Acoustics
Acoustics
Acoustics, sometimes called acoustical physics, is the science that deals with the production, transmission, reception, control, and effects of sound in gases, liquids, and solids. The word acoustic was derived from the ancient Greek word akoustikos, meaning able to be heard. Sound may be produced when a material body vibrates; it is transmitted only when there is some material body, called the medium, that can carry the vibrations away from the producing body; it is received when a third material body, attached to some indicating device, is set into vibratory motion by that intervening medium. However, the only vibrations that are considered sound (or sonic vibrations) are those in which the medium vibrates in the same direction as the sound travels, and for which the vibrations are very small. When the rate of vibration is below the range of human hearing, the sound is termed infrasonic; when it is above that range, it is called ultrasonic. The term supersonic refers to bodies moving at speeds greater than the speed of sound, and is not normally involved in the study of acoustics.
Production of sound
There are many examples of vibrating bodies producing sounds. Some examples are as simple as a string in a violin or piano, or a column of air in an organ pipe or in a clarinet; some are as complex as the vocal chords of a human. Sound may also be caused by a large disturbance that causes parts of a body to vibrate, such as sounds caused by a falling tree.
Vibrations of a string
To understand some of the fundamentals of sound production and propagation it is instructive to first consider the small vibrations of a stretched string held at both ends under tension. While these vibrations are not an example of sound, they do illustrate many of the properties of importance in acoustics as well as in the production of sound. The string may vibrate in a variety of different ways, depending upon whether it is struck or rubbed to set it in motion, and where on the string the action took place. However, its motion can be analyzed into a combination of a large number of simple motions. The simplest, called the fundamental (or the first harmonic), appears in Figure 1, which shows the outermost extensions of the string carrying out this vibration.
The second harmonic is shown in Figure 2; the third harmonic in Figure 3; and so forth (the whole set of harmonics beyond the first are called the
overtones). The rate at which these vibrations take place (number of times per second the motion is repeated) is called the frequency, denoted by f (the reciprocal of the frequency, which is the time for one cycle to be competed, is called the period). A single complete vibration is normally termed a cycle, so that the frequency is usually given in cycles per second,
or the equivalent modern unit, the hertz (abbreviated Hz). It is characteristic of the stretched string that the second harmonic has a frequency twice that of the fundamental; the third harmonic has a frequency three times that of the fundamental; and so forth. This is true for only a few very simple systems, with most sound-producing systems having a far more complex relationship among the harmonics.
Those points on the string that do not move are called the nodes; the maximum extension of the string (from the horizontal in the Figures) is called the amplitude, and is denoted by A in Figures 1-3. The distance one must go along the string at any instant of time to reach a section having the identical motion is called the wavelength, and is denoted by L in Figures 1-3. It can be seen that the string only contains one-half wavelength of the fundamental; that is, the wavelength of the fundamental is twice the string length. The wavelength of the second harmonic is the length of the string. The string contains one-and-one-half (3/2) wavelengths of the third harmonic, so that its wavelength is two-thirds (2/3) of the length of the string. Similar relationships hold for all the other harmonics.
If the fundamental frequency of the string is called f0, and the length of the string is l, it can be seen from the above that the product of the frequency and the wavelength of each harmonic is equal to 2f0 l. The dimension of this product is a velocity (e.g., feet per second or centimeters per second); detailed analysis of the motion of the stretched string shows that this is the velocity with which a small disturbance on the string would travel down the string.
Vibrations of an air column
When air is blown across the entrance to an organ pipe, it causes the air in the pipe to vibrate, so that there are alternate small increases and decreases of the density of the air (condensations and rarefactions). These alternate in space, with the distance between successive condensations (or rarefactions) being the wavelength; they alternate in time, with the frequency of the vibration. One major difference here is that the string vibrates transversely (perpendicular to the length of the string), while the air vibrates longitudinally (in the direction of the column of air). If the pipe is open at both ends, then the density of the air at the ends must be the same as that of the air outside the pipe, while the density inside the pipe can vary above or below that value. Again, as for the vibrations of the string, the density of the air in the pipe can be analyzed into a fundamental and overtones. If the density of the air vibrating in the fundamental mode (of the open pipe) is plotted across the pipe length, the graph is as in Figure 4.
The zero value at the ends denotes the fact that the density at the ends of the pipe must be the same as outside the pipe (the ambient density), while inside the pipe the density varies above and below that value with the frequency of the fundamental, with a maximum (and minimum) at the center. The density plot for the fundamental looks just like that for the fundamental of the vibrating stretched string (Figure 1). In the same manner, plots of the density for the various overtones would look like those of the string overtones. The frequency of the fundamental can be calculated from the fact that the velocity, which is analogous to that found for vibrations of the string, is the velocity with which sound travels in the air, usually denoted by c. Since the wavelength of the fundamental is twice the pipe length, its frequency is (c/2) l, where l is the length of the organ pipe. (While the discussion here is in terms of the density variations in the air, these are accompanied by small variations in the air pressure, and small motions of the air itself. At places of increased density the pressure is increased; where the pressure is changing rapidly, the air motion is greatest.) When a musician blows into the mouthpiece of a clarinet, the air rushing past the reed causes it to vibrate, which then causes the column of air in the clarinet to vibrate in a manner similar to, but more complicated than, the motion of the organ pipe. These vibrations (as for all vibrations) can also be analyzed into harmonics. By opening and closing the keyholes in the clarinet, different harmonics of the clarinet are made to grow louder or softer causing different tones to be heard.
Sound production in general
Thus, the production of sound depends upon the vibration of a material body, with the vibration being transmitted to the medium that carries the sound away from the sound producer. The vibrating violin string, for example, causes the body of the violin to vibrate; the back-and-forth motion of the parts of the body of the violin causes the air in contact with it to vibrate. That is, the motion of the violin body produces small variations in the density of the air, and these variations are carried forth into the air surrounding the violin. As the sound is carried away, the small variations in air density are propagated in the direction of travel of the sound.
Sounds from humans, of course, are produced by forcing air across the vocal cords, which causes them to vibrate. The various overtones are enhanced or diminished by the size and shape of the various cavities in the head (the sinuses, for example), as well as the placement of the tongue and the shape of the mouth. These factors cause specific wavelengths, of all that are produced by the vocal cords, to be amplified differently so that different people have their own characteristic voice sounds. These sounds can be then controlled by changing the placement of the tongue and the shape of the mouth, producing speech. The frequencies usually involved in speech are from about 100 to 10,000 Hz. However, humans can hear sounds in the frequency range from about 20 to 18,000 Hz. These outer limits vary from person to person, with age, and with the loudness of the sound. The density variations (and corresponding pressure variations) produced in ordinary speech are extremely small, with ordinary speech producing less than one-millionth the power of a 100 watt light bulb! In the sonic range of frequencies (those produced by humans), sounds are often produced by loudspeakers, devices using electronic and mechanical components to produce sounds. The sounds to be transmitted are first changed to electrical signals by a microphone (see Reception of sounds, below), for example, or from a compact disc; the frequencies carried by the electrical signals are those to be produced as the sound signals. In the simplest case, the wires carrying the electrical signals are used to form an electromagnet, which attracts and releases a metal diaphragm. This, in turn, causes the variations in the density in the air adjacent to the diaphragm. These variations in density will have the same frequencies as were in the original electrical signals.
