A vibration

Vibration

Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...

 in a string

Strings (music)

A string is the vibrating element that produces sound in string instruments, such as the guitar, harp, piano, and members of the violin family. Strings are lengths of a flexible material kept under tension so that they may vibrate freely, but controllably. Strings may be "plain"...

 is a wave

Wave

In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

. Usually a vibrating string produces a sound

Sound

Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...

 whose frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

 in most cases is constant. Therefore, since frequency characterizes the pitch

Pitch (music)

Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...

, the sound produced is a constant note

Note

In music, the term note has two primary meanings:#A sign used in musical notation to represent the relative duration and pitch of a sound;#A pitched sound itself....

.
Vibrating strings are the basis of any string instrument

String instrument

A string instrument is a musical instrument that produces sound by means of vibrating strings. In the Hornbostel-Sachs scheme of musical instrument classification, used in organology, they are called chordophones...

 like guitar

Guitar

The guitar is a plucked string instrument, usually played with fingers or a pick. The guitar consists of a body with a rigid neck to which the strings, generally six in number, are attached. Guitars are traditionally constructed of various woods and strung with animal gut or, more recently, with...

, cello

Cello

The cello is a bowed string instrument with four strings tuned in perfect fifths. It is a member of the violin family of musical instruments, which also includes the violin, viola, and double bass. Old forms of the instrument in the Baroque era are baryton and viol .A person who plays a cello is...

, or piano

Piano

The piano is a musical instrument played by means of a keyboard. It is one of the most popular instruments in the world. Widely used in classical and jazz music for solo performances, ensemble use, chamber music and accompaniment, the piano is also very popular as an aid to composing and rehearsal...

.

The speed of propagation of a wave in a string () is proportional to the square root of the tension of the string () and inversely proportional to the square root of the linear density () of the string:


Let be the length

Length

In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

 of a piece of string, its mass

Mass

Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

, and its linear mass.