓘ small amplitude vibrations ⓘ uniform linear mass density ⓘ
category	classical mechanics ⓘ theoretical acoustics ⓘ
combinedFormula	f = (1 / 2L) · √(T / μ) ⓘ
describedIn	Harmonie universelle ⓘ
field	mechanics ⓘ musical acoustics ⓘ physics ⓘ vibrations ⓘ
formulatedInCentury	17th century ⓘ
formulatedInDecade	1630s ⓘ
foundationFor	theory of musical pitch for string instruments ⓘ
historicalSignificance	early quantitative link between music and mathematics ⓘ precursor to modern string vibration theory ⓘ
implies	wave speed on a string equals √(T / μ) ⓘ
influenced	development of wave equation ⓘ later work in mathematical physics of vibrations ⓘ
involvesQuantity	fundamental frequency ⓘ harmonics ⓘ wave speed on a string ⓘ
mathematicalForm	f ∝ 1 / L ⓘ f ∝ 1 / √μ ⓘ f ∝ √T ⓘ
namedAfter	Marin Mersenne ⓘ
publicationYear	1636 ⓘ
relatesQuantity	frequency of vibration ⓘ mass per unit length ⓘ string length ⓘ string tension ⓘ
states	frequency is inversely proportional to string length ⓘ frequency is inversely proportional to the square root of mass per unit length ⓘ frequency is proportional to the square root of tension ⓘ
usedIn	design of stringed musical instruments ⓘ tuning of stringed instruments ⓘ
validUnderCondition	fixed boundary conditions at both ends ⓘ linear elastic behavior of the string ⓘ negligible stiffness of the string ⓘ

How these facts were elicited

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Marin Mersenne → knownFor → Mersenne’s laws of vibrating strings ⓘ

Marin Mersenne → formulated → Mersenne’s laws relating frequency, length, and tension of a string ⓘ

linked to: Mersenne’s laws of vibrating strings

Mersenne → hasEponymousConcept → Mersenne’s laws of acoustics ⓘ