Ultrasonic vibrations are of great importance in industry and medicine, as well as in investigations in pure science. They are usually produced by applying an alternating electric voltage across certain types of crystals (quartz is a typical one) that expand and contract slightly as the voltage varies; the frequency of the voltage then determines the frequency of the sounds produced.
Transmission of sound
In order for sound to travel between the source and the receiver there must be some material between them that can vibrate in the direction of travel (called the propagation direction). (The fact that sounds can only be transmitted by a material medium means that, for example, an explosion outside a spaceship would not be heard by its occupants!) The motion of the sound-producing body causes density variations in the medium (see Figure 5, which schematically shows the density variations associated with a sound wave), which move along in the direction of propagation. The transmission of sounds in the form of these density variations is termed a wave since these variations are carried forward without significant change, although eventually friction in the air itself causes the wave to dissipate. (This is analogous to a water wave in which the particles of water vibrate up and down, while the wave propagates forward.) Since the motion of the medium at any point is a small vibration back and forth in the direction in which the wave is proceeding, sound is termed a longitudinal wave. (The water wave, like the violin string, is an example of a transverse wave.) The most usual medium of sound transmission is air, but any substance that can be compressed can act as a medium for sound propagation. A fundamental characteristic of a wave is that it carries energy and momentum away from a source without transporting matter from the source.
Since the speed of sound in air is about 1,088 ft/sec (331 m/sec), human speech involves wavelengths from about 1.3 in to 11 ft (3.3 cm to 3.3 m). Thus, the wavelengths of speech are of the size of ordinary objects, unlike light, whose wavelengths are extremely small compared to items that are part of everyday life. Because of this, sound does not ordinarily cast acoustic shadows but, because its wavelengths are so large, can be transmitted around ordinary objects. For example, if a light is shining on a person, and a book is placed directly between them, the person will no longer be able to see the light (a shadow is cast by the book on the eyes of the observer). However, if one person is speaking to another, then placing a book between them will hardly affect the sounds heard at all; the sound waves are able to go around the book to the observer’s ears. On the other hand, placing a high wall between a highway and houses can greatly decrease the sounds of the traffic noises if the dimensions of the wall (height and length) are large compared with the wavelength of the traffic sounds. Thus, sound waves (as for all waves) tend to go around (e.g., ignore the presence of) obstacles that are small compared with the wavelength of the wave; and are reflected by obstacles that are large compared with the wavelength. For obstacles of approximately the same size as the wavelength, waves exhibit a very complex behavior known as diffraction, in which there are enhanced and diminished values of the wave amplitude, but which is too complicated to be described here in detail.
The speed of sound in a gas is proportional to the square root of the pressure divided by the density. Thus, helium, which has a much lower density than air, transmits sound at a greater speed than air. If a person breathes some helium, the characteristic wavelengths are still determined by the shape of the mouth, but the greater sound speed causes the speech to be emitted at a higher frequency—thus, the Mickey Mouse-like sounds from someone who speaks after taking a breath of helium from a balloon.
In general, the speed of sound in liquids is greater than in gases, and greater still in solids. In seawater, for example, the speed is about 4,750 ft/sec (1,447 m/sec); in a gas, the speed increases as the pressure increases, and as the density decreases. Typical speeds of sound in solids are 5,450 yd/sec (5,000 m/sec), but vary considerably from one solid to another.
Reception of sound
Physiological acoustics is the study of the transmission of sound and how it is heard by the human ear. Sound travels in waves, vibrations that cause compression and rarefaction of molecules in the air. The organ of hearing, the ear, has three basic parts that collect and transmit these vibrations: the outer, middle and inner ear. The outer ear is made of the pinna, the external part of the ear that can be seen, which acts to funnel sound through the ear canal toward the eardrum or tympanic membrane. The membrane is highly sensitive to vibrations; it also protects the middle and inner ear. When the eardrum vibrates, it sets up vibrations in the three tiny bones of the middle ear: the malleus, incus, and stapes, which are often called the hammer, anvil, and stirrup because of their resemblance to those objects. These bones amplify the sound. The stapes is connected to the oval window, the entrance to the inner ear, which contains a spiral-shaped, fluid-filled chamber called the cochlea. When vibrations are transmitted from the stapes to the oval window, the fluid within the cochlea is put into motion. Tiny hairs that line the basilar membrane of the cochlea, a membrane that divides the cochlea lengthwise, move in accordance with the wave pattern. The hair cells convert the mechanical energy of the waveform into nerve signals that reach the auditory nerve and then the brain. In the brain, the sound is interpreted.
In the sonic range of frequencies, the microphone, a device using electrical and mechanical components, is the common method of receiving sounds. One simple form is to have a diaphragm as one plate of an electrical condenser. When the diaphragm vibrates under the action of a sound wave, the current in the circuit varies due to the varying capacitance of the condenser. This varying current can then be used to activate a meter or oscilloscope or, after suitable processing, make an audio tape or some such permanent record.
Applications
The applications of acoustical devices are far too numerous to describe; one only has to look around residential homes to see some of them: telephones, radios and television sets, and compact disc players; even clocks that speak the time. Probably one of the most important from the human point of view is the hearing aid, a miniature microphone-amplifier-loudspeaker that is designed to enhance whatever range of frequencies a person finds difficulty hearing.
However, one of the first large-scale industrial uses of sound propagation was by the military in World War I (1914–1918), in the detection of enemy submarines by means of sonar (for so und n avigation a nd r anging). This was further developed during the period leading upt to World War II (1939–1945), and since then. The ship-hunting submarine has a sound source and receiver projecting from the ship’s hull that can be used for either listening or in an echo-ranging mode; the source and receiver are directional, so that they can send and receive an acoustic signal from only a small range of directions at one time. In the listening mode of operation, the operator tries to determine what are the sources of any noise that might be heard: the regular beat of an engine heard underwater can tell that an enemy might be in the vicinity. In the echo-ranging mode, a series of short bursts of sound is sent out, and the time for the echo to return is noted; that time interval multiplied by the speed of sound in water indicates (twice) the distance to the reflecting object. Since the sound source is directional, the direction in which the object lies is also known. This is now such a well developed method of finding underwater objects that commercial versions are available for fishermen to hunt for schools of fish.
Ultrasonic sources, utilizing pulses of frequencies in the many millions of cycles per second (and higher), are now used for inspecting metals for flaws. The small wavelengths make the pulses liable to reflection from any imperfections in a piece of metal. Castings may have internal cracks which will weaken the structure; welds may be imperfect, possibly leading to failure of a metal-to-metal joint; metal fatigue may produce cracks in areas impossible to inspect by eye. The use of ultrasonic inspection techniques is increasingly important for failure prevention in bridges, aircraft, and pipelines, to name just a few.
The use of ultrasonics in medicine is also of growing importance. The detection of kidney stones or
KEY TERMS
Amplitude —The maximum displacement of the material that is vibrating.
Condensations —When air is the vibrating medium there are alternate small increases and decreases of the density of the air; the increases are called condensations.
