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sci.string-vibration-harmonics Calculator
Calculates vibrating string harmonics: f_n = n/(2L) × √(T/µ), where T is tension, µ is linear density, and L is length. Guitar A-string (L = 65 cm, T = 80 N, µ = 3.9 g/m): f₁ = 110 Hz — harmonics f₂ = 220, f₃ = 330, f₄ = 440 Hz (the next A) give the characteristic timbre.
Inputs
L M
Linear measurement. Ensure consistent units: 1 m = 1,000 mm = 3.281 ft.
T N
Reference formula or conversion factor shown for context.
Mu G M
Mass per unit volume (kg/m³). Water: 1,000. Air: 1.225. Steel: 7,850. Affects buoyancy, flow, and structural loads.
Results
fundamental frequency f₁ (Hz)
Sample size or count used in the calculation.
2nd harmonic f₂ (Hz)
Sample size or count used in the calculation.
3rd harmonic f₃ (Hz)
Sample size or count used in the calculation.
4th harmonic f₄ (Hz)
Sample size or count used in the calculation.
f₁ = √(T/μ) / (2L)
Reference formula or conversion factor shown for context.