Freq. Fundamental Corda
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
corda
About this calculator
The fundamental frequency calculator for a string determines the lowest vibration frequency of a string fixed at both ends. This frequency, called the fundamental or first harmonic, depends on the string length, tension, and linear mass density. The formula used is f = (1/2L) * √(T/μ), where L is length, T is tension, and μ is linear density. The result is given in hertz (Hz).
To use the calculator, enter the string length in meters, tension in newtons, and linear density in kg/m. The tool automatically computes the fundamental frequency. For example, a guitar string with 0.65 m, tension 80 N, and density 0.004 kg/m has a fundamental frequency of about 110 Hz (A2 note). This calculator is useful for musicians, audio engineers, and physics students.
Ensure tension is in newtons and linear density in kg/m. Convert other units beforehand. The formula applies only to ideal strings (no stiffness) and the fundamental frequency is the lowest; higher harmonics are integer multiples. The calculator does not account for damping or nonlinear effects.
Frequently asked questions
What is the fundamental frequency of a string?
It is the lowest frequency at which the string naturally vibrates, corresponding to the first mode of vibration. It determines the musical note produced.
How does tension affect frequency?
Frequency increases with the square root of tension. Tightening the string (increasing tension) raises the frequency (higher pitch).
Can I use the calculator for strings of different materials?
Yes, as long as you know the linear mass density (μ) of the material. The formula is general for ideal strings.
What is the unit of linear density used?
kg/m (kilogram per meter). If you have g/m, divide by 1000 to convert.
Does the calculator account for string stiffness?
No. The formula assumes a perfectly flexible string. For very thick or stiff strings, the actual frequency may be slightly higher.