Linear mass density or simply linear density is defined in the International System of Quantities (ISQ) as the quotient of mass and length. It is also called titer in textile engineering.
Although (linear) density is most often used to mean (linear) mass density, the concept can be generalized for the any other quantity per unit of length, called lineic quantities in ISQ.For example, linear charge density or lineic electric charge is the amount of electric charge per unit length.
A vibration in a string is a wave. Initial disturbance (such as plucking or striking) causes a vibrating string to produce a sound with constant frequency, i.e., constant pitch. The nature of this frequency selection process occurs for a stretched string with a finite length, which means that only particular frequencies can survive on this string. If the length, tension, and linear density (e.g., the thickness or material choices) of the string are correctly specified, the sound produced is a musical tone. Vibrating strings are the basis of string instruments such as guitars, cellos, and pianos. For a homogeneous string, the motion is given by the wave equation.
The scale length of a string instrument is the maximum vibrating length of the strings that produce sound, and determines the range of tones that string can produce at a given tension. It is also called string length. On instruments in which strings are not "stopped" (typically by frets or the player's fingers) or divided in length (such as in the piano), it is the actual length of string between the nut and the bridge.
String instruments produce sound through the vibration of their strings. The range of tones these strings can produce is determined by three primary factors: the linear density of the string, that is its mass per unit length (which is determined by its thickness and the density of the material), the tension placed upon it, and the instrument's scale length.