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The following is from The Funk & Wagnalls New Encyclopedia,
1994*
SOUND
physical phenomenon that stimulates the sense of hearing. In
humans, hearing takes place whenever vibrations of frequencies
between about 15 and 20,000 hertz reach the inner ear. The hertz,
or Hz, is a unit of frequency equaling one cycle per second.
Such vibrations reach the inner ear when they are transmitted
through air, and the term sound is something restricted to such
airborne vibrational waves. Modern physicists, however, usually
extend the term to include similar vibrations in liquid or solid
media. Sounds of frequencies higher than about 20,000 Hz are
called ultrasonic. See Frequency ; Ultrasonics .
This article deals with the major outlines of this field of
physics. For the architectural science of designing rooms and
buildings for desirable properties of sound propagation and
reception, see Acoustics . For the nature of the physiological
process of hearing sounds, see Hearing . For the anatomy of
the human and animal hearing mechanism, see Ear . For the general
properties of the generation and propagation of vibrational
waves, including sound waves, see Wave Motion . See also Oscillation
.
In general, waves can be propagated transversely or longitudinally.
In both cases, only the energy of wave motion is propagated
through the medium; no portion of the medium itself actually
moves very far. As a simple example, a rope may be tied securely
to a post at one end, and the other end pulled almost taut and
then shaken once. A wave will travel down the rope to the post,
and at that point it will be reflected and returned to the hand.
No part of the rope actually moves longitudinally toward the
post, but each successive portion of the rope moves transversely.
This type of wave motion is called a transverse wave. Similarly,
if a rock is thrown into a pool of water, a series of transverse
waves moves out from the point of impact. A cork floating near
the point of impact will bob up and down, that is, move transversely
with respect to the direction of wave motion, but will show
little if any outward, or longitudinal, motion. A sound wave,
on the other hand, is a longitudinal wave. As the energy of
wave motion is propagated outward from the center of disturbance,
the individual air molecules that carry the sound move back
and forth, parallel to the direction of wave motion. Thus, a
sound wave is a series of alternate compressions and rarefactions
of the air. Each individual molecule passes the energy on to
neighboring molecules, but after the sound wave has passed,
each molecule remains in about the same location.
PHYSICAL CHARACTERISTICS
Any simple sound, such as a musical note, may be completely
described by specifying three perceptual characteristics: pitch,
loudness (or intensity), and quality (or timbre). These characteristics
correspond exactly to three physical characteristics: frequency,
amplitude, and harmonic constitution, or waveform, respectively.
Noise is a complex sound, a mixture of many different frequencies
or notes not harmonically related.
Frequency.
Sounds can be produced at a desired frequency by different
methods. For example, a sound of 440 Hz can be created by actuating
a loudspeaker with an oscillator tuned to this frequency ( see
Radio ). An air blast can be interrupted by a toothed wheel
with 44 teeth, rotating at 10 revolutions/sec; this method is
used in operating an ordinary siren. The sound of the speaker
and that of the siren at the same frequency are very different
in quality, but will correspond closely in pitch, equivalent
to the A above middle C on a piano. The next higher A on the
piano, the note one octave above, has a frequency of 880 Hz.
Similarly, notes one or two octaves below have frequencies of
220 or 110 Hz, respectively. Thus, by definition, an octave
is the interval between any two notes the frequencies of which
are in a two-to-one ratio.
A fundamental law of harmony states that two notes an octave
apart, when sounded together, produce a euphonious combination.
A fifth and a major third produce successively less euphonious
combinations. Physically, an interval (q.v.) of a fifth consists
of two notes, the frequencies of which bear the arithmetical
ratio three to two, and a major third, the ratio five to four.
Fundamentally, then, the law of harmony states that two or more
notes sound euphonious when played together if their frequencies
bear the ratio of small, whole numbers; if the frequencies do
not bear such ratios, a dissonance is produced. On a fixed-pitch
instrument, such as a piano, it is not possible to arrange the
notes so that all of these ratios hold exactly, and some compromise
is necessary in tuning, called the meantone system, or tempered
scale.
Amplitude.
The amplitude of a sound wave is the degree of motion of air
molecules within the wave, which corresponds to the extent of
rarefaction and compression that accompanies the wave. The greater
the amplitude of the wave, the harder the molecules strike the
ear drum and the louder the sound that is perceived. The amplitude
of a sound wave can be expressed in terms of absolute units
by measuring the actual distance of displacement of the air
molecules, or the pressure differential in the compression and
rarefaction, or the energy involved. Ordinary speech, for example,
produces sound energy at the rate of about one hundred-thousandth
of a watt. All of these measurements are extremely difficult
to make, however, and the intensity of sounds is generally expressed
by comparing them to a standard sound, measured in decibels
(see Sensations of Tone below).
Intensity.