Cycle —A single complete vibration.
Cycles per second —The number of complete vibrations per second.
Frequency —The rate at which vibrations take place (number of times per second the motion is repeated), denoted here by f and given in cycles per second or in hertz.
Fundamental —The lowest frequency of vibration of a sound-producing body (also called the first harmonic).
Harmonics (first, second, etc.) —The various frequencies of vibration of a sound-producing body, numbered from the lowest frequency to higher frequencies.
Hertz —A unit of measurement for frequency, abbreviated Hz. One hertz is one cycle per second.
Infrasonic vibrations —When the rate of vibration is below the range of human hearing, e.g., below about 10 cycles per second.
Longitudinal wave —The case where the motion of the vibrating body is in the wave propagation direction.
Loudspeaker —A device to produce sounds from an electric current, by electrical and mechanical means, in the range of frequencies around the sonic range (that is produced by humans).
Medium —A material body that carries the acoustic vibrations away from the body producing them.
Microphone —A device to change sounds, by electrical and mechanical means, into an electric current having the same frequencies as the sound, in the range of frequencies around the sonic range (that is produced by humans).
Nodes —Places where the amplitude of vibration is zero.
Overtones —The set of harmonics, beyond the first, of a soundproducing body.
Period —The length of time for one cycle to be completed; the reciprocal of the frequency.
Propagation direction —The direction in which the wave is traveling.
Rarefactions —When air is the vibrating medium there are alternate small increases and decreases of the density of the air; the decreases are called rarefactions.
Sonar —Sound Navigation And Ranging. A device utilizing sound to determine the range and direction to an underwater object.
Supersonic —Refers to bodies moving at speeds greater than the speed of sound (not normally involved in the study of acoustics).
Transverse wave —The case where the motion of the vibrating body is perpendicular to the wave propagation direction.
Ultrasonic vibrations —Acoustic vibrations with frequencies higher than the human threshold of hearing.
Wave —A motion, in which energy and momentum is carried away from some source, which repeats itself in space and time with little or no change.
Wavelength —The distance between two consecutive crests or troughs in a wave.
gallstones is routine, as is the imaging of fetuses to detect suspected birth defects, cardiac imaging, blood flow measurements, and so forth.
Thus, the field of acoustics covers a vast array of different areas of use, and they are constantly expanding. Acoustics in the communications industry, in various phases of the construction industries, in oil field exploration, in medicine, in the military, and in the entertainment industry, all attest to the growth of this field and to its continuing importance in the future.
Resources
BOOKS
Deutsch, Diana. Ear and Brain: How We Make Sense of Sounds. New York: Copernicus Books, 2003.
Kinsler, Lawrence E., et. al. Fundamentals of Acoustics, 4th ed. New York: John Wiley & Sons, 2000.
OTHER
The Acoustical Society of America (ASA). “Homepage for the ASA.” <http://asa.aip.org/index.html> (accessed accessed November 9, 2006).
The University of New South Wales. “Music Acoustics.” <http://www.phys.unsw.edu.au/music/> (accessed accessed November 9, 2006).
David Mintzer
Acoustics
ACOUSTICS
ACOUSTICS. When he first mentioned the "Acoustique Art" in his Advancement of Learning (1605), Francis Bacon (1561–1626) was drawing a distinction between the physical acoustics he expanded in the Sylva Sylvarum (1627) and the harmonics of the Pythagorean mathematical tradition. The Pythagorean tradition still survived in Bacon's time in the works of such diverse people as Gioseffo Zarlino (1517–1590), René Descartes (1596–1650), and Johannes Kepler (1571–1630). In Bacon's words: "The nature of sounds, in some sort, [hath been with some diligence inquired,] as far as concerneth music. But the nature of sounds in general hath been superficially observed. It is one of the subtilest pieces of nature" (Bacon, p. 390).
Bacon's "Acoustique Art" was therefore concerned with the study of "immusical sounds" and with experiments in the "majoration in sounds" (p. 451), that is, the harnessing of sounds in buildings (architectural acoustics) by their "enclosure" in artificial channels inside the walls or in the environment (hydraulic acoustics). The aim of Baconian acoustics was to catalog, quantify, and shape human space by means of sound. This stemmed from the echometria, an early modern tradition of literature on echo, as studied by the mathematicians Giuseppe Biancani (1566–1624), Marin Mersenne (1588–1648), and Daniello Bartoli (1608–1685), in which the model of optics was applied in acoustics to the behavior of sound. It was in a sense a historical antecedent to Isaac Newton's (1642–1727) analogy between colors and musical tones in Opticks (1704). Athanasius Kircher's (1601–1680) Phonurgia Nova of 1673 was the outcome of this tradition. Attacking British acoustics traditions, Kircher argued that the "origin of the Acoustical Art" (p. 111) lay in his own earlier experiments with sounding tubes at the Collegio Romano in 1649 and sketched the ideology of a Christian baroque science of acoustics designed to dominate the world by exploiting the "boundless powers of sound" (p. 2).
Seventeenth-century empirical observations and mathematical explanations of the simultaneous vibrations of a string at different frequencies were important in the development of modern experimental acoustics. The earliest contribution in this branch of acoustics was made by Mersenne, who derived the mathematical law governing the physics of a vibrating string. Around 1673 Christiaan Huygens (1629–1695) estimated its absolute frequency, and in 1677 John Wallis (1616–1703) published a report of experiments on the overtones of a vibrating string. In 1692 Francis Robartes (1650–1718) followed with similar findings.
These achievements paved the way for the eighteenth-century acoustique of Joseph Sauveur (1653–1716) and for the work of Brook Taylor (1685–1731), Leonhard Euler (1707–1783), Jean Le Rond d'Alembert (1717–1783), Daniel Bernoulli (1700–1782), and Giordani Riccati (1709–1790), who all attempted to determine mathematically the fundamental tone and the overtones of a sonorous body. Modern experimental acoustics sought in nature, as a physical law of the sounding body, the perfect harmony that in the Pythagorean tradition sprang from the mind of the "geometrizing God." Experimental epistemology in acoustics also influenced the studies of the anatomy and physiology of hearing, especially the work of Joseph-Guichard Duverney (1648–1730) and Antonio Maria Valsalva (1666–1723), that in the nineteenth century gave rise to physiological and psychological acoustics.
See also Alembert, Jean Le Rond d' ; Bacon, Francis ; Euler, Leonhard ; Huygens Family ; Kircher, Athanasius ; Mersenne, Marin ; Newton, Isaac ; Physics ; Scientific Revolution .
BIBLIOGRAPHY
Bacon, Francis. Sylva sylvarum. In The Works of Francis Bacon. Edited by J. Spedding, R. L. Ellis, and D. D. Heath, vol. 2, pp. 385–436. London, 1858–1859.
Dostrovsky, Sigalia. "Early Vibration Theory: Physics and Music in the Seventeenth Century." Archive for History of Exact Sciences 14 (1974–1975): 169–218.
Gouk, Penelope Mary. "Acoustics in the Early Royal Society, 1660–1680." Notes and Records of the Royal Society of London 36 (1982): 155–175.
