# Acoustics/Human Vocal Fold

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

## Physiology of vocal fold

The human vocal fold is a set of lip-like tissues located inside the
larynx, and is the source of
sound for humans and many animals.

The larynx is located at the top of the trachea. It is mainly composed
of cartilages and muscles, and the largest cartilage, thyroid, is well
known as the \"Adam\'s Apple.\"

The organ has two main functions; to act as the last protector of the
airway, and to act as a sound source for voice. This page focuses on the
latter function.

Links on Physiology:

-   Discover The
    Larynx

## Voice production

Although the science behind sound production for a vocal fold is
complex, it can be thought of as similar to a brass player\'s lips, or a
whistle made out of grass. Basically, vocal folds (or lips or a pair of
grass) make a constriction to the airflow, and as the air is forced
through the narrow opening, the vocal folds oscillate. This causes a
periodical change in the air pressure, which is perceived as sound.

Vocal Folds Video

When the airflow is introduced to the vocal folds, it forces open the
two vocal folds which are nearly closed initially. Due to the stiffness
of the folds, they will then try to close the opening again. And now the
airflow will try to force the folds open etc\... This creates an
oscillation of the vocal folds, which in turn, as I stated above,
creates sound. However, this is a damped oscillation, meaning it will
eventually achieve an equilibrium position and stop oscillating. So how
are we able to \"sustain\" sound?

As it will be shown later, the answer seems to be in the changing shape
of vocal folds. In the opening and the closing stages of the
oscillation, the vocal folds have different shapes. This affects the
pressure in the opening, and creates the extra pressure needed to push
the vocal folds open and sustain oscillation. This part is explained in
more detail in the \"Model\" section.

This flow-induced oscillation, as with many fluid mechanics problems, is
not an easy problem to model. Numerous attempts to model the oscillation
of vocal folds have been made, ranging from a single mass-spring-damper
system to finite element models. In this page I would like to use my
single-mass model to explain the basic physics behind the oscillation of
a vocal fold.

Information on vocal fold models: National Center for Voice and
Speech

## Model

thumb\|Figure 1:
Schematics.png "wikilink")

The most simple way of simulating the motion of vocal folds is to use a
single mass-spring-damper system as shown above. The mass represents one
vocal fold, and the second vocal fold is assumed to be symmetry about
the axis of symmetry. Position 3 represents a location immediately past
the exit (end of the mass), and position 2 represents the glottis (the
region between the two vocal folds).

### The pressure force

The major driving force behind the oscillation of vocal folds is the
pressure in the glottis. The Bernoulli\'s equation from fluid mechanics
states that:

$P_1 + \frac{1}{2}\rho U^2 + \rho gh = Constant$ \-\-\-\--EQN 1

Neglecting potential difference and applying EQN 1 to positions 2 and 3
of Figure 1,

$P_2 + \frac{1}{2}\rho U_2^2 = P_3 + \frac{1}{2}\rho U_3^2$ \-\-\-\--EQN
2

Note that the pressure and the velocity at position 3 cannot change.
This makes the right hand side of EQN 2 constant. Observation of EQN 2
reveals that in order to have oscillating pressure at 2, we must have
oscillation velocity at 2. The flow velocity inside the glottis can be
studied through the theories of the orifice flow.

The constriction of airflow at the vocal folds is much like an orifice
flow with one major difference: with vocal folds, the orifice profile is
continuously changing. The orifice profile for the vocal folds can open
or close, as well as change the shape of the opening. In Figure 1, the
profile is converging, but in another stage of oscillation it takes a
diverging shape.

The orifice flow is described by Blevins as:

$U = C\frac{2(P_1 - P_3)}{\rho}$ \-\-\-\--EQN 3

Where the constant C is the orifice coefficient, governed by the shape
and the opening size of the orifice. This number is determined
experimentally, and it changes throughout the different stages of
oscillation.

Solving equations 2 and 3, the pressure force throughout the glottal
region can be determined.

### The Collision Force

As the video of the vocal folds shows, vocal folds can completely close
during oscillation. When this happens, the Bernoulli equation fails.
Instead, the collision force becomes the dominating force. For this
analysis, Hertz collision model was applied.

$F_H = k_H delta^{3/2} (1 + b_H delta')$ \-\-\-\--EQN 4

where

$k_H = \frac{4}{3} \frac{E}{1 - \mu_H^2} \sqrt{r}$

Here delta is the penetration distance of the vocal fold past the line
of symmetry.

## Simulation of the model

The pressure and the collision forces were inserted into the equation of
motion, and the result was simulated.

thumb\|Figure 2: Area Opening and Volumetric Flow
Rate

Figure 2 shows that an oscillating volumetric flow rate was achieved by
passing a constant airflow through the vocal folds. When simulating the
oscillation, it was found that the collision force limits the amplitude
of oscillation rather than drive the oscillation. Which tells us that
the pressure force is what allows the sustained oscillation to occur.

## The acoustic output

This model showed that the changing profile of glottal opening causes an
oscillating volumetric flow rate through the vocal folds. This will in
turn cause an oscillating pressure past the vocal folds. This method of
producing sound is unusual, because in most other means of sound
production, air is compressed periodically by a solid such as a speaker
cone.

Past the vocal folds, the produced sound enters the vocal tract.
Basically this is the cavity in the mouth as well as the nasal cavity.
These cavities act as acoustic filters, modifying the character of the
sound. These are the characters that define the unique voice each person
produces.

## Related links

-   FEA
    Model
-   Two Mass
    Model

## References

1.  Fundamentals of Acoustics; Kinsler et al, John Wiley & Sons, 2000
2.  Acoustics: An introduction to its Physical Principles and
    Applications; Pierce, Allan D., Acoustical Society of America, 1989.
3.  Blevins, R.D. (1984). Applied Fluid Dynamics Handbook. Van Nostrand
    Reinhold Co. 81-82.
4.  Titze, I. R. (1994). Principles of Voice Production. Prentice-Hall,
    Englewood Cliffs, NJ.
5.  Lucero, J. C., and Koenig, L. L. (2005). Simulations of temporal
    patterns of oral airflow in men and women using a two-mass model of
    the vocal folds under dynamic control, Journal of the Acostical
    Society of America 117, 1362-1372.
6.  Titze, I.R. (1988). The physics of small-amplitude oscillation of
    the vocal folds. Journal of the Acoustical Society of America 83,
    1536--1552

