Essentials of Audiology

1Acoustics and Sound Measurement

We begin our study of audiology by reviewing the nature of sound because, after all, sound is what we hear. The science of sound is called acoustics, which is a branch of physics, and relies on several basic physical principles. Many useful sources are available for students wishing to pursue the areas covered in this chapter in greater detail (e.?g., Peterson & Gross 1972; Hewitt 1974; Kinsler, Frey, Coppens, & Sanders 1982; Sears, Zemansky, & Young 1982; Beranek 1986; Gelfand 2018).

■ Physical Quantities

The basic physical quantities are mass, time, and length (or distance). All other physical quantities are derived by combining these three basic ones, as well as other derived quantities, in a variety of ways. The principal basic and derived quantities are summarized in Table 1.1. These basic quantities are expressed in terms of conventional units that are measurable and repeatable. The unit of mass (M) is the kilogram (kg) or the gram (g); the unit of length (L) is the meter (m) or the centimeter (cm); and the unit of time (t) is the second (s). Mass is not really synonymous with weight even though we express its magnitude in kilograms. The mass of a body is related to its density, but its weight is related to the force of gravity. If two objects are the same size, the one with greater density will weigh more. However, even though an object's mass would be identical on the earth and the moon, it would weigh less on the moon, where there is less gravity.

Table 1.1 Principal physical quantities

Quantity

Formula

MKS (SI) units

cgs units

Comments

Mass (M)

M

kilogram (kg)

gram (g)

1 ?kg ?= ?103 g

Time (t)

t

second (s)

s

Area (A)

A

m2

cm2

1 m2 ?= ?104 cm2

Displacement (x)

x

meter (m)

centimeter (cm)

1 m ?= ?102 cm

Velocity (v)

v = x/t

m/s

cm/s

1 ?m/s =102 cm/s

Acceleration (a)

a = v/t

m/s2

cm/s2

1 ?m/s2 ?= ?102 cm/s2

Force (F)

F = Ma

kg · m/s2

g · cm/s2

1 N ?= ?105 dyne

= Mv/t

newton (N)

dyne

Pressure (p)

p = F/A

N/m2

Pascal (Pa)

dyne/cm2

microbar (µbar)

2 ?× ?10-5 N/m2 or 20 µPa

(reference value)

2 ?× ?10-4 dyne/cm2 or µbar

(reference value)

Work (W)

W ?= ?Fx

N · m

joule (J)

dyne · cm erg

1 J ?= ?107 erg

Power (P)

P ?= ?W/t

joule/s

erg/s

1 W ?= ?1 J/s

= Fx/t

watt (W)

watt (W)

1 W ?= ?107 erg/s

= Fv

Intensity (I)

I ?= ?P/A

W/m2

W/cm2

10-12 W/m2 (reference value)

10-16 W/cm2 (reference value)

When we express mass in kilograms and length in meters, we are using the meter-kilogram-second or MKS system. Expressing mass in grams and length in centimeters constitutes the centimeter-gram-second or cgs system. These two systems also have different derived quantities. For example, the units of force and work are called newtons and joules in the MKS system and dynes and ergs in the cgs system, respectively. We will emphasize the use of MKS units because this is the internationally accepted standard in the scientific community, known as the Système International d'Unites (SI). Equivalent cgs values will often be given as well because the audiology profession has traditionally worked in cgs units, and the death of old habits is slow and labored. These quantities are summarized with equivalent values in MKS and cgs units in Table 1.1. In addition, the correspondence between scientific notation and conventional numbers, and the meanings of prefixes used to describe the sizes of metric units are shown for convenience and ready reference in Table 1.2 and Table 1.3.

Table 1.2 Expressing numbers in standard notation and scientific notation

Standard notation

Scientific notation

0.000001

10-6

0.00001

10-5

0.0001

10-4

0.001

10-3

0.01

10-2

0.1

10-1

1

100

10

101

100

102

1000

103

10,000

104

100,000

105

1,000,000

106

3600

3.6 ?× ?103

0.036

3.6 ?× ?10-2

0.0002

2 ?× ?10-4

0.00002

2 ?× ?10-5

Table 1.3 Examples of prefixes used to express metric units

Prefix

Symbol

Definition

Multiply by

Standard notation

Scientific notation

micro

µ

millionths

1/1,000,000 or 0.000001

10-6

milli

m

thousandths

1/1000 or 0.001

10-3

centi

c

hundredths

1/100 or 0.01

10-2

deci

d

tenths

1/10 or 0.1

10-1

deka

da

tens

10

101

hecto

h

hundreds

100

102

kilo

k

thousands

1000

103

mega

M

millions

1,000,000

106

Quantities may be scalars or vectors. A scalar can be fully described by its magnitude (amount or size), but a vector has both direction and magnitude. For example, length is a scalar because an object that is one meter long is always one meter long. However, we are dealing with a vector when we measure the distance between two coins that are one meter apart because their relationship has both magnitude and direction (from point x 1 to point x 2). This quantity is called displacement (x). Derived quantities will be vectors if they have one or more components that are vectors; for example, velocity is a vector because it is derived from displacement, and acceleration is a vector because it involves velocity. We distinguish between scalars and vectors because they are handled differently when calculations are being made.

Velocity Everyone knows that "55 miles per hour" refers to the speed of a car that causes it to travel a distance of 55 miles in a one-hour period of time. This is an example of velocity (v), which is equal to the amount of displacement (x) that occurs over time (t):

Displacement is measured in meters and time is measured in seconds (s); thus,...