Hunt, Frederick Vinton. Origins in Acoustics: The Science of Sound from Antiquity to the Age of Newton. New Haven and London, 1978.
Kircher, Athanasius. Phonurgia Nova. Kempten, 1673.
Paolo Gozza
Acoustics
ACOUSTICS
CONCEPT
The area of physics known as acoustics is devoted to the study of the production, transmission, and reception of sound. Thus, wherever sound is produced and transmitted, it will have an effect somewhere, even if there is no one present to hear it. The medium of sound transmission is an all-important, key factor. Among the areas addressed within the realm of acoustics are the production of sounds by the human voice and various instruments, as well as the reception of sound waves by the human ear.
HOW IT WORKS
Wave Motion and Sound waves
Sound waves are an example of a larger phenomenon known as wave motion, and wave motion is, in turn, a subset of harmonic motion—that is, repeated movement of a particle about a position of equilibrium, or balance. In the case of sound, the "particle" is not an item of matter, but of energy, and wave motion is a type of harmonic movement that carries energy from one place to another without actually moving any matter.
Particles in waves experience oscillation, harmonic motion in one or more dimensions. Oscillation itself involves little movement, though some particles do move short distances as they interact with other particles. Primarily, however, it involves only movement in place. The waves themselves, on the other hand, move across space, ending up in a position different from the one in which they started.
A transverse wave forms a regular up-and-down pattern in which the oscillation is perpendicular to the direction the wave is moving. This is a fairly easy type of wave to visualize: imagine a curve moving up and down along a straight line. Sound waves, on the other hand, are longitudinal waves, in which oscillation occurs in the same direction as the wave itself.
These oscillations are really just fluctuations in pressure. As a sound wave moves through a medium such as air, these changes in pressure cause the medium to experience alternations of density and rarefaction (a decrease in density). This, in turn, produces vibrations in the human ear or in any other object that receives the sound waves.
Properties of Sound Waves
CYCLE AND PERIOD.
The term cycle has a definition that varies slightly, depending on whether the type of motion being discussed is oscillation, the movement of transverse waves, or the motion of a longitudinal sound wave. In the latter case, a cycle is defined as a single complete vibration.
A period (represented by the symbol T ) is the amount of time required to complete one full cycle. The period of a sound wave can be mathematically related to several other aspects of wave motion, including wave speed, frequency, and wavelength.
THE SPEED OF SOUND IN VARIOUS MEDIA.
People often refer to the "speed of sound" as though this were a fixed value like the speed of light, but, in fact, the speed of sound is a function of the medium through which it travels. What people ordinarily mean by the "speed of sound" is the speed of sound through air at a specific temperature. For sound traveling at sea level, the speed at 32°F (0°C) is 740 MPH (331 m/s), and at 68°F (20°C), it is 767 MPH (343 m/s).
In the essay on aerodynamics, the speed of sound for aircraft was given at 660 MPH (451 m/s). This is much less than the figures given above for the speed of sound through air at sea level, because obviously, aircraft are not flying at sea level, but well above it, and the air through which they pass is well below freezing temperature.
The speed of sound through a gas is proportional to the square root of the pressure divided by the density. According to Gay-Lussac's law, pressure is directly related to temperature, meaning that the lower the pressure, the lower the temperature—and vice versa. At high altitudes, the temperature is low, and, therefore, so is the pressure; and, due to the relatively small gravitational pull that Earth exerts on the air at that height, the density is also low. Hence, the speed of sound is also low.
It follows that the higher the pressure of the material, and the greater the density, the faster sound travels through it: thus sound travels faster through a liquid than through a gas. This might seem a bit surprising: at first glance, it would seem that sound travels fastest through air, but only because we are just more accustomed to hearing sounds that travel through that medium. The speed of sound in water varies from about 3,244 MPH (1,450 m/s) to about 3,355 MPH (1500 m/s). Sound travels even faster through a solid—typically about 11,185 MPH (5,000 m/s)—than it does through a liquid.
FREQUENCY.
Frequency (abbreviated f ) is the number of waves passing through a given point during the interval of one second. It is measured in Hertz (Hz), named after nineteenth-century German physicist Heinrich Rudolf Hertz (1857-1894) and a Hertz is equal to one cycle of oscillation per second. Higher frequencies are expressed in terms of kilohertz (kHz; 103 or 1,000 cycles per second) or megahertz (MHz; 106 or 1 million cycles per second.)
The human ear is capable of hearing sounds from 20 to approximately 20,000 Hz—a relatively small range for a mammal, considering that bats, whales, and dolphins can hear sounds at a frequency up to 150 kHz. Human speech is in the range of about 1 kHz, and the 88 keys on a piano vary in frequency from 27 Hz to 4,186 Hz. Each note has its own frequency, with middle C (the "white key" in the very middle of a piano keyboard) at 264 Hz. The quality of harmony or dissonance when two notes are played together is a function of the relationship between the frequencies of the two.
Frequencies below the range of human audibility are called infrasound, and those above it are referred to as ultrasound. There are a number of practical applications for ultrasonic technology in medicine, navigation, and other fields.
WAVELENGTH.
Wavelength (represented by the symbol λ, the Greek letter lambda) is the distance between a crest and the adjacent crest, or a trough and an adjacent trough, of a wave. The higher the frequency, the shorter the wavelength, and vice versa. Thus, a frequency of 20 Hz, at the bottom end of human audibility, has a very large wavelength: 56 ft (17 m). The top end frequency of 20,000 Hz is only 0.67 inches (17 mm).
There is a special type of high-frequency sound wave beyond ultrasound: hypersound, which has frequencies above 107 MHz, or 10 trillion Hz. It is almost impossible for hypersound waves to travel through all but the densest media, because their wavelengths are so short. In order to be transmitted properly, hypersound requires an extremely tight molecular structure; otherwise, the wave would get lost between molecules.
Wavelengths of visible light, part of the electromagnetic spectrum, have a frequency much higher even than hypersound waves: about 109 MHz, 100 times greater than for hypersound. This, in turn, means that these wavelengths are incredibly small, and this is why light waves can easily be blocked out by using one's hand or a curtain.
The same does not hold for sound waves, because the wavelengths of sounds in the range of human audibility are comparable to the size of ordinary objects. To block out a sound wave, one needs something of much greater dimensions—width, height, and depth—than a mere cloth curtain. A thick concrete wall, for instance, may be enough to block out the waves. Better still would be the use of materials that absorb sound, such as cork, or even the use of machines that produce sound waves which destructively interfere with the offending sound.
AMPLITUDE AND INTENSITY.
Amplitude is critical to the understanding of sound, though it is mathematically independent from the parameters so far discussed. Defined as the maximum displacement of a vibrating material, amplitude is the "size" of a wave. The greater the amplitude, the greater the energy the wave contains: amplitude indicates intensity, commonly known as "volume," which is the rate at which a wave moves energy per unit of a cross-sectional area.
Intensity can be measured in watts per square meter, or W/m2. A sound wave of minimum intensity for human audibility would have a value of 10−12, or 0.000000000001, W/m2. As a basis of comparison, a person speaking in an ordinary tone of voice generates about 10−4, or 0.0001, watts. On the other hand, a sound with an intensity of 1 W/m2 would be powerful enough to damage a person's ears.
