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 the high 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.

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.

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

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 Resonance.