// multi-utility computation suite · offline · instant · precise
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sci.standing-wave-modes Calculator
Calculates standing wave resonance frequencies and mode shapes for strings, air columns (open and closed pipes), and 2D membranes. Fundamental frequency of a string: f₁ = (1/2L)√(T/μ) — a 65 cm guitar string at 80 N tension and 3.9 g/m linear density plays A = 110 Hz (open string A).
Inputs
String Length M
Linear measurement. Ensure consistent units: 1 m = 1,000 mm = 3.281 ft.
Wave Speed M S
Rate of movement. 1 m/s = 3.6 km/h = 2.237 mph.
Boundary
Reference formula or conversion factor shown for context.
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.
boundary conditions
Sample size or count used in the calculation.
f₁ string: v=√(T/µ)/2L
Sample size or count used in the calculation.
open pipe vs closed
LOS (length of stay) -- the number of days from admission to discharge. A key hospital efficiency metric.