How Does a Guitar Make Sound? Strings, Bodies and Pickups
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Stretch a steel string between two nails on a board and pluck it, and it makes a faint buzz that nobody across the room would hear, because a thin string moving back and forth pushes almost no air. A guitar is the device that solves that problem, twice over: the acoustic one by attaching the string to a thin wooden plate that moves air in quantity, and the electric one by ignoring the air altogether and turning the string's motion into a voltage. The instrument is a few hundred years old in its present form, the electric version less than a century, and between them they are the most played instruments in the world.
The string
A plucked string vibrates at a frequency set by three things: its length, its tension and its weight per unit length. Shorter, tighter and lighter strings vibrate faster and sound higher, which is why the six strings of a guitar are of different thicknesses, tuned to different tensions, and why pressing a string against a fret shortens its vibrating length and raises the note. The frets are spaced so that each one raises the pitch by a semitone, which means each is closer to the next by a fixed ratio, the twelfth root of two, and the twelfth fret sits exactly halfway along the string, an octave up. A string does not vibrate at one frequency only; it vibrates at its fundamental and, at the same time, at two, three, four and more times that frequency, the harmonics, and the mix of them is what makes a guitar sound unlike a violin playing the same note. Plucking near the bridge excites more of the high harmonics and gives a brighter tone; plucking over the neck gives a rounder one.
The body
In an acoustic guitar the string passes over a bridge glued to the soundboard, the thin spruce or cedar top of the body, and the string's vibration rocks the bridge and sets the whole top moving like a drumskin. The top is large enough to push a great deal of air, and the air inside the body resonates as well, at a frequency set by the size of the sound hole, which reinforces the bass. Almost all the sound comes from the top and the air, very little from the back and sides, and the bracing glued under the top, a pattern of struts in an X on most steel-string guitars and a fan on classical ones, is what lets a plate two or three millimetres thick take the pull of the strings, around 80 kilograms on a steel-string, and still vibrate freely. The luthier's craft is in tuning the top: too stiff and the guitar is quiet and thin, too flexible and it bellies up and dies. What decides the sound:
- •The strings: steel for volume and brightness, nylon for the softer classical voice, wound with bronze or nickel on the lower strings to add weight without stiffness
- •The top: spruce or cedar, and how it is braced
- •The body's size and shape, which set the air resonance and the bass
- •The bridge and saddle, which pass the vibration to the top
- •The player: where and how hard the string is plucked, and with what
The electric guitar
An electric guitar can have a solid body because it does not use the body to make sound. Under the strings sit pickups, each a magnet wound with thousands of turns of fine wire; the steel string above the magnet is magnetised, and when it vibrates it disturbs the magnetic field through the coil, which by Faraday's law induces a small alternating voltage at the string's frequency. That signal, a few hundredths of a volt, goes down a cable to an amplifier, which makes it large enough to drive a loudspeaker. Because the pickup senses only the string, the body's job is to hold the strings still and sustain them, and a solid plank does that better than a hollow box, which is why the first practical electrics of the 1940s and 1950s, by Leo Fender and Les Paul, were slabs of ash and mahogany. Where the pickup sits changes the tone, since a string's harmonics have different strengths at different points along it, and the switch on an electric guitar chooses between the warm neck pickup and the sharp bridge one.
Distortion and effects
The electric guitar's voice is as much the amplifier's as the instrument's. A valve amplifier driven harder than it can cleanly handle clips the top of the signal, adding harmonics that were not there and sustaining the note as the string decays, and that distortion, discovered by accident and by guitarists slashing their speaker cones in the 1950s and 1960s, became the sound of rock. Pedals between guitar and amplifier bend the signal further: delay, reverb, wah, chorus, and fuzz. Feedback, in which the speaker's sound sets the string vibrating again through the pickup in an endless loop, is a fault in any other instrument and a technique in this one. The acoustic guitar makes sound; the electric guitar makes a signal, and the signal can be anything.
A short history
Plucked instruments with necks and frets go back to the Hittites and the lute of the Islamic world, and the guitar in something like its present form, with six single strings, is Spanish, from the late eighteenth century; Antonio de Torres in the 1850s set the classical guitar's size and fan bracing, and the American steel-string with its X bracing was developed by the Martin company in the 1840s to 1850s. The electric guitar answered the problem of being heard in a dance band, with a pickup fitted to a hollow guitar in 1931, the solid body by 1950, and it was the instrument of the popular music of the second half of the twentieth century. About two and a half million guitars are sold each year in the United States alone, and the physics in every one of them is a string that cannot be heard until something moves the air or the electrons on its behalf.
Why a guitar is never perfectly in tune
Two notes sound sweetest together when their frequencies form simple ratios, such as 3 to 2 for a fifth or 5 to 4 for a major third. Frets cannot give every interval its ideal ratio in every key, so guitars use equal temperament, which divides the octave into twelve identical steps. The octave comes out perfect and the fifths are very close, but the major thirds are noticeably wide, about a seventh of a semitone sharp of the pure ratio. This is why a big open chord can sound faintly restless, and why some players retune slightly for a particular song.
There is a second, mechanical problem. Pressing a string down to a fret stretches it a little, raising its tension and pushing the note sharp, and a thicker string is affected more than a thin one. Guitar makers correct for this by setting the saddle, where the strings rest at the bridge, slightly further back than the simple halfway rule would suggest, and by angling it or giving each string its own adjustable point. On an electric guitar you can test the result yourself: the harmonic touched lightly above the twelfth fret should match the note fretted there.
Mersenne's laws with real numbers
In 1636 the French friar and mathematician Marin Mersenne published the rules connecting a string's pitch to its length, tension and weight, and they explain much about how a guitar is built. Frequency falls in direct proportion as length rises, so halving a string doubles its pitch. Tension has a weaker effect, because frequency rises only with its square root. Doubling the pull on a string raises the note by just six semitones, and raising it a full octave by tightening alone would need four times the tension, enough to snap almost any guitar string long before it got there.
Weight works the same way in reverse. Frequency falls with the square root of the mass per unit length, so to sound an octave lower at the same length and tension a string must be four times as heavy. The high E string of a guitar vibrates about 330 times a second and the low E about 82, two octaves lower, so at similar tensions, which a typical set roughly has, the low string needs about sixteen times the mass per length. That factor is why a light set runs from about a quarter of a millimetre thick at the treble end to over a millimetre at the bass.
Placing the frets
Each fret on a guitar shortens the vibrating part of the string by just the right amount to raise the pitch by one semitone. Because every semitone in equal temperament multiplies the frequency by the same ratio, about 1.0595, each fret must remove the same fraction of whatever string length remains, so the frets get steadily closer together as they approach the body.
Instrument makers once used a rule of thumb called the rule of eighteen: measure from the nut to the bridge, divide by eighteen to place the first fret, then divide the remaining length by eighteen again for the next, and so on. The exact figure for equal temperament is closer to 17.817, and modern makers calculate positions precisely, but the old rule came close enough for centuries of instruments.
The takeaway
A guitar string's pitch is set by its length, tension and weight, its tone by the mix of harmonics, and it is nearly silent alone; an acoustic guitar makes it audible by passing the vibration through the bridge to a thin braced soundboard that moves air, with the body's air cavity reinforcing the bass, while an electric guitar turns the vibration into a voltage through magnetic pickups and leaves the amplifier to make the sound, which is why it can have a solid body and why distortion and feedback became its voice.