Strings and Waves

    The root frequency for a string is proportional to the suqare root of the tension, ... inversly proportional to its length, and [inversly proportional] to the square root of its mass per unit length (Roederer 109). This ten accounts for the different masses and tensions of strings of the same length to create different pitches of guitar strings. Individual pitches on the strings are created by pressing down beneath a fret, thus affectively shortening the length of the string. This new string legth is L [1 - 1/(2^1/12)] where L is the length of the string at the last fret. or L/17.817. This number is figured out by determining that the semitone intervial, or relationship between two of the twelve notes that create a chromatic scale, is 2¹² (Evans 85). By applying this to itself, after 12 times, the length of the string is halved, creating an octave, or a frequency of twice the hertz.

    How the string resonates on a simple pluck can be found. A relatively high ratio of transverse to longitudinal force along the string makes the face plate and bridge resonate, while higher longitudninal forces makes the back and cavity resonate more. These forces can be measured as F_T = (T₀ + dT)sinø, and F_L = T₀ + EA/L₀ dL where T is the tension, ø is the angle between the string and the neck, E is the electic modulus of the string, A is the cross-sectional area, and L is the length of the string (Fletcher 209).

    In adition, the method by which the string is plucked will also affect the sound produced. There are too many forces that interact with each other in too many complex ways to list them all. In itís lightest a guitar can be viewed as the simple harmonic motion of a string, but the sound representing that sine wave is quite different than that of the guitar. It is all the unmeasurable, and unique qualities on the guitar that truly make it sound the way it does.