Modeling

[Dr. Linton Hutchinson]

Modeling of the Vocal Tract:

A basic tool in science is modeling. Since vocal tracts, brains,
galaxies, etc. are too complex to be studied in their natural state, a
model of the actual physical object is constructed and studied. For
example, a model of the vocal tract begins with a tube with a uniform
diameter along its length. The tube is closed at one end and open at
the other. The closed end of the tube can be thought of as the glottis
and the open end of the tube can be thought of as the lips. The tube is
then modified to more closely approximate that of an actual vocal tract,
therefore, the length of the tube is modified (longer or shorter)
depending on the speaker (adult or child). Next, the tube's diameter is
modified along its entire length so that the open end (lips) is wider
than the closed end (glottis), lastly the tube is bent so that its shape
has a distinctive right-angled configuration. This final model gives us
one configuration of an actual human vocal tract.

Modeling of one vowel:

The simple tube we just described has a simple pattern of resonance.
The resonance of the tube will depend on the relation between the
frequency of the sound (rate of vibration) and the length of the tube
(resonance or formant frequencies). The relation between the frequency
of a sound and the length of the tube is known as the odd-quarter
wavelength relation.

The wavelength of the sound has to do with the distance that the sound
travels during one period of vibration. In this case, the wavelength of
the sound depends on the frequency of vibration and the speed of sound.
The formula to calculate this is: wavelength = speed of sound in
meters/sec divided by the frequency in hertz. So lets look at a
simplified example: If the speed of sound in meters/sec is 150 and the
frequency of vibration of the vibrating source is 300 Hz, we take
150/300 and this gives us 2. Therefore, according to this example, the
distance that the sound will travel during one period of vibration will
be 2 meters. This is our wavelength. So again the wavelength that a
sound will travel will depend on the speed of sound and the frequency of
the sound source. We also know that the simple resonance emitted by
the simple tube we described earlier will depend on the frequency of the
sound source and the length of the simple tube, this is better known as
the odd-quarter wavlength relation.