Handbook for Sound Engineers

1648 Chapter 48

48.1.3 Derived Quantities

Derived quantities are those defined in terms of the
seven fundamental quantities, for instance, speed =
length/time. There are sixteen derived quantities with
names of their own: energy (work, quantity of heat),
force, pressure, power, electric charge, electric poten-
tial difference (voltage), electric resistance, electric
conductance, electric capacitance, electric inductance,
frequency, magnetic flux, magnetic flux density, lumi-
nous flux, illuminance, and customary temperature.
Following are thirteen additional derived quantities that
carry the units of the original units that are combined.
They are area, volume, density, velocity, acceleration,
angular velocity, angular acceleration, kinematic
viscosity, dynamic viscosity, electric field strength,
magnetomotive force, magnetic field strength, and
luminance.

48.1.4 Definition of the Quantities

The quantities will be defined in SI units, and their U.S.
customary unit equivalent values will also be given.

Length (L). Length is the measure of how long some-
thing is from end to end. The meter (abbreviated m) is
the SI unit of length. (Note: in the United States the
spelling “meter” is retained, while most other countries
use the spelling “metre.”) The meter is the 1 650 763.73
wavelengths, in vacuum, of the radiation corresponding
to the unperturbed transition between energy level 2P 10
and 5D 5 of the krypton-86 atom. The result is an
orange-red line with a wavelength of 6057.802 × 10–10
meters. The meter is equivalent to 39.370 079 inches.

Mass (M). Mass is the measure of the inertia of a
particle. The mass of a body is defined by the equation

(48-1)

where,
As is the acceleration of the standard mass Ms,

a is the acceleration of the unknown mass, M, when the
two bodies interact.

The kilogram (kg) is the unit of mass. This is the
only base or derived unit in the SI system that contains a
prefix. Multiples are formed by attaching prefixes to the
word gram. Small masses may be described in grams
(g) or milligrams (mg) and large masses in megagrams.
Note the term tonnes is sometimes used for the metric
ton or megagram, but this term is not recommended.

The present international definition of the kilogram

is the mass of a special cylinder of platinum iridium

alloy maintained at the International Bureau of Weights

and Measures, Sevres, France. One kilogram is equal to

2.204 622 6 avoirdupois pounds (lb). A liter of pure

water at standard temperature and pressure has a mass

of 1 kg ± one part in 10^4.

Mass of a body is often revealed by its weight, which

the gravitational attraction of the earth gives to that

body.

If a mass is weighed on the moon, its mass would be

the same as on earth, but its weight would be less due to

the small amount of gravity.

(48-2)

where,

W is the weight,

g is the acceleration due to gravity.

Time (t). Time is the period between two events or the

point or period during which something exists, happens,

etc.

The second (s) is the unit of time. Time is the one

dimension that does not have powers of ten multipliers

in the SI system. Short periods of time can be described

in milliseconds (ms) and microseconds (μs). Longer

periods of time are expressed in minutes (1 min = 60 s)

and hours (1 h = 3600 s). Still longer periods of time are

the day, week, month, and year. The present interna-

tional definition of the second is the time duration of 9,

192, 631, 770 periods of the radiation corresponding to

the transition between the two hyperfine levels of the

ground state of the atom of caesium 133. It is also

defined as 1/86, 400 of the mean solar day.

Current (I). Current is the rate of flow of electrons.

The ampere (A) is the unit of measure for current. Small

currents are measured in milliamperes (mA) and micro-

amperes (μA), and large currents are in kiloamperes

(kA). The international definition of the ampere is the

constant current that, if maintained in two straight

parallel conductors of infinite length and negligible

cross-sectional area and placed exactly 1 m apart in a

vacuum, will produce between them a force of

2×10^7 N/m^2 of length.

A simple definition of one ampere of current is the

intensity of current flow through a 1 ohm resistance

under a pressure of 1 volt of potential difference.

Temperature (T). Temperature is the degree of hotness

or coldness of anything. The kelvin (K) is the unit of

temperature. The kelvin is 1/273.16 of the thermody-

M

As

a

-----

©¹

§·M

= s

M W

g

---- -=