How does a guitar work?
Contents
First, something about sound
If you put your finger gently on
a loudspeaker you will feel it vibrate - if it is playing a low note loudly
you can see it moving. When it moves forwards, it compresses the air next
to it, which raises its pressure. Some of this air flows outwards, compressing
the next layer of air. The disturbance in the air spreads out as a travelling
sound wave. Ultimately this sound wave causes a very tiny vibration
in your eardrum - but that's another story.
At any point in the air near the source of sound, the molecules are
moving backwards and forwards, and the air pressure varies up and down
by very small amounts. The number of vibrations per second is called the
frequency which is measured in cycles per second or Hertz (Hz). The pitch
of a note is almost entirely determined by the frequency: high frequency
for high pitch and low for low. For example, 110 vibrations per second
(110 Hz) is the frequency of vibration of the A string on a guitar. The
A above that (second fret on the G string) is 220 Hz. The next A (5th fret
on top E string) is 440 Hz, which is the orchestral tuning A. (The guitar
A string plays the A normally written at the bottom of the bass clef. In
guitar music, however, it is normally written an octave higher.) We can
hear sounds from about 15 Hz to 20 kHz (1 kHz = 1000 Hz). The lowest note
on the standard guitar is E at about 83 Hz, but a bass guitar can play
down to 41 Hz. The orginary guitar can play notes with fundamental frequencies
above 1 kHz. Human ears are most sensitive to sounds between 1 and 4 kHz
- about two to four octaves above middle C. Although the fundamental frequency
of the guitar notes do not usually go up into this range, the instrument
does output acoustic power in this range, in the higher harmonics of the
most of its notes. (For an introduction to harmonics, see Strings and standing
waves. To relate notes to frequencies, see Notes and frequencies. )
The strings
The pitch of a vibrating string depends on four things.
- The mass of the string: more massive strings vibrate more slowly. On steel string guitars,
the strings get thicker from high to low. On classical guitars, the size
change is complicated by a change in density: the low density nylon strings
get thicker from the E to B to G; then the higher density wire-wound nylon
strings get thicker from D to A to E.
- The frequency can also be changed
by changing the tension in the string using the tuning pegs: tighter gives
higher pitch. This is what what you do when you tune up.
- The frequency
also depends on the length of the string that is free to vibrate. In playing, you
change this by holding the string firmly against the fingerboard with a
finger of the left hand. Shortening the string (stopping it on a higher
fret) gives higher pitch.
- Finally there is the mode of vibration,
which is a whole interesting topic on its own. For more about strings and
harmonics, see Strings and standing waves.
The strings themselves make hardly any noise: they are thin and slip
easily through the air without making much of disturbance - and a sound
wave is a disturbance of the air. An electric guitar played without an
amplifier makes little noise, and an acoustic guitar would be much quieter
without the vibrations of its bridge and body. In an acoustic guitar, the
vibration of the string is transferred via the bridge and saddle to the
top plate body of the guitar.
The bodyThe body serves to transmit the vibration of the bridge
into vibration of the air around it. For this it needs a relatively large
surface area so that it can push a reasonable amount of air backwards and
forwards. The top plate is made so that it can vibrate up and down relatively easily.
It is usually made of spruce or another light, springy wood, about 2.5
mm thick. On the inside of the plate is a series of braces. These strengthen
the plate. An important function is to keep the plate flat, despite the
action of the strings which tends to make the saddle rotate. The braces
also affect the way in which the top plate vibrates. For more information
about vibrations in the top plate and in the body, see the links below. The back plate is much
less important acoustically for most frequencies, partly because it is
held against the player's body. The sides of the guitar do not vibrate
much in the direction perpendicular to their surface, and so do not radiate
much sound.
The air insideThe air inside the body is quite important, especially for the low range
on the instrument. It can vibrate a little like the air in a bottle when
you blow across the top. In fact if you sing a note somewhere between
F#2 and A2 (it depends on the guitar) while holding your ear close to the
sound hole, you will hear the air in
the body resonating. This is called the Helmholtz resonance and is introduced below. Another way to hear the effect of this
resonance is to play the open A string and, while it is sounding, move
a piece of cardboard or paper back and forth across the soundhole. This
stops the resonance (or shifts it to a lower frequency) and you will notice
the loss of bass response when you close up the hole. The air inside is
also coupled effectively to the lowest resonance of the top plate. Together
they give a strong resonance at about an octave above the main air resonance. The air also couples the motion of the top and back plates to some extent.
The Helmholtz resonance of a guitar is due to the air at the
soundhole oscillating, driven by the springiness of the air inside the body. I expect that everyone has blown across the top of a bottle and enjoyed the
surprisingly low pitched note that results. This lowest guitar resonance is
similar. Air is springy: when you compress it, its pressure increases. Consider
a 'lump' of air at the soundhole. If this moves into the body a small distance, it compresses the internal air. That pressure now drives the 'lump' of air out but,
when it gets to its original position, its momentum takes it on outside the
body a small distance. This rarifies the air inside the body, which then
sucks the 'lump' of air back in. It can thus vibrate like a mass on a spring.
In practice, it is not just the compression of the air in the body, but also
the distension of the body itself which generates the higher pressure. This is analysed quantitatively in Helmholtz Resonance.
More detail and other links
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