Music & Acoustics
Advanced

Vibrating String Frequency

Fundamental pitch of a string from length, tension and mass.

Formula

f=12LTμf = \frac{1}{2L}\sqrt{\frac{T}{\mu}}

Variables

fFrequency (Hz)
LString length (m)
TTension (N)
μMass per length (kg/m)

Example

L=0.65 m, T=80 N, μ=0.002: f ≈ 152 Hz

Did You Know?

Tightening a guitar string raises pitch as the square root of tension — quadruple the tension only doubles the note.

musicstringguitarharmonic

Share this formula

More in Music & Acoustics

View all

Equal-Temperament Note Frequency

Intermediate

Frequency of a note n semitones from a reference pitch.

Octave Frequency Ratio

Basic

An octave above a note has exactly double its frequency.

Sound Intensity Level (dB)

Intermediate

Sound intensity expressed in decibels relative to the hearing threshold.

Combining Two Sound Levels

Advanced

Total level when two sound sources play together.

Wave Speed

Basic

Sound speed equals frequency times wavelength.

Harmonic Series

Intermediate

Overtones of a note are whole-number multiples of the fundamental.