The distance at which a sound can be heard depends on its intensity,
which is the average rate of flow of energy per unit area perpendicular
to the direction of propagation. In the case of spherical waves
spreading from a point source, the intensity varies inversely
as the square of the distance, provided that no loss of energy
is due to viscosity, heat conduction, or other absorption effects.
Thus, in a perfectly homogeneous medium, a sound will be nine
times as intense at a distance of 1 unit from its origin as
at a distance of 3 units; that is, intensity varies inversely
as the square of the distance. In the actual propagation of
sound through the atmosphere, changes in the physical properties
of the air, such as temperature, pressure, and humidity, produce
damping and scattering of the directed sound waves, so that
the inverse-square law generally is not applicable in direct
measurements of the intensity of sound.
Quality.
If A above middle C is played on a violin, a piano, and a tuning
fork, all at the same volume, the tones are identical in frequency
and amplitude, but very different in quality. Of these three
sources, the simplest tone is produced by the tuning fork, the
sound in this case consisting almost entirely of vibrations
having frequencies of 440 Hz. Because of the acoustical properties
of the ear and the resonance properties of the ear's vibrating
membrane, however, it is doubtful whether a pure tone reaches
the inner hearing mechanism in an unmodified form. The principal
component of the note produced by the piano or violin also has
a frequency of 440 Hz, but these notes also contain components
with frequencies that are exact multiples of 440, called overtones,
such as 880, 1320, and 1760. The exact intensity of these other
components, which are called harmonics (q.v.) , determines the
quality of the note.
Velocity of Sound.
The frequency of a sound wave is a measure of the number of
waves passing a given point in 1 sec. The distance between two
successive crests of the wave is called the wavelength. The
product of the wavelength and the frequency must equal the speed
of propagation of the wave, and is the same for sounds of all
frequencies (if the sound is propagated through the same medium
at the same temperature). Thus, the wavelength of A above middle
C is about 78.2 cm (about 2.6 ft), and the wavelength of A below
middle C is about 156.4 cm (about 5.1 ft).
The speed of propagation of sound in dry air at a temperature
of 0j C (32j F) is 331.6 m/sec (1088 ft/sec). If the temperature
is increased, the speed of sound increases; thus, at 20j C (68j
F), the velocity of sound is 344 m/sec (1129 ft/sec). Changes
in pressure at controlled density have virtually no effect on
the speed of sound. The velocity of sound in many other gases
depends only on their density. If the molecules are heavy, they
move less readily, and sound progresses through such a medium
more slowly. Thus, sound travels slightly faster in moist air
than in dry air, because moist air contains a greater number
of lighter molecules. The velocity of sound in most gases depends
also on one other factor, the specific heat (q.v.) , which affects
the propagation of sound waves. See Temperature .
Sound generally moves much faster in liquids and solids than
in gases. In both liquids and solids, density (q.v.) has the
same effect as in gases; that is, velocity varies inversely
as the square root of the density. The velocity also varies
directly as the square root of the elasticity (q.v.) . The speed
of sound in water, for example, is slightly less than 1525 m/sec
(5000 ft/sec) at ordinary temperatures but increases greatly
with an increase in temperature. The speed of sound in copper
is about 3353 m/sec (about 11,000 ft/sec) at ordinary temperatures
and decreases as the temperature is increased (due to decreasing
elasticity); in steel, which is more elastic, sound moves at
a speed of about 4877 m/sec (about 16,000 ft/sec). Sound is
propagated very efficiently in steel.
Refraction, Reflection, and Interference.
Sound moves forward in a straight line when traveling through
a medium having uniform density. Like light, however, sound
is subject to refraction, which bends sound waves from their
original path. In polar regions, for example, where air close
to the ground is colder than air that is somewhat higher, a
rising sound wave entering the warmer region, in which sound
moves with greater speed, is bent downward by refraction. The
excellent reception of sound downwind and the poor reception
upwind are also due to refraction. The velocity of wind is generally
greater at an altitude of many meters than near the ground;
a rising sound wave moving downwind is bent back toward the
ground, whereas a similar sound wave moving upwind is bent upward
over the head of the hearer.
Sound is also governed by reflection (q.v.) , obeying the fundamental
law that the angle of incidence equals the angle of reflection.
An echo is the result of reflection of sound. Sonar (q.v.) depends
on the reflection of sounds propagated in water. A megaphone
is a funnellike tube that forms a beam of sound waves by reflecting
some of the diverging rays from the sides of the tube. A similar
tube can gather sound waves if the large end is pointed at the
source of the sound; an ear trumpet is such a device.
Sound is also subject to diffraction and interference (qq.v.)
