Certain laws in physics can be described by using partial differential
equations. One such equation, the wave equation, is especially useful
for quantifying the movement of a wavelength. This could be a wave in
the water, a sound wave, an electromagnetic wave, or a wave along a vibrating
string. In particular, we want to study the latter case. (Stewart, p.
The wave equation can be expressed by any equation having the form:
as, "The second partial of 'u' with respect to 't' is equal to
some constant 'a' squared times the second partial of 'u' with respect
Before delving into the core physics of electric guitars, some basic
information must be understood. These ideas will be discussed more thoroughly
later on in this section.
Sound from an electric guitar is produced by electromagnetic
pick-ups that sense vibrations in the strings electronically and route
the electronic signal to an amp and speaker.
The vibrations of the strings can be quantified and calculated
according to basic laws in physics. These include certain relationships
between velocity, wavelength, and frequency and equations that describe
the motion of a string fixed at both ends.
Sam Hokin, the author of "The Physics of Everyday Stuff", explained
how guitars employ these two relationships this way:
"Since the fundamental wavelength of a standing wave on a guitar
string is twice the distance between the bridge and the fret, all six
strings use the same range of wavelengths. To have different pitches (frequencies)
of the strings, then, one must have different wave speeds. There are two
ways to do this: by having different tension T or by having different
mass density u (or a combination of the two). If one varied pitch only
by varying tension, the high strings would be very tight and the low strings
would be very loose and it would be very difficult to play. It is much
easier to play a guitar if the strings all have roughly the same tension;
for this reason, the lower strings have higher mass density, by making
them thicker and, for the 3 low strings, wrapping them with wire."
(Hokin, n. p.)
Electric guitar pick-ups work by employing "principles of magnetic
induction." The pick-ups are composed of small electromagnets
(magnets that are wrapped with a coil of wire, thus allowing an electric
current to flow through them). Because of their close proximity to the
strings, these magnets induce a north and south pole on the strings. When
the string is played, it begins to oscillate, or move in a wave-like
fashion. This affects the field surrounding the pick-up and causes a change
in the magnetic field. These changes, or fluctuations in the magnetic
field are transmitted through the wires connecting the pick-up(s) to the
output jack and are thus relayed to the amplifier where they are sent
to the speaker and converted from electrical energy once again into motion
energy (sound). (Brain, n.p.)
A guitar string is an example of "a string fixed at both ends which
is elastic and can vibrate." Such vibrations are called standing
waves, and all of them satisfy "the relationship between wavelength
and frequency that comes from the definition of waves." (Hokin, n.p.)
'v' is the velocity of the wave, 'f' is the frequency, and 'lambda' is wavelength.
speed of the wave depends on two factors: the tension 't' and
the mass density of the string (mass/length) 'u'. This gives us another
Any wave that has its nodes (points at which it intersects the axis of
oscillation) at the ends of the string can exist on a guitar. To illustrate
this fact, refer to the following illustrations taken from Hokin's web
Fundamental (l = /2)
"The fundamental satisfies the condition l
= /2, where l
is the length of the freely vibrating portion of the string."
1st Overtone (l =2 /2)
"The 1st overtone satisfies the condition l =
. Each higher overtone
fits an additional half wavelength on the string."
It is commonly known that frets (bars that "divide" the string
into sections of certain lengths) get closer together towards the bridge
of the guitar. This is due to the fact that "each successive note
is r = 1.0595 higher in pitch" and the fact that the velocity of
the waves is held constant on a given string. So given an open string
of length 'l' we can determine the fret spacing from this. (Hokin, n.
"The first fret must be placed l/1.0595 from the neck, the second
fret a distance of l/1.0595^2, and so on." (Hokin, n. pag.) Thus
this gives us the relationship:
D is the distance from the neck, l is the length of the string, and n
is the number of the fret starting with 1 (the fret closest to the neck).
While there are many other aspects of electric guitars (i.e. methods
of amplification, effects, etc.), a good grasp of the physics involved
in electric guitars can be obtained by bearing in mind the following:
Electric guitars use pickups to convert motion energy
into electrical energy. This electrical energy is processed and amplified
by an amp and outputted to a speaker where it is converted back into motion
energy (i.e. sound).
Velocity of a wave is equal to frequency x wavelength.
Since all the strings use the same range of wavelengths, in order to produce
different frequencies (pitches), velocity must be varied.
Velocity is varied by changing either linear mass density
and/or tension in the string. It is desirable to play a guitar with nearly
uniform tension from string to string, thus strings are of varying masses.