Physics of the acoustic guitar

Ok, let's get started.

Many musicians who play guitar do not have an idea about the workings of their guitar - the physics and the math that makes playing of a guitar possible.

Throw your mind back to your high-school physics (or check here if your mind refuses to get thrown!) and recall string vibration theory, where,

f = 1/(2L) * √(T/u), where,
f = frequency of vibration of string,
L = Vibrating length of string
T = Tension in string
u = mass/unit length of string

In a guitar (see here for the parts of a guitar)
- The frequency (f) is percieved as the pitch of the note played on the guitar.
- The vibrating length (L) of an open string is the length between the bridge and the nut, and this is changed by fretting any of the frets, decreasing the vibrating length.
- The tension (T) in the string is adjusted using the tuning screws
- The mass/unit length (u) is characteristic of a string, with the thicker bass strings having a higher 'u' than the thinner treble ones.

All these combine to produce the working of a guitar. Fretting a fret, decreases L and increases f. Tightening the tuning screws increases T and hence f. The bass strings have a higher u as compared to the treble strings, and that makes their f lower in comparison (for the same fret).

This simple equation is also the reason it is possible to play harmonics on a guitar. Lightly touching your finger on a vibrating string creates a "node" at that point, effectively decreasing the vibrating length. If the ratio of the new vibrating length to the original is a rational number, a harmonic is formed.

Human ears can only detect the harmonics if the fraction is a simple one with small integers, e.g. 2/1, 3/2, 4/3 etc.