Free String Vibration Calculator
Calculate the frequency of a vibrating string using f = (n / (2L)) * sqrt(T / mu).
m
N
kg/m
Frequency
207.83 Hz
Wave Speed on String270.19 m/s
Frequency vs Harmonic Number (n)
Vibrating String
A string fixed at both ends supports standing waves whose frequencies depend on string length, tension, and mass per unit length.
Formula
f_n = (n / 2L) * sqrt(T / mu)
where T is tension, mu is linear mass density (kg/m), L is string length, and n is the harmonic number.
Example Calculation
A guitar string: L = 0.65 m, T = 73 N, mu = 0.001 kg/m, fundamental.
- 01v = sqrt(T / mu) = sqrt(73 / 0.001) = sqrt(73000) = 270.2 m/s
- 02f = (1 / (2 * 0.65)) * 270.2
- 03f = 0.769 * 270.2
- 04f = 207.8 Hz
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