. If sound from a single source reaches a listener by two different
paths-one direct and the other reflected-the two sounds may
reinforce one another; but if they are out of phase they may
interfere, so that the resultant sound is actually less intense
than the direct sound without reflection. Interference paths
are different for sounds of different frequencies, so that interference
produces distortion in complex sounds. Two sounds of different
frequencies may combine to produce a third sound, the frequency
of which is equal to the sum or difference of the original two
frequencies.
SENSATIONS OF TONE
If the ear of an average young person is tested by an audiometer,
it will be found to be sensitive to all sounds from 15 to 20
Hz to 15,000 or 20,000 Hz. The hearing of older persons is less
acute, particularly to the higher frequencies. The ear is most
sensitive in the range from A above middle C up to A four octaves
higher; in this range a sound can be perceived hundreds of times
fainter than a sound an octave higher or two octaves lower.
The degree to which a sensitive ear can distinguish between
two pure notes of slightly different loudness or slightly different
frequency varies in different ranges of loudness and frequency
of the tones. A difference in loudness of about 20 percent (1
decibel, dB), and a difference in frequency of 1/3 percent (about
1/20 of a note) can be distinguished in sounds of moderate intensity
at the frequencies to which the ear is most sensitive (about
1000 to 2000 Hz). In this same range, the difference between
the softest sound that can be heard and the loudest sound that
can be distinguished as sound (louder sounds are "felt,"
or perceived, as painful stimuli) is about 120 dB (about 1 trillion
times as loud).
All of these sensitivity tests refer to pure tones, such as
those produced by an electronic oscillator. Even for such pure
tones the ear is imperfect. Notes of identical frequency but
differing greatly in intensity may seem to differ slightly in
pitch. More important is the difference in apparent relative
intensities with different frequencies. At high intensities
the ear is approximately equally sensitive to most frequencies,
but at low intensities the ear is much more sensitive to the
middle high frequencies than to the lowest and highest. Thus,
sound-reproducing equipment that is functioning perfectly will
seem to fail to reproduce the lowest and highest notes if the
volume is decreased.
Three Important Types of Ordinary Sound.
In speech, music, and noise, pure tones are seldom heard. A
musical note contains, in addition to a fundamental frequency,
higher tones that are harmonics of the fundamental frequency.
Speech contains a complex mixture of sounds, some (but not all)
of which are in harmonic relation to one another. Noise consists
of a mixture of many different frequencies within a certain
range; it is thus comparable to white light, which consists
of a mixture of light of all different colors. Different noises
are distinguished by different distributions of energy in the
various frequency ranges ( see Spectrum ).
When a musical tone containing some harmonics of a fundamental
tone, but missing other harmonics or the fundamental itself,
is transmitted to the ear, the ear forms various beats in the
form of sum and difference frequencies, thus producing the missing
harmonics or the fundamental not present in the original sound.
These notes are also harmonics of the original fundamental note.
This incorrect response of the ear may be valuable. Sound-reproducing
equipment without a large speaker, for example, cannot generally
produce sounds of pitch lower than two octaves below middle
C; nonetheless, a human ear listening to such equipment can
resupply the fundamental note by resolving beat frequencies
from its harmonics. Another imperfection of the ear in the presence
of ordinary sounds is the inability to hear high-frequency notes
when low-frequency sound of considerable intensity is present.
This phenomenon is called masking.
In general, speech is understandable and musical themes can
be satisfactorily understood if only the frequencies between
250 and 3000 Hz, the frequency range of ordinary telephones,
are reproduced, although a few speech sounds, such as th, require
frequencies as high as 6000 Hz. For naturalness, however, the
range of about 100 to 10,000 Hz must be reproduced. Sounds produced
by a few musical instruments can be reproduced naturally only
at somewhat lower frequencies, and a few noises can be reproduced
at somewhat higher frequencies.
For the conversion of sound waves into electrical waves and
electrical waves into sound waves, see Microphone ; Telephone
.
HISTORICAL DEVELOPMENT
The elementary phenomena of sound were the subject of much
speculation among the ancient peoples; however, with the exception
of a few lucky guesses, little was known about the science of
sound until about ad 1600. Starting at that time, the knowledge
of sound increased more rapidly than knowledge of the corresponding
phenomena of light, because the latter are more difficult to
observe and measure.
The ancient Greeks cared little for the scientific study of
sound, but they had a great interest in music, and considered
music to represent "applied number," in contrast to
"pure number," the science of arithmetic. The Greek
philosopher Pythagoras discovered that an octave represents
a two-to-one frequency ratio and enunciated the law connecting
consonance with numerical ratios; on this law, however, he built
a fantastic and unscientific edifice of mystical speculation.
Aristotle, in brief remarks on sound, made a fairly accurate
guess concerning the nature of the generation and transmission
of sound, but no scientifically valid experimental studies were
made until about 1600, when Galileo made a scientific study
of sound and enunciated many of its fundamental laws. Galileo
stated the relationship between pitch and frequency and the
laws of musical harmony and dissonance, essentially as stated
above in this article. He also explained theoretically how the
natural frequency of vibration of a stretched string, and hence
the frequency of sound produced by a string instrument, depends
on the length, weight, and tension of the string.
