HPP Activity A47v2
How does the larynx produce a pressure wave?
We have seen that the larynx contains vocal folds that vibrate, causing the vocal tract to open and
close. What causes the vocal folds to open and close?
Exploration
Here is a very simplified diagram of the vocal tract around the larynx.
vocal tract
P2
vocal folds
P1
trachea
GE 1.
1. Assume that the vocal folds are closed, as shown above. To open them you
must make the pressure P1 larger than P2. What do you do with your body to
accomplish this?
2. Assume that the vocal folds have opened and a stream of air is moving
through the opening. Why do you think the vocal folds would start closing
again?
3. Let’s play with air streams a bit to understand the problem better. Place a
sheet of notebook paper between two books.
Now, get down so you are level with the table top. What do you think will
happen to the paper if you blow through the opening?
4. Try it. What happens?
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 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
HPP Activity A47v2
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5. How does the pressure above the paper compare with the pressure in the
opening between the books while you are blowing?
6. How do you think the air velocity in the opening between the books
compares with the air velocity above the books?
We want to develop some hypotheses that will help us understand this phenomenon and
eventually provide insight into why the vocal folds can undergo sustained oscillations. Let’s
focus on the air speed question suggested above and come back to the pressure changes later.
In some ways, it is easier to visualize and measure properties of water flow than airflow, so we
will think about water for a bit.
GE 2.
1. Imagine turning on a hose and measuring the speed of the water molecules
coming out of it. What happens to this speed as you cover the end of the hose
with your thumb?
2. Consider the following pipe that is carrying water.
v1
1
2
If there are no sources or leaks of water between points 1 and 2, how should
the mass of water that enters point 1 in one second compare with the mass of
water that leaves point 2 in one second?
3. Estimate the mass of water that enters point 1 in one second. Assume the
speed is v1, the cross-sectional area is A1, and the density is . Express the
entering mass in terms of these variables.
4. Estimate the mass of water that exits point 2 in one second. Assume that
the water is incompressible, so that the density remains constant.
5. Write an equation that relates v1 to v2.
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Invention
This last result is called the equation of continuity. If a fluid is incompressible then the law of
conservation of mass implies the equation of continuity for the fluid. For the pipe with changing
cross-sectional area shown above we have
A1v1  A2 v2
Equation (6)
Application of energy principles in a fluid leads to another relationship that can help us
understand vocal fold oscillation. This relationship is called Bernoulli’s equation.
Imagine a fluid moving through space. If the fluid does not move too quickly then all particles
passing a certain point will all travel in the same direction. This is called laminar flow. If the
fluid speed passes a certain critical value then different particles passing a point can end up
travelling in many different directions. This is turbulent flow.
Let’s assume the fluid is showing laminar flow. The fluid particles follow well-defined paths
called streamlines. Bernoulli’s equation says that if we add the pressure, the kinetic energy per
unit volume, and the potential energy per unit volume we get a constant value for any point along
a streamline. Mathematically we say
P1  12 v 2  gy  constant
Equation (7)
where
 = density of the fluid
v = speed of the fluid
y = position of the point with respect to the reference level for gravitational potential energy
We will ignore the changes in gravitational potential energy for now.
Application
We will follow conceptually the opening and closing of the vocal folds and see how the equation
of continuity and Bernoulli’s equation help us to understand the oscillation.
First, consider a simpler situation than the soft tissue of the vocal cords. Consider a set of hinged
doors, as shown below. The hinges have springs on them that provide a restoring force back to
the equilibrium, unopened situation shown.
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HPP Activity A47v2
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2
1
A source of air produces a steady flow through the doors. This will open the doors. If the
pressure against the doors does not change, the hinge springs cannot return the doors to their
equilibrium position. Would we expect the pressure against the doors to change after the airflow
starts?
Let’s investigate this conceptually. We will compare pressures and air particle velocities at three
points, as indicated in the above figure, at various times. We want to compare pressures by
indicating positions on a vertical pressure axis with a small dot, one for each position. We will
plot the deviation from atmospheric pressure. So, if position 1 has a higher pressure than
position 2, which in turn is higher than position 3, we would indicate it as
0
1
2
3
A similar comparison can be done for air speed.
GE 3.
1. Assume that the air has not started to flow. Draw the relative pressures and
air speeds.
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HPP Activity A47v2
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5
Pressure
2
Speed
0
0
1
1
2
3
1
2
3
2. Now the airflow begins. Draw relative pressures and speeds.
Pressure
Speed
0
0
1
2
3
1
2
Explain your choice in terms of the equation of continuity and Bernoulli’s
equation.
3. Draw a force vector for the net force on the doors at this instant.
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The vocal fold oscillations are more complex than this, because each vocal cord is more like a
thick flexible ribbon rather than a rigid door on a hinge. The figures below show the vocal folds
at various stages of an oscillation. We will assume that the three indicated points are all at
atmospheric pressure in figure 1. The figures show one cycle of an oscillation.
3 2
1
1
2
3
4
5
GE 4.
1. Draw relative pressures air speeds for the first figure.
Pressure
Speed
0
0
1
2
3
1
2
3
2. Now consider the second figure.
Pressure
Speed
0
0
1
2
3
3. Figure 3:
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1
2
3
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Pressure
Speed
0
0
1
2
3
1
2
3
Provide some explanation for your choice in terms of the equation of
continuity and Bernoulli’s equation.
4. Figure 4:
Pressure
Speed
0
0
1
2
3
1
2
3
Provide some explanation for your choice in terms of the equation of
continuity and Bernoulli’s equation.
5. Figure 5:
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Pressure
Speed
0
0
1
2
3
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1
2
3