Recherches sur la courbe que forme une corde tendue mise en vibration.

d'Alembert, J. l. R. (1747). Recherches sur la courbe que forme une corde tendue mise en vibration. Histoire de l'Académie Royale des Sciences et Belles-Lettres de Berlin, 3, 214-219.

Type

Journal article

Intellectual base

Primary research

Year

1747

Link

no authoritative link yet

Cited from

physics

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Oscillation
  • . Amplitude and phase. The oscillation has a definable amplitude (how far it swings) and phase (where in the cycle it currently sits), allowing diagnostic characterization. Source of energy or driving, if persistent. Free oscillations decay through dissipation unless undriven and conservative; sustained oscillations require either conservative dynamics (idealized) or a driving source that resupplies what dissipation removes. d'Alembert's 1747 analysis of coupled oscillation in vibrating strings

    This sourceDerives and solves the wave equation for a vibrating string as a coupled oscillator system; establishes the principle that spatial oscillators couple through elastic forces, linking the local oscillation at each point to neighboring points and introducing wave propagation as a manifestation of coupled oscillation.

• Wave
  • The modern wave equation

    This sourceDerives and solves the one-dimensional wave equation for a vibrating string; establishes d'Alembert's solution and the principle of superposition for waves; first rigorous treatment of wave propagation.

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