Download MEASUREMENT UNITS and DESCRIPTIVE QUANTITIES

SPPA 4030 Speech Science
DESCRIPTIVE QUANTITIES
In Speech Science, we measure and
describe all physical correlates of talkers talking
(e.g., variations in air pressure that talkers create;
or, the movements of body parts that cause those
pressure variations) in terms of three types of
base units: one unit to describe length or
distance; one unit to describe time; and, one unit
to describe mass. These three kinds of unit
descriptors are the building blocks for our entire
vocabulary for physical description.
As a rule, when we describe the physical act and
effects of speech production, we tend to follow
what is known as the cgs (centimeter-gramsecond) system, a fore-runner of the more
modern mks (meter-kilogram-second) system
often referred to as the System International or
SI system that has been the standard for most
physical sciences since about 1971. The fact that
speech people often persist in old-fashioned
(cgs) ways, and do not follow the modern (mks)
standard, sometimes causes a little confusion.
But, we might defend using the cgs system to
describe speech on the grounds that cgs base
units tend to match the magnitudes of physical
objects and events associated with speech better
than mks units. For example, many of the things
we move when we speak -- the class of things we
call articulators, including the tongue, lips, jaws,
vocal folds -- are neither large nor dense. At
least some articulators certainly aren't on the
order of "kilograms heavy." (Remember: 1
kilogram ~ 2.2 pounds.)1 Instead, they are more
likely to weigh only fractions of a kilogram. For
example, both vocal folds together might weigh
about 2/1000 of a kilogram (= 2 grams). Each
lip might weigh 25-50 grams or so, and the soft
palate probably weighs about the same amount.
The human tongue might weigh 150 grams. We
have to talk about the human jaw, combined with
the associated tissues tied to it, before we begin
to approach an object that is a “kilogram heavy.”
1
It is common to “confuse” weight and mass, and
possible to “confuse” volume and mass. Technically,
neither association is correct, though it is obvious that
the former conceit has been applied in a foregoing
argument about the “masses” of articulators. For the
time being, excuse the loose talk. Some will say that
perhaps the best way to think about mass is to think in
terms of stuff. Your mass – the amount of stuff that is
you – is the same on Earth and the Moon, though you
will certainly weigh less on the Moon.
Thus, grams (abbreviated with a lower-case “g”)
are a dimensionally appropriate way to talk about
most articulatory masses.
It is also true that the things we move when we
speak typically do not move great distances.
Movements spanning meters are out of the
question, for most speakers and speaking
situations. Movements spanning a few
hundredths (e.g., the lower jaw, when speaking
loudly), or even a few thousandths of a meter
(e.g., the tongue surface during so-called speech
diadochokinesis), are the rule. Consequently,
centimeters (abbreviated with the two lower case
letters “cm”) are a more suitable measure of
articulatory distance or length. And, we don't
move whatever we move, when we speak, either
for long periods of time, or at great speeds.
Significant events in speech "last" on the order
of seconds, or more often, parts of seconds. In
fact, a fair case could be made that milliseconds
(thousandths of a second) and millimeters (tenths
of a centimeter) are better measures of speech
time and distance than seconds and centimeters,
though even speech scientists aren't quite that
radical. Certainly when we talk about the speeds
of speech movements (expressed in terms of
change in the position of an articulator, per
change in time), seconds (abbreviated with a
lower case “s”) seem to be about the best time
unit to use, far better than the more familiar time
units of minutes or hours that we might apply to
our day-to-day lives. The fastest speech
movements, for example, are strikingly slow
when we think about them in miles per hour.
For your own amusement, you might want to
work out an answer to Practice Problem 7,
figuring out how fast 50 centimeters-per-second
is in miles per hour. Fifty cm/s is about as fast
as we ever move any articulator when we speak,
even when we try to talk as fast as a speeding
locomotive.
Thus, in the cgs system, which we encounter
most often in the speech science literature, the
standard base measures of
distance =
mass
time
centimeter (cm),
=
gram (g) ,
=
second (s).
These units contrast with the mks or System
International units now followed in most of
physics, where the standard base measure of
SPPA 4030 Speech Science
distance =
mass
time
meter (m),
=
kilogram (kg),
=
second (s).
We can refer to any combination of base
measures (i.e., any quantity, expression, or
concept involving at least two kinds of base
units) as a derived unit. We use many derived
units when we describe physical aspects of
speech production. One of the more important of
these derived quantities is pressure (as in the
sound pressure wave). In words, we define
pressure as force per unit area. In unit terms, a
definition of pressure will thus involve some
reference to area (= distance squared), and force,
and it is obvious that we must define the latter
before we can finally generate a derived unit
expression for pressure. What follows are some
derived units that are particularly relevant for
quantifying events of interest during speech
production.
DISPLACEMENT: Displacement is perhaps the
simplest derived unit. It is the base unit of
length or distance, with the added dimension of
direction. Displacement is considered a vector
quantity because it has both a direction (e.g. up,
down, west, east etc) and a magnitude (how
much). In contrast, a scalar quantity has only a
magnitude. For example, 2 cm is a base quantity
of distance. It is a scalar quantity. A distance of
2 cm in the along an axis perpendicular to the
earth’s surface is a displacement.