REAL-LIFE APPLICATIONS
Decibel Levels
For measuring the intensity of a sound as experienced by the human ear, we use a unit other than the watt per square meter, because ears do not respond to sounds in a linear, or straight-line, progression. If the intensity of a sound is doubled, a person perceives a greater intensity, but nothing approaching twice that of the original sound. Instead, a different system—known in mathematics as a logarithmic scale—is applied.
In measuring the effect of sound intensity on the human ear, a unit called the decibel (abbreviated dB) is used. A sound of minimal audibility (10−12 W/m2) is assigned the value of 0 dB, and 10 dB is 10 times as great—10−11 W/m2. But 20 dB is not 20 times as intense as 0 dB; it is 100 times as intense, or 10−10 W/m2. Every increase of 10 dB thus indicates a tenfold increase in intensity. Therefore, 120 dB, the maximum decibel level that a human ear can endure without experiencing damage, is not 120 times as great as the minimal level for audibility, but 1012 (1 trillion) times as great—equal to 1 W/m2, referred to above as the highest safe intensity level.
Of course, sounds can be much louder than 120 dB: a rock band, for instance, can generate sounds of 125 dB, which is 5 times the maximum safe decibel level. A gunshot, firecracker, or a jet—if one is exposed to these sounds at a sufficiently close proximity—can be as high as 140 dB, or 20 times the maximum safe level. Nor is 120 dB safe for prolonged periods: hearing experts indicate that regular and repeated exposure to even 85 dB (5 less than a lawn mower) can cause permanent damage to one's hearing.
Production of Sound Waves
MUSICAL INSTRUMENTS.
Sound waves are vibrations; thus, in order to produce sound, vibrations must be produced. For a stringed instrument, such as a guitar, harp, or piano, the strings must be set into vibration, either by the musician's fingers or the mechanism that connects piano keys to the strings inside the case of the piano.
In other woodwind instruments and horns, the musician causes vibrations by blowing into the mouthpiece. The exact process by which the vibrations emerge as sound differs between woodwind instruments, such as a clarinet or saxophone on the one hand, and brass instruments, such as a trumpet or trombone on the other. Then there is a drum or other percussion instrument, which produces vibrations, if not musical notes.
ELECTRONIC AMPLIFICATION.
Sound is a form of energy: thus, when an automobile or other machine produces sound incidental to its operation, this actually represents energy that is lost. Energy itself is conserved, but not all of the energy put into the machine can ever be realized as useful energy; thus, the automobile loses some energy in the form of sound and heat.
The fact that sound is energy, however, also means that it can be converted to other forms of energy, and this is precisely what a microphone does: it receives sound waves and converts them to electrical energy. These electrical signals are transmitted to an amplifier, and next to a loudspeaker, which turns electrical energy back into sound energy—only now, the intensity of the sound is much greater.
Inside a loudspeaker is a diaphragm, a thin, flexible disk that vibrates with the intensity of the sound it produces. When it pushes outward, the diaphragm forces nearby air molecules closer together, creating a high-pressure region around the loudspeaker. (Remember, as stated earlier, that sound is a matter of fluctuations in pressure.) The diaphragm is then pushed backward in response, freeing up an area of space for the air molecules. These, then, rush toward the diaphragm, creating a low-pressure region behind the high-pressure one. The loudspeaker thus sends out alternating waves of high and low pressure, vibrations on the same frequency of the original sound.
THE HUMAN VOICE.
As impressive as the electronic means of sound production are (and of course the description just given is highly simplified), this technology pales in comparison to the greatest of all sound-producing mechanisms: the human voice. Speech itself is a highly complex physical process, much too involved to be discussed in any depth here. For our present purpose, it is important only to recognize that speech is essentially a matter of producing vibrations on the vocal cords, and then transmitting those vibrations.
Before a person speaks, the brain sends signals to the vocal cords, causing them to tighten. As speech begins, air is forced across the vocal cords, and this produces vibrations. The action of the vocal cords in producing these vibrations is, like everything about the miracle of speech, exceedingly involved: at any given moment as a person is talking, parts of the vocal cords are opened, and parts are closed.
The sound of a person's voice is affected by a number of factors: the size and shape of the sinuses and other cavities in the head, the shape of the mouth, and the placement of the teeth and tongue. These factors influence the production of specific frequencies of sound, and result in differing vocal qualities. Again, the mechanisms of speech are highly complicated, involving action of the diaphragm (a partition of muscle and tissue between the chest and abdominal cavities), larynx, pharynx, glottis, hard and soft palates, and so on. But, it all begins with the production of vibrations.
Propagation: Does It Make a Sound?
As stated in the introduction, acoustics is concerned with the production, transmission (sometimes called propagation), and reception of sound. Transmission has already been examined in terms of the speed at which sound travels through various media. One aspect of sound transmission needs to be reiterated, however: for sound to be propagated, there must be a medium.
There is an age-old "philosophical" question that goes something like this: If a tree falls in the woods and there is no one to hear it, does it make a sound? In fact, the question is not a matter of philosophy at all, but of physics, and the answer is, of course, "yes." As the tree falls, it releases energy in a number of forms, and part of this energy is manifested as sound waves.
Consider, on the other hand, this rephrased version of the question: "If a tree falls in a vacuum—an area completely devoid of matter, including air—does it make a sound?" The answer is now a qualified "no": certainly, there is a release of energy, as before, but the sound waves cannot be transmitted. Without air or any other matter to carry the waves, there is literally no sound.
Hence, there is a great deal of truth to the tagline associated with the 1979 science-fiction film Alien : "In space, no one can hear you scream." Inside an astronaut's suit, there is pressure and an oxygen supply; without either, the astronaut would perish quickly. The pressure and air inside the suit also allow the astronaut to hear sounds within the suit, including communications via microphone from other astronauts. But, if there were an explosion in the vacuum of deep space outside the spacecraft, no one inside would be able to hear it.
Reception of Sound
RECORDING.
Earlier the structure of electronic amplification was described in very simple terms. Some of the same processes—specifically, the conversion of sound to electrical energy—are used in the recording of sound. In sound recording, when a sound wave is emitted, it causes vibrations in a diaphragm attached to an electrical condenser. This causes variations in the electrical current passed on by the condenser.
These electrical pulses are processed and ultimately passed on to an electromagnetic "recording head." The magnetic field of the recording head extends over the section of tape being recorded: what began as loud sounds now produce strong magnetic fields, and soft sounds produce weak fields. Yet, just as electronic means of sound production and transmission are still not as impressive as the mechanisms of the human voice, so electronic sound reception and recording technology is a less magnificent device than the human ear.
HOW THE EAR HEARS.
As almost everyone has noticed, a change in altitude (and, hence, of atmospheric pressure) leads to a strange "popping" sensation in the ears. Usually, this condition can be overcome by swallowing, or even better, by yawning. This opens the Eustachian tube, a passageway that maintains atmospheric pressure in the ear. Useful as it is, the Eustachian tube is just one of the human ear's many parts.
