HOW GUITAR STRING VIBRATE
How does a guitar string vibrate? When a string is plucked and starts to vibrate, the interference caused by the vibration to the
magnetic field of the pickup will cause a change in the energy flux passing through the pickup itself.
The energy will so go to from the guitar to the amp and from there to the speakers and in the end becoming a sound to our ears.
Guitar and bass strings vibrate as a sinusoidal wave moving in infinite patterns called "partials" or "harmonics".
The resulted sound depends from the pickup placement along the vibration pattern of the string (scale). If we play an open E we will note that the string is firm at the sides and that its maximum vibration width corresponds to the half of it's length. The note produced by this first vibration is the first harmonics (fundamental) it's the loudest one and it gives the name to the note.
The points where the strings is firm (nut and saddle on the guitar) are named "nodes" while the points where the string reaches it's maximum width are called "anti-nodes".
The next harmonic in volume order is the second harmonic which correspond to the next octave: the harmonic
has a node at the centre of the string (the harmonic we use to intonate tune the guitar). The anti-nodes of
the second harmonic (its more audible points) are placed half way between the anchor points of the strings
(nut and saddle on the guitar) and the centre of the string (the node of the first harmonic) i.e. at 1/4 and 3/4 of the string's length.
It's the same note you hear by playing the harmonic in 12th position but seldom recognize it as having plucked the open string, the first harmonics is louder and has a higher volume. The third harmonic divides the strings in 3 parts with nodes at 1/3, 2/3 and so on ad libitum.