The 16th, 17th, and 18th Centuries.
Quantitative measurement of sound was made by the French mathematician
Marin Mersenne (1588-1648), who measured the time of return
of an echo, and arrived at a figure that was in error by less
than 10 percent. Mersenne also made the first crude determination
of the actual frequency of a note of a given pitch. He measured
the frequency of vibration of a long, heavy wire that moved
so slowly that its motion could be followed by the eye; then,
from theoretical considerations, he calculated the frequency
of a short, light wire that produced an audible sound.
In 1660, the dependence of sound on a gaseous, liquid, or solid
medium for transmission was demonstrated by the Anglo-Irish
scientist Robert Boyle, who suspended a bell in a vacuum by
means of a string and showed that, although the clapper could
be seen to strike the bell, no sound was heard.
The mathematical treatment of the theory of sound was begun
by the English mathematician and physicist Sir Isaac Newton
in his Philosophiae Naturalis Principia Mathematica (Mathematical
Principles of Natural Philosophy, 1687). The propagation of
sound through any fluid was shown to depend only on measurable
physical properties of the fluid, such as elasticity and density,
and Newton calculated from theoretical considerations the velocity
of sound in air.
The 18th century was primarily a period of theoretical development.
The calculus (q.v.) provided a powerful new tool to scientists
in many fields, and such mathematicians as the French Jean le
Rond d'Alembert and Joseph Louis Lagrange, the Dutch mathematician
Johann Bernoulli (1667-1748), and the Swiss mathematician Leonhard
Euler contributed to the knowledge of such subjects as the pitch
and quality of sound produced by a particular musical instrument
and the speed and nature of transmission of sound in various
media. The complete mathematical treatment of sound, however,
depends on harmonic analysis, which was discovered by the French
mathematician Baron Jean Baptiste Joseph Fourier in 1822 and
applied to sound by the German physicist Georg Simon Ohm.
Variations in sound, called beats, inherent in sound waves,
were discovered about 1740 by the Italian violinist Giuseppe
Tartini and the German organist Georg Sorge (1703-78). The German
physicist Ernst Chladni (1756-1827) made numerous discoveries
in acoustics at the close of the 18th century, notably concerning
the vibration of strings and rods.
The 19th and 20th Centuries.
The 19th century was primarily a period of experimental development.
The first accurate measurements of the speed of sound in water
were made in 1826 by the French mathematician Jacques Sturm
(1803- 55), and throughout the century numerous experiments
were made determining the speed of sound of various frequencies
in various media with extreme accuracy. The fundamental law
that the speed is the same for sounds of different frequencies
and depends on the density and elasticity of the medium was
determined in these experiments. The stroboscope, the stethoscope,
and the siren were all used in the study of sound during the
19th century.
The standardization of pitch occupied much attention in the
19th century. The first suggestion for a standard had been made
about 1700 by the French physicist Joseph Sauveur (1653-1716),
who proposed C equals 256, a convenient standard for mathematical
purposes. The German physicist Johann Heinrich Scheibler (1777-1838)
made the first accurate determination of pitch corresponding
to frequency and proposed the standard A equals 440 in 1834.
In 1859 the French government decreed that the standard should
be A equals 435, based on the research of the French physicist
Jules Antoine Lissajous (1822-80). This standard was accepted
in many parts of the world, including the U.S., until well into
the 20th century.
During the 19th century the telephone, the microphone, and
the phonograph, all of which were useful for further study of
sound, were invented. In the 20th century, physicists for the
first time had instruments that made possible simple, accurate,
quantitative study of sound. By means of electronic oscillators,
waves of any type may be produced electronically, then converted
into sounds by electromagnetic or piezoelectric means ( see
Electronics ). Conversely, sounds may be converted into electrical
currents by means of a microphone, amplified electronically
without distortion, and then analyzed by means of a cathode-ray
oscilloscope. Modern techniques permit extremely high-fidelity
recording and reproduction of sound. See also Phonograph ; Sound
Recording and Reproduction .
Military necessity in World War I led to the first use of sound
for underwater detection of vessels; sound is now also used
for studies of ocean currents and layers, and for sea-bottom
mapping ( see Sonar ). In addition, ultrahigh-frequency sound
waves are now used in a wide range of technical and medical
applications.
* Infopedia 2.0 © 1992-1996 SoftKey Multimedia, a subsidiary
of SoftKey International Inc. SoftKey is a registered trademark
and INFOPEDIA is a trademark of SoftKey Multimedia Inc. The
Funk & Wagnalls New Encyclopedia are licensed from K-III
Reference Corporation. ©1994-96 K-III Reference Corporation.
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