The "funny" shape of the ear helps it to capture and amplify sound waves, which passthrough the ear canal and cause the eardrum tovibrate. Though humans can hear sounds over amuch wider range, the optimal range of audibility is from 3,000 to 4,000 Hz. This is because thestructure of the ear canal is such that sounds in this frequency produce magnified pressure fluctuations. Thanks to this, as well as other specific properties, the ear acts as an amplifier of sounds.
Beyond the eardrum is the middle ear, an intricate sound-reception device containing some of the smallest bones in the human body—bones commonly known, because of their shapes, as the hammer, anvil, and stirrup. Vibrations pass from the hammer to the anvil to the stirrup, through the membrane that covers the oval window, and into the inner ear.
Filled with liquid, the inner ear contains the semicircular canals responsible for providing a sense of balance or orientation: without these, a person literally "would not know which way is up." Also, in the inner ear is the cochlea, an organ shaped like a snail. Waves of pressure from the fluids of the inner ear are passed through the cochlea to the auditory nerve, which then transmits these signals to the brain.
The basilar membrane of the cochlea is a particularly wondrous instrument, responsible in large part for the ability to discriminate between sounds of different frequencies and intensities. The surface of the membrane is covered with thousands of fibers, which are highly sensitive to disturbances, and it transmits information concerning these disturbances to the auditory nerve. The brain, in turn, forms a relation between the position of the nerve ending and the frequency of the sound. It also equates the degree of disturbance in the basilar membrane with the intensity of the sound: the greater the disturbance, the louder the sound.
WHERE TO LEARN MORE
Adams, Richard C. and Peter H. Goodwin. Engineering Projects for Young Scientists. New York: Franklin Watts, 2000.
Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.
Friedhoffer, Robert. Sound. Illustrated by Richard Kaufman and Linda Eisenberg; photographs by Timothy White. New York: F. Watts, 1992.
Gardner, Robert. Science Projects About Sound. Berkeley Heights, NJ: Enslow Publishers, 2000.
Internet Resources for Sound and Light (Web site). <http://electro.sau.edu/SLResources.html> (April 25, 2001).
"Music and Sound Waves" (Web site). <http://www.silcom.com/~aludwig/musicand.htm> (April 28, 2001).
Oxlade, Chris. Light and Sound. Des Plaines, IL: Heinemann Library, 2000.
Physics Tutorial System: Sound Waves Modules (Web site). <http://csgrad.cs.vt.edu/~chin/chin_sound.html> (April 25, 2001).
"Sound Waves and Music." The Physics Classroom (Web site). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/soundtoc.html> (April 28, 2001).
"What Are Sound Waves?" (Web site). <http://rustam.uwp.edu/GWWM/sound_waves.html> (April 28, 2001).
KEY TERMS
ACOUSTICS:
An area of physics devoted to the study of the production, transmission, and reception of sound.
AMPLITUDE:
The maximum displacement of a vibrating material. In wave motion, amplitude is the "size" of a wave, and for sound waves, amplitude indicates the intensity or volume of sound.
CYCLE:
For a sound wave, a cycle is a single complete vibration.
DECIBEL:
A unit for measuring intensity of sound. Decibels, abbreviated dB, are calibrated along a logarithmic scale whereby every increase of 10 dB indicates an increase in intensity by a factor of 10. Thus if the level of intensity is increased from 30 to 60 dB, the resulting intensity is not twice as great as that of the earlier sound—it is 1,000 times as great.
ENERGY:
The ability to perform work, which is the exertion of force over a givendistance. Work is the product of force and distance, where force and distance are exerted in the same direction.
FREQUENCY:
In wave motion, frequency is the number of waves passing through a given point during the interval of one second. The higher the frequency, the shorter the wavelength. Measured in Hertz, frequency is mathematically related to wave speed, wavelength, and period.
HARMONIC MOTION:
The repeated movement of a particle about a position of equilibrium, or balance.
HERTZ:
A unit for measuring frequency, named after nineteenth-century German physicist Heinrich Rudolf Hertz (1857-1894). High frequencies are expressed in terms of kilohertz (kHz; 103 or 1,000 cycles per second) or megahertz (MHz; 106 or 1 million cycles per second.)
INTENSITY:
Intensity is the rate at which a wave moves energy per unit of cross-sectional area. Where sound wavesare concerned, intensity is commonly known as "volume."
LONGITUDINAL WAVE:
A wave in which the movement of vibration is in the same direction as the wave itself. A sound wave is an example of a longitudinal wave.
MATTER:
Physical substance that has mass; occupies space; is composed of atoms; and is ultimately convertible to energy.
MEDIUM:
Material through which sound travels. (It cannot travel through a vacuum.) The most common medium (plural, media) of sound transmission experienced in daily life is air, but in fact sound can travel through any type of matter.
OSCILLATION:
The vibration experienced by individual waves even as the wave itself is moving through space. Oscillation is a type of harmonic motion, typically periodic, in one or more dimensions.
PERIOD:
For wave motion, a period is the amount of time required to complete one full cycle. Period is mathematically related to frequency, wavelength, and wave speed.
PERIODIC MOTION:
Motion that is repeated at regular intervals. These intervals are known as periods.
RAREFACTION:
A decrease in density.
ULTRASOUND :
Sound waves with a frequency above 20,000 Hertz, which makes them in audible to the human ear.
VACUUM:
An area entirely devoid of matter, including air.
WAVELENGTH:
The distance between a crest and the adjacent crest, or the trough and an adjacent trough, of a wave. Wavelength, symbolized by λ (the Greek letter lambda) is mathematically related to wave speed, period, and frequency.
WAVE MOTION:
A type of harmonic motion that carries energy from one place to another without actually moving anymatter.
Acoustics
Acoustics
Acoustics is the science that deals with the production, transmission, and reception of sound. Sound may be produced when a material body vibrates; it is transmitted only when there is some material body, called the medium, that can carry the vibrations away from the producing body; it is received when a third material body, attached to some indicating device, is set into vibratory motion by that intervening medium. However, the only vibrations that are considered sound (or sonic vibrations) are those in which the medium vibrates in the same direction as the sound travels, and for which the vibrations are very small. When the rate of vibration is below the range of human hearing , the sound is termed infrasonic; when it is above that range, it is called ultrasonic. The term supersonic refers to bodies moving at speeds greater than the speed of sound, and is not normally involved in the study of acoustics.
Production of sound
There are many examples of vibrating bodies producing sounds. Some are as simple as a string in a violin or piano, or a column of air in an organ pipe or in a clarinet; some are as complex as the vocal chords of a human. Sound may also be caused by a large disturbance which causes parts of a body to vibrate, such as sounds caused by a falling tree.
Vibrations of a string
To understand some of the fundamentals of sound production and propagation it is instructive to first consider the small vibrations of a stretched string held at both ends under tension. While these vibrations are not an example of sound, they do illustrate many of the properties of importance in acoustics as well as in the production of sound. The string may vibrate in a variety of different ways, depending upon whether it is struck or rubbed to set it in motion, and where on the string the action took place. However, its motion can be analyzed into a combination of a large number of simple motions. The simplest, called the fundamental (or the first harmonic), appears in Figure 1, which shows the outermost extensions of the string carrying out this vibration.
