How does a guitar work?
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
and frequencies. )
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
- 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 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 inside
The 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
More detail and other links