The first guitar designed to be
electrically amplified was created in 1931 by George Beauchamp, and was a
hollow body guitar that utilised a tungsten pickup, see Fig1. This was a one-piece
cast aluminium body and utilised electromagnetic transducers. Considered by most
to be the known as the “frying pan”, created by George for Rickenbacker Electro
    Guitars
1. This guitar utilised all the features common to modern day
electric guitar such as potentiometers to control volume and treble, and
magnetic pickups to send the signal to an amplifier.Something to consider with the
guitar is the range of pitches available to a player. For a standard six string
model, the lowest note is the low E, at 82.41Hz and the highest is the high E,
4 octaves above this, at 1320Hz. However, guitarists can change the pitch of a
note by applying more tension to the string through bending the string,
allowing a high G to be reached at 1568Hz. However, for guitars over 6 strings
such as those up to 8 or 9 strings, the lowest note can be as low as 36.7Hz,
which is almost below the point of human hearing. When changing the pitch of a
note, the guitarist must apply varying degrees of force at different original
pitches to change the note to the desired pitch, depending on where they are
playing the note on the neck. This is due to the height the string changes when
it is pushed onto the frets of the fretboard, see Fig 2, the closer the fret is
to either the nut or bridge of the guitar, the locations where the string ends,
the longer the overall string shall become. This means that to bend to pitch at
frets closer to either the bridge or nut, greater pressure must be applied to
reach the same change in pitch.

While
playing a note, one of the main differences between a guitar and almost every
other type of instrument is the ability to play achromatic notes, notes which
are outside the established Western scales. This is due to the ability to bend
a string and apply vibrato, which is when the length of the string is subtly
changed with a regular such that the pitch is shifted slightly out of the
chromatic range established by Western scales, allowing a continuous range of
pitches to be reached as opposed to the discrete range which is possible from most
instruments.Different pitches are achieved on
the guitar in several ways. One of which is the scale length, which is broken
at 21, 22 or 24 places by frets. Each of these frets is located in a
mathematically calculated place, so that the correct pitch can be achieved. The
formula used for this isThis recursive formula shows that,
for a typical guitar of scale length, distance between the nut and brige,
25.5″, the first fret is at 1.431″, the second at 2.782″, the third at 4.057″
and so on. The value of 18 used to be used, referred to as the “rule of 18” but
by further refinement this has been narrowed down to 17.817 5, known
as the equal temperament constant.

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In
the same way as for other stringed instruments, it is simple to work out the
lowest harmonics available on the guitar. We can do this by considering a
standing wave on the guitar. As it is a closed string, we must have a minimum
at each end, so the largest wavelength available for the string is twice the
length of the string, with the second being the length of the string and so on,
following the formulaThe key thing that differentiates
the electric guitar from an acoustic guitar is the magnetic pickup. A pickup is
created by coiling a metal with a high intrinsic magnetic moment around 6 permanent
magnets roughly 5 to 10 thousand times, creating a dynamo.

The
magnets in the pickups cause the portion of the strings above them to become
magnetised and thus to produce a magnetic field. Therefore, when the string
vibrates after being plucked, the string vibrates with a certain frequency and
therefore so does the magnetic field generated by it. This changes the flux
through the coils of the pickup, so the rate of change of the flux is non zero.
The induced potential difference is caused by the electromotive force, described
by:When the string vibrates above the
pickup, it generates a potential difference which, when the guitar is plugged
in and makes a complete circuit, creates a voltage and current flows to the
amplifier, allowing for amplification of the note. The pickup is either one
coil, or two coils wired in series but placed in opposite polarities, known as
a humbucker. This humbucker design was created by Gibson and the patent was
applied for on June 22nd, 1955 6. The design was
necessary as single coil pickups are very effective at picking up frequencies
of 50 Hertz 7, frequencies produced by mains wiring, leading to a
distinctive and irritating hum. As the level of electronic gain is increased, a
layer of natural compressions is added which increases the volume of this hum
and leads to feedback loops when playing at high volumes. The design of the
humbucker pickups deals with this by having each coil pick up the same amount
of string vibration and background hum, meaning the voltages are added together
but the ratio of noise to signal is the same. However, as one coil is reversed
relative to the other, the signal produced by the vibrating string is unchanged,
while the hum produced by the pickup receiving signals from radio sources and
AC current nearby is reversed between the coils, which cancels out the hum in
the output of the pickup as a whole. In practise, as the two coils cannot be identical,
not all hum is cancelled although the majority is.

Using
humbuckers, however, changes the “tone” of the guitar. It does this for several
reasons. One of these is that, by utilising two coils, the total number of
turns is more, and a greater potential difference is generated by the vibrating
string. This results in the output having a higher amplitude, which, when
amplified by a valve amplifier, changes the tone. For example, the natural
compression by the valves is increased by the greater strength of the input
signal, resulting in a slightly more artificial sound. This natural compression
in valve amplifiers also results in a more pronounced bass end of the tone due
to the bass elements of the sound being relatively lower in presence, meaning
the sound will cut through a mix with greater difficulty and therefore will have
a harder time being perceived by the audience. The compression has a third
factor to it as well; due to the signal compressions resulting in asymmetric
clipping of the generated wave, distortion is generated by the amplifier. This
change in sound is desirable for certain genres such as rock and metal where
humbucker equipped guitars are predominantly used but for other genres such as
funk, this sound is not. Therefore, most players in this genre will use low
output single coil equipped guitars to achieve the correct sound.After this, the signal travels through
the circuit of the guitar, often through two potentiometers, one which controls
volume and the other which controls tone. These work by reducing the voltage of
the signal travelling through and therefore reducing the amplitude of the
signal. For the volume control this reduces the volume. For the tone control,
the processes are slightly more complicated. With this potentiometer, a
capacitor is wired between terminal of the potentiometer and the ground, and as
the voltage is changed by the potentiometer, the capacitor acts as a high
frequency drain on the signal, by the formulaIn conclusion, the physics of the electric
guitar are fascinating and allow it to produce a far wider variety of sounds
than most other physical instruments, rather than the technological, for
example by the ability to bend strings and apply vibrato to change the pitch of
a note subtly outside of the chromatic 12 interval Western scale structure. In
addition to this, the pickups of the guitar, by converting the mechanical wave
to an electrical signal by electromagnetic inductance, allow a guitar to be
amplified and have analogue processing applied to the signal, resulting in a
plethora of tones varying both in gain level as well as tonal structure and
balance. This is one of the reasons the guitar is one of the most played
instruments on the planet.