The second harmonic is shown in Figure 2; the third harmonic in Figure 3; and so forth (the whole set of harmonics beyond the first are called the overtones). The rate at which these vibrations take place (number of times per second the motion is repeated) is called the frequency , denoted by f (the reciprocal of the frequency, which is the time for one cycle to be competed, is called the period). A single complete vibration is normally termed a cycle, so that the frequency is usually given in cycles per second, or the equivalent modern unit, the hertz (abbreviated Hz). It is characteristic of the stretched string that the second harmonic has a frequency twice that of the fundamental; the third harmonic has a frequency three times that of the fundamental; and so forth. This is true for only a few very simple systems, with most sound-producing systems having a far more complex relationship among the harmonics.
Those points on the string which do not move are called the nodes; the maximum extension of the string (from the horizontal in the Figures) is called the amplitude, and is denoted by A in Figures 1-3. The distance one must go along the string at any instant of time to reach a section having the identical motion is called the wavelength, and is denoted by L in Figures 1-3. It can be seen that the string only contains one-half wavelength of the fundamental, that is, the wavelength of the fundamental is twice the string length. The wavelength of the second harmonic is the length of the string. The string contains one-and-one-half (3/2) wavelengths of the third harmonic, so that its wavelength is two-thirds (2/3) of the length of the string. Similar relationships hold for all the other harmonics.
If the fundamental frequency of the string is called f0, and the length of the string is l, it can be seen from the above that the product of the frequency and the wavelength of each harmonic is equal to 2f0l. The dimension of this product is a velocity (e.g., feet per second or centimeters per second); detailed analysis of the motion of the stretched string shows that this is the velocity with which a small disturbance on the string would travel down the string.
Vibrations of an air column
When air is blown across the entrance to an organ pipe, it causes the air in the pipe to vibrate, so that there are alternate small increases and decreases of the density of the air (condensations and rarefactions). These alternate in space , with the distance between successive condensations (or rarefactions) being the wavelength; they alternate in time, with the frequency of the vibration. One major difference here is that the string vibrates transversely (perpendicular to the length of the string), while the air vibrates longitudinally (in the direction of the column of air). If the pipe is open at both ends, then the density of the air at the ends must be the same as that of the air outside the pipe, while the density inside the pipe can vary above or below that value. Again, as for the vibrations of the string, the density of the air in the pipe can be analyzed into a fundamental and overtones. If the density of the air vibrating in the fundamental mode (of the open pipe) is plotted across the pipe length, the graph is as in Figure 4.
The "zero value" at the ends denotes the fact that the density at the ends of the pipe must be the same as outside the pipe (the ambient density), while inside the pipe the density varies above and below that value with the frequency of the fundamental, with a maximum (and minimum) at the center. The density plot for the fundamental looks just like that for the fundamental of the vibrating stretched string (Figure 1). In the same manner, plots of the density for the various overtones would look like those of the string overtones. The frequency of the fundamental can be calculated from the fact that the velocity, which is analogous to that found for vibrations of the string, is the velocity with which sound travels in the air, usually denoted by c. Since the wavelength of the fundamental is twice the pipe length, its frequency is (c/2)l, where l is the length of the organ pipe. (While the discussion here is in terms of the density variations in the air, these are accompanied by small variations in the air pressure , and small motions of the air itself. At places of increased density the pressure is increased; where the pressure is changing rapidly, the air motion is greatest.) When a musician blows into the mouthpiece of a clarinet, the air rushing past the reed causes it to vibrate which then causes the column of air in the clarinet to vibrate in a manner similar to, but more complicated than, the motion of the organ pipe. These vibrations (as for all vibrations) can also be analyzed into harmonics. By opening and closing the keyholes in the clarinet, different harmonics of the clarinet are made to grow louder or softer causing different tones to be heard.
Sound production in general
Thus, the production of sound depends upon the vibration of a material body, with the vibration being transmitted to the medium that carries the sound away from the sound producer. The vibrating violin string, for example, causes the body of the violin to vibrate; the "back-and-forth" motion of the parts of the body of the violin causes the air in contact with it to vibrate. That is, small variations in the density of the air are produced by the motion of the violin body, and these are carried forth into the air surrounding the violin. As the sound is carried away, the small variations in air density are propagated in the direction of travel of the sound.
Sounds from humans, of course, are produced by forcing air across the vocal cords, which causes them to vibrate. The various overtones are enhanced or diminished by the size and shape of the various cavities in the head (the sinuses, for example), as well as the placement of the tongue and the shape of the mouth. These factors cause specific wavelengths, of all that are produced by the vocal cords, to be amplified differently so that different people have their own characteristic voice sounds. These sounds can be then controlled by changing the placement of the tongue and the shape of the mouth, producing speech . The frequencies usually involved in speech are from about 100 to 10,000 Hz. However, humans can hear sounds in the frequency range from about 20 to 18,000 Hz. These outer limits vary from person to person, with age, and with the loudness of the sound. The density variations (and corresponding pressure variations) produced in ordinary speech are extremely small, with ordinary speech producing less than one-millionth the power of a 100 watt light bulb! In the sonic range of frequencies (those produced by humans), sounds are often produced by loudspeakers, devices using electronic and mechanical components to produce sounds. The sounds to be transmitted are first changed to electrical signals by a microphone (see Reception of sounds, later), for example, or from an audio tape or compact disc ; the frequencies carried by the electrical signals are those to be produced as the sound signals. In the simplest case, the wires carrying the electrical signals are used to form an electromagnet which attracts and releases a metal diaphragm. This, in turn, causes the variations in the density in the air adjacent to the diaphragm. These variations in density will have the same frequencies as were in the original electrical signals.
Ultrasonic vibrations are of great importance in industry and medicine, as well as in investigations in pure science. They are usually produced by applying an alternating electric voltage across certain types of crystals (quartz is a typical one) that expand and contract slightly as the voltage varies; the frequency of the voltage then determines the frequency of the sounds produced.
Transmission of sound
In order for sound to travel between the source and the receiver there must be some material between them that can vibrate in the direction of travel (called the propagation direction). (The fact that sound can only be transmitted by a material medium means that an explosion outside a spaceship would not be heard by its occupants!) The motion of the sound-producing body causes density variations in the medium (see Figure 5, which schematically shows the density variations associated with a sound wave), which move along in the direction of propagation. The transmission of sounds in the form of these density variations is termed a wave since these variations are carried forward without significant change, although eventually friction in the air itself causes the wave to dissipate. (This is analogous to a water wave in which the particles of water vibrate up and down, while the "wave" propagates forward.) Since the motion of the medium at any point is a small vibration back and forth in the direction in which the wave is proceeding, sound is termed a longitudinal wave. (The water wave, like the violin string, is an example of a transverse wave.) The most usual medium of sound transmission is air, but any substance that can be compressed can act as a medium for sound propagation. A fundamental characteristic of a wave is that it carries energy and momentum away from a source without transporting matter from the source.
