Vibrating string

The string vibration is used in stringed instruments such as violin, guitar or piano to sound production. After excitation by brushing, plucking or stop the string performs a damped harmonic oscillation, whereby forming a standing transverse wave.

Physical Basics

The propagation velocity of the back and returning wave (not to be confused with the quickness with which the string vibrates ) is determined at homogeneous ( unwrapped ) strings of clamping force, string diameter and material density:

The propagation velocity of a wave is related to wavelength, and the oscillation period, or the frequency:

With the string length creates a fundamental frequency at which the vibration nodes located at the ends of the string, thus the wavelength is twice the length of string (). For the frequency applies:

This has the following dependencies that are also practically used in musical instruments when tuning or games found:

  • The shorter the ( oscillating) the string length, the higher the frequency (half the length is twice the frequency ).
  • The higher the clamping force, the higher the frequency ( of four times the force is double the frequency ).
  • A thinner string is, the higher the frequency ( half the diameter results in double the frequency ).

For braided strings, the calculation based on the mass of coating (kg / m) is helpful:

It can be seen that the mass coating received only by the root, that is, you have to weave around a string up to four times the mass per length to halve their resonant frequency. Therefore, metals with a high density ( copper, silver ) will be used for this purpose, to achieve deep shades with short, not too thick strings.

Strings have an amplitude-dependent resonance frequency, because it significantly increases the average clamping force at higher amplitude. This effect occurs especially at low tension and results in particular the low strings of an instrument sound a bit higher if they are heavily painted or plucked.

Swell

  • Manfred Zollner: Physics of Electric Guitar ( Research Documentation, PDF download available).
  • Acoustics
  • Chordophone
Wave propagation speed
702142
de