AREA and VOLUME: Length or distance is
measured along a single spatial dimension. But
we know that the world around us has three
spatial dimensions and often we need to capture
these extra dimensions when describing an
object. Measuring something with two spatial
dimensions yields an area and measuring
something in three spatial dimensions yields a
volume. Area is expressed as distance2 and
volume is expressed as distance3. In the cgs
system, area takes the unit cm2 and volume takes
the unit cm3. As an added annoyance, volume is
often expressed in terms of liters or milliliters
(which is equal to cm3). Both area and volume
are frequently used for quantifying speech
events. For example, during phonation, the
vocal folds open and close causing an oscillating
change in the glottal area. When we inhale and
exhale for speech, it involves moving a volume
of air into and out of the lungs.
RATE MEASURES: Often we are interested in
how quickly something happens. This is
expressed as a change in some unit per unit
change in time. When the unit of interest is
displacement, the derived unit is
displacement/time. We call this velocity. In the
cgs system, the unit expression is cm/s. Like
displacement, velocity is a vector quantity. The
magnitude of velocity is commonly called speed
and is familiar to anyone who drives a car. The
speedometer tells us how fast we are going, but
not our direction of travel. When the unit of
interest is volume, we use the term flow rate (or
volume velocity). As the name in parentheses
implies, flow rate refers to the volume of a fluid
(in speech, usually air) that moves past some
place of observation per unit time. The unit
expression is therefore cm3/s, though speech
scientists often (and perversely?) describe
airflow rates in liters/second (which will then
equal cm3/s * 10-3). In the speech literature, we
find at least two symbols used to represent flow
rate: a capital letter "U", or a lower-case "i",
though sometimes the reverse symbols are used
(e.g., either a lower-case "u" or an upper-case
"I"). We worry about flow rates in speech, for
example, when we describe speaking habits of
the hearing impaired who seem to be forever
"running out of air" as they speak. The
subjective impression is that such speakers spend
a good bit more air per syllable (or word, or
some other unit of speech) than normal speakers
do. Put another way, flow rates for hearing
impaired speakers often seem to be too high.
Flow rate is analogous to current in an electrical
system. This last fact is a handy thing to know
since electrical circuits are often used to “model”
acoustical systems (like the speech production
system). Acceleration is the change in velocity
per unit time. This may be represented as
distance/time/time or simply distance/time2. In
the cgs system, the unit expression is cm/s2.
Like velocity, acceleration has a sign and a
magnitude. You were probably first exposed to
the concept of acceleration in high school
physics. Recall that the Earth’s gravity causes
objects to accelerate toward it at about 9.81 m/s2
or 981 cm/s2. However, we return to driving a
car for a more concrete example of acceleration.
Acceleration informs us about whether an object
(i.e. a car) is speeding up (positive) or slowing
down (negative).
Rate measures such as velocity (and speed), flow
rate and acceleration may be measured over
different time scales. If the time scale is the
SPPA 4030 Speech Science
same as the duration of the event of interest,
measurement would yield an average
velocity/flow rate/acceleration. However, you
can use a very small time scale which if small
enough will yield something we call
instantaneous velocity/flow rate/acceleration.
For example, if you drive to Chicago, you look
at the speedometer and get an estimate of your
instantaneous speed, or you can wait until you
get to Chicago and use the distance and overall
driving time to calculate your average speed.
FORCE: The unit force in the cgs system is the
dyne. By definition, this is the force that will
accelerate a 1-gram mass at 1 cm/s2. Thus, cgs
quantities of force (as per Euler's expression of
Newton's Second Law: F = ma) will have a 'unit
expression' dyne = (g * cm)/s2, or some
equivalent. Since the acceleration due to the
Earth's gravity, at sea level, is about 981cm/s2, so
that 1 "gram-force" is about 981dyne. In the
“big” mks world, the unit force is the newton, by
definition the force that will accelerate a 1kilogram mass at 1 m/s2. Since force is derived
from acceleration, it too is a vector quantity with
both a sign and a magnitude.
PRESSURE: Pressure is generally defined as
force per unit area, and will therefore have a cgs
unit expression of dyne/cm2, or equivalently,
g/(cm * s2). Atmospheric pressure (often
abbreviated Patm) is about 1.013 x 106 dyne/cm2
at sea level. Interestingly, in the speech
literature, air pressures are most commonly
described in terms of cm of water (cm H20) or
less often, mm of mercury (mm Hg). These
ways of describing pressure derive from a
method for measuring Patm that involves a
column of water (or mercury) in a tube, whose
height is read in centimeters (or millimeters).
Patm in these terms is about 1033 cm H20 (or, 760
mm Hg). As you will learn later, the typical
driving pressures for speech production,
generated within the respiratory system, are
about +10 cm H20 (with respect to Patm), or 1%
higher than the ambient pressure exerted by the
atmosphere. It is generally convenient to think
of one cm H20 as equal to 1000 dyne/cm2 -close enough to merit a cigar. Among some
speech scientists, the (modern) fashion is to
describe air pressures in terms of a unit called the
kilopascal (kPa). [A pascal, abbreviated Pa, is
the pressure generated by one newton, acting
over a one-square-meter area. As you might
guess, a kilopascal is 1000 Pa.] Roughly
speaking, Patm = 100 kPa, and thus, 1cm H20 is
about 0.1 kPa. All these expressions for pressure
can make things a little confusing. No matter
what expression we choose, we worry a lot about
pressures in speech production. For example, we
know that the vocal folds will not vibrate if the
difference between air pressures in the trachea
(below the vocal folds) and pharynx (above the
folds) is too small. Solving the "problem of
phonation" (i.e., making the vocal folds vibrate)
means that speakers must solve the problem of
maintaining an adequate pressure “drop” or
difference, above and below the vocal folds.
Pressure is usually represented by a capital letter
"P", and is analogous to voltage in an electrical
circuit.
WORK: Work is accomplished when a force is
applied to an object and causes it to move.
Therefore, work is defined as the product of
force and distance. In the cgs system, the unit of
work is called an erg (dynes*cm). The mks
system uses the term joule. Raising your
mandible 5 cm requires more work than raising
your jaw 2 cm.
POWER: Power represents the amount of work
accomplished per unit time. This is a rate
measure and the standard unit of watt uses the
mks system (joules/s). Raising your jaw 2 cm in
1 second requires more power than raising your
jaw 2 cm in 2 seconds.
INTENSITY: Intensity is power per unit area
and typically uses the unit watt/cm2. This is not
strictly cgs since the watt is uses the mks system.
Work and power are described mainly because
they are building blocks for the derivation of
intensity. We will not routinely use work and
power. However, intensity is a quantity that has
relevance for understanding the loudness of
sounds. Note that pressure and intensity are both
expressed as units (respectively force and power)
per unit area
RESISTANCE: Resistance refers to energy
“losses” (e.g., due to friction and heat) that might
arise when a fluid like air moves across a surface
(e.g., through some tube). Analogous to an
electrical circuit, and following the spirit of
Ohm's Law (E = I*R -- i.e., voltage E equals the
product of current I and resistance R), acoustic
resistance, typically represented by an uppercase "R", is defined as a pressure difference
(e.g., between two points along a tube) divided
by flow rate (e.g., through the tube length
defined by those two points), and will have a
SPPA 4030 Speech Science
'unit expression' of (dyne * s)/cm5, or
equivalently, g/(cm4 * s). Sometimes, a lowercase "r" is used instead of an upper-case one to
indicate resistance. It is quite uncommon in the
literature to see acoustic resistances represented
explicitly in terms of either derived base-unit
expression [(dyne * s)/cm5, or g/(cm4 * s)].
Rather, resistance is most often referred to in
terms of “acoustic ohms,” or in terms of pressure
(cm H2O) divided by flow rate (in liters/sec, of
all things)! It is not an accident, in quantitative
terms, that this poses no great problem relative to
the strict definition since (about) 1000 dynes per
cm2 corresponds to a pressure of 1 cm H2O, and
1000 cm3 correspond to a liter. Generally, we
worry about acoustic resistance when we worry
about the length, cross-sectional area, and shape
of vocal tract constrictions. For (potential)
speakers with cleft palates, for example, a major
problem for the reconstructive surgeon is to
provide the patient some means of creating a
large enough velopharyngeal resistance so that
every utterance doesn't seem to "come out of the
nose."
USEFUL CONSTANTS: Density of air
(customarily represented by lower-case Greek
letter 'rho', or the character ρ, is often given as
1.14 * 10-3 g/cm3 (i.e., mass per unit volume), for
moist air at 37 degrees centigrade. Velocity of
sound (customarily represented by a lower-case
"c"), in moist air at 37 degrees centigrade is
approximately 3.5 * 104 cm/s. A more common
figure, for cooler air (e.g., ca. 0 degrees
centigrade) is 3.31 * 104 cm/s. Of course, in the
mks system, this is the same as 331 m/s.
BRANCHES OF PHYSICS AND THEIR ROLE
IN SPEECH SCIENCE
The quantities outlined above are helpful in
generating an organized account of our physical
world. In this class, we are interested in
understanding the physical basis of speech
production. In a sense, this class may be
considered a course in applied physics.
Therefore, we should recognize that our
descriptions and theories of speech
communication borrow heavily from various
branches of physics. The branch of physics that
deals with sound is called acoustics.
Aerodynamics is the branch of physics that
deals with air volumes, air flows and air
pressures. The description of bodily movement
(for example, the displacement, velocity and
acceleration of our articulators) is a branch of
physics termed kinematics. We learned in SPPA
205 that movement (kinematics) arises from the
generation of forces within the body and from
external forces such as gravity. The branch of
physics that deals with understanding the forces
that underlie motion is dynamics.