Since the speed of sound in air is about about 1,088 ft/sec (331 m/sec), human speech involves wavelengths from about 1.3 in to 11 ft (3.3 cm to 3.3 m). Thus, the wavelengths of speech are of the size of ordinary objects, unlike light, whose wavelengths are extremely small compared to items that are part of everyday life. Because of this, sound does not ordinarily cast "acoustic shadows" but, because its wavelengths are so large, can be transmitted around ordinary objects. For example, if a light is shining on a person, and a book is placed directly between them, the person will no longer be able to see the light (a shadow is cast by the book on the eyes of the observer). However, if one person is speaking to another, then placing a book between them will hardly affect the sounds heard at all; the sound waves are able to go around the book to the observer's ears. On the other hand, placing a high wall between a highway and houses can greatly decrease the sounds of the traffic noises if the dimensions of the wall (height and length) are large compared with the wavelength of the traffic sounds. Thus, sound waves (as for all waves) tend to "go around" (e.g., ignore the presence of) obstacles which are small compared with the wavelength of the wave; and are reflected by obstacles which are large compared with the wavelength. For obstacles of approximately the same size as the wavelength, waves exhibit a very complex behavior known as diffraction , in which there are enhanced and diminished values of the wave amplitude, but which is too complicated to be described here in detail.
The speed of sound in a gas is proportional to the square root of the pressure divided by the density. Thus, helium, which has a much lower density than air, transmits sound at a greater speed than air. If a person breathes some helium, the characteristic wavelengths are still determined by the shape of the mouth, but the greater sound speed causes the speech to be emitted at a higher frequency—thus the "Donald Duck" sounds from someone who speaks after taking a breath of helium from a balloon .
In general, the speed of sound in liquids is greater than in gases, and greater still in solids. In sea water, for example, the speed is about 4,750 ft/sec (1,447 m/sec); in a gas, the speed increases as the pressure increases, and as the density decreases. Typical speeds of sound in solids are 5,450 yd/sec (5,000 m/sec), but vary considerably from one solid to another.
Reception of sound
Physiological acoustics is the study of the transmission of sound and how it is heard by the human ear . Sound travels in waves, vibrations that cause compression and rarefaction of molecules in the air. The organ of hearing, the ear, has three basic parts that collect and transmit these vibrations: the outer, middle and inner ear. The outer ear is made of the pinna, the external part of the ear that can be seen, which acts to funnel sound through the ear canal toward the eardrum or tympanic membrane . The membrane is highly sensitive to vibrations and also protects the middle and inner ear. When the eardrum vibrates it sets up vibrations in the three tiny bones of the middle ear, the malleus, incus and stapes, which are often called the hammer, anvil and stirrup because of their resemblance to those objects. These bones amplify the sound. The stapes is connected to the oval window, the entrance to the inner ear, which contains a spiral-shaped, fluid-filled chamber called the cochlea. When vibrations are transmitted from the stapes to the oval window, the fluid within the cochlea is put into motion. Tiny hairs that line the basilar membrane of the cochlea, a membrane that divides the cochlea lengthwise, move in accordance with the wave pattern. The hair cells convert the mechanical energy of the waveform into nerve signals that reach the auditory nerve and then the brain . In the brain, sound is interpreted.
In the sonic range of frequencies, the microphone, a device using electrical and mechanical components, is the common method of receiving sounds. One simple form is to have a diaphragm as one plate of an electrical condenser. When the diaphragm vibrates under the action of a sound wave, the current in the circuit varies due to the varying capacitance of the condenser. This varying current can then be used to activate a meter or oscilloscope or, after suitable processing, make an audio tape or some such permanent record.
Applications
The applications of acoustical devices are far too numerous to describe; one only has to look around our homes to see some of them: telephones, radios and television sets, compact disc players and tape recorders; even clocks that "speak" the time. Probably one of the most important from the human point of view is the hearing aid, a miniature microphone-amplifier-loudspeaker that is designed to enhance whatever range of frequencies a person finds difficulty hearing.
However, one of the first large-scale industrial uses of sound propagation was by the military in World War I, in the detection of enemy submarines by means of sonar (for sound navigation and ranging). This was further developed during the period between then and World War II, and since then. The ship-hunting submarine has a sound source and receiver projecting from the ship's hull that can be used for either listening or in an echo-ranging mode; the source and receiver are directional, so that they can send and receive an acoustic signal from only a small range of directions at one time. In the listening mode of operation, the operator tries to determine what are the sources of any noise that might be heard: the regular beat of an engine heard underwater can tell that an enemy might be in the vicinity. In the echo-ranging mode, a series of short bursts of sound is sent out, and the time for the echo to return is noted; that time interval multiplied by the speed of sound in water indicates (twice) the distance to the reflecting object. Since the sound source is directional, the direction in which the object lies is also known. This is now such a well developed method of finding underwater objects that commercial versions are available for fishermen to hunt for schools of fish .
Ultrasonic sources, utilizing pulses of frequencies in the many millions of cycles per second (and higher), are now used for inspecting metals for flaws. The small wavelengths make the pulses liable to reflection from any imperfections in a piece of metal. Castings may have internal cracks which will weaken the structure; welds may be imperfect, possibly leading to failure of a metal-to-metal joint; metal fatigue may produce cracks in areas impossible to inspect by eye . The use of ultrasonic inspection techniques is increasingly important for failure prevention in bridges , aircraft , and pipelines, to name just a few.
The use of ultrasonics in medicine is also of growing importance. The detection of kidney stones or gallstones is routine, as is the imaging of fetuses to detect suspected birth defects , cardiac imaging, blood flow measurements, and so forth.
Thus, the field of acoustics covers a vast array of different areas of use, and they are constantly expanding. Acoustics in the communications industry, in various phases of the construction industries, in oil field exploration, in medicine, in the military, and in the entertainment industry, all attest to the growth of this field and to its continuing importance in the future.
Resources
books
Deutsch, Diana. Ear and Brain: How We Make Sense of Sounds New York: Copernicus Books, 2003.
Kinsler, Lawrence E., et. al. Fundamentals of Acoustics, 4th ed. New York: John Wiley & Sons, 1999.
Organizations
The Acoustical Society of America. 2 Huntington Quadrangle, Suite 1NO1, Melville, NY 11747–4502 Phone: (516) 576–2360. <http://asa.aip.org/index.html>
Other
The University of New South Wales. "Music Acoustics" [cited March 10, 2003]. <http://www.phys.unsw.edu.au/music/>.
David Mintzer
KEY TERMS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
- Amplitude
—The maximum displacement of the material that is vibrating.
- Condensations
—When air is the vibrating medium there are alternate small increases and decreases of the density of the air; the increases are called condensations.
- Cycle
—A single complete vibration.
- Cycles per second
—The number of complete vibrations per second.
- Frequency
—The rate at which vibrations take place (number of times per second the motion is repeated), denoted here by f and given in cycles per second or in hertz.
- Fundamental
—The lowest frequency of vibration of a sound-producing body (also called the first harmonic).
- Harmonics (first, second, etc.)
—The various frequencies of vibration of a sound-producing body, numbered from the one of lowest frequency to higher frequencies.
- Hertz
—A hertz (abbreviated as Hz) is one cycle per second.
- Infrasonic vibrations
—When the rate of vibration is below the range of human hearing, e.g., below about 10 cycles