# Acoustics/How an Acoustic Guitar Works

![](Acoustics_how_an_acoustic_guitar_works.JPG "Acoustics_how_an_acoustic_guitar_works.JPG")

What are sound vibrations that contribute to sound production? First of
all, there are the strings. Any string that is under tension will
vibrate at a certain frequency. The weight and length of the string, the
tension in the string, and the compliance of the string determine the
frequency at which it vibrates. The guitar controls the length and
tension of six differently weighted strings to cover a very wide range
of frequencies. Second, there is the body of the guitar. The guitar body
is very important for the lower frequencies of the guitar. The air mass
just inside the sound hole oscillates, compressing and decompressing the
compliant air inside the body. In practice this concept is called a
Helmholtz resonator. Without this, it would be difficult to produce the
wonderful timbre of the guitar.

![](Acoustic_guitar-en.svg "Acoustic_guitar-en.svg"){width="320"}

## The strings

The strings of the guitar vary in linear density, length, and tension.
This gives the guitar a wide range of attainable frequencies. The larger
the linear density is, the slower the string vibrates. The same goes for
the length; the longer the string is the slower it vibrates. This causes
a low frequency. Inversely, if the strings are less dense and/or shorter
they create a higher frequency. The resonance frequencies of the strings
can be calculated by

$$f_1 = \frac{\sqrt{\frac{T}{\rho_l}}}{2 L}\quad \text{with}\quad T = \text{string tension},\ \rho_l = \text{linear density of string},\ L = \text{string length}.$$

The string length, $L$, in the equation is what changes when a player
presses on a string at a certain fret. This will shorten the string
which in turn increases the frequency it produces when plucked. The
spacing of these frets is important. The length from the nut to bridge
determines how much space goes between each fret. If the length is 25
inches, then the position of the first fret should be located
(25/17.817) inches from the nut. Then the second fret should be located
 inches from the
first fret. This results in the equation

$$d = \frac{L}{17.817} \quad \text{with}\quad d = \text{spacing between frets}, L = \text{length from previous fret to bridge}.$$

When a string is plucked, a disturbance is formed and travels in both
directions away from point where the string was plucked. These \"waves\"
travel at a speed that is related to the tension and linear density and
can be calculated by

$$c = \sqrt{\frac{T}{\rho_l}} \quad \text{with}\quad c = \text{wave speed},\ T = \text{string tension},\ \rho_l = \text{linear density}.$$

The waves travel until they reach the boundaries on each end where they
are reflected back. The link below displays how the waves propagate in a
string.

Plucked String @
www.phys.unsw.edu

The strings themselves do not produce very much sound because they are
so thin. They can\'t \"push\" the air that surrounds them very
effectively. This is why they are connected to the top plate of the
guitar body. They need to transfer the frequencies they are producing to
a large surface area which can create more intense pressure
disturbances.

## The body

The body of the guitar transfers the vibrations of the bridge to the air
that surrounds it. The top plate contributes to most of the pressure
disturbances, because the player dampens the back plate and the sides
are relatively stiff. This is why it is important to make the top plate
out of a light springy wood, like spruce. The more the top plate can
vibrate, the louder the sound it produces will be. It is also important
to keep the top plate flat, so a series of braces are located on the
inside to strengthen it. Without these braces the top plate would bend
and crack under the large stress created by the tension in the strings.
This would also affect the magnitude of the sound being transmitted. The
warped plate would not be able to \"push\" air very efficiently. A good
experiment to try, in order to see how important this part of the guitar
is in the amplification process, is as follows:

1.  Start with an ordinary rubber band, a large bowl, adhesive tape, and
    plastic wrap.
2.  Stretch the rubber band and pluck it a few times to get a good sense
    for how loud it is.
3.  Stretch the plastic wrap over the bowl to form a sort of drum.
4.  Tape down one end of the rubber band to the plastic wrap.
5.  Stretch the rubber band and pluck it a few times.
6.  The sound should be much louder than before.

## The air

The final part of the guitar is the air inside the body. This is very
important for the lower range of the instrument. The air just inside the
soundhole oscillates compressing and expanding the air inside the body.
This is just like blowing across the top of a bottle and listening to
the tone it produces. This forms what is called a Helmholtz resonator.
For more information on Helmholtz resonators go to Helmholtz
Resonance. This link
also shows the correlation to acoustic guitars in great detail. The
acoustic guitar makers often tune these resonators to have a resonance
frequency between F#2 and A2 (92.5 to 110.0 Hz). Having such a low
resonance frequency is what aids the amplification of the lower
frequency strings. To demonstrate the importance of the air in the
cavity, simply play an open A on the guitar (the fifth string - second
lowest note). Now, as the string is vibrating, place a piece of
cardboard over the soundhole. The sound level is reduced dramatically.
This is because you\'ve stopped the vibration of the air mass just
inside the soundhole, causing only the top plate to vibrate. Although
the top plate still vibrates a transmits sound, it isn\'t as effective
at transmitting lower frequency waves, thus the need for the Helmholtz
resonator.

