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Radiology => Ultrasound => Sound
Sound
INTRODUCTION
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. For the nature of the physiological process of hearing sounds. For the anatomy of the human and animal hearing mechanism. For the general properties of the generation and propagation of vibrational waves, including sound waves.
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 . 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 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 .
° 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, determines the quality, or timbre, 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 second. 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 0° C (32° F) is 331.6 m/sec (1088 ft/sec). If the temperature is increased, the speed of sound increases; thus, at 20° C (68° 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, which affects the propagation of sound waves.
Sound generally moves much faster in liquids and solids than in gases. In both liquids and solids, density 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. 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, obeying the fundamental law that the angle of incidence equals the angle of reflection. An echo is the result of reflection of sound. Sonar depends on the reflection of sounds propagated in water. A megaphone is a funnel-like 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. 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.
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.
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 AD1600. 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, 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 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, 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. The German physicist Ernst Chladni 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, 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, who proposed C equals 256, a convenient standard for mathematical purposes. The German physicist Johann Heinrich Scheibler 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. This standard was accepted in many parts of the world, including the United States, 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. 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.
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. In addition, ultrahigh-frequency sound waves are now used in a wide range of technical and medical applications.
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