Mersenne’s laws of vibrating strings
E609411
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.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Mersenne’s laws relating frequency, length, and tension of a string | 1 |
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 NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| 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 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Mersenne’s laws relating frequency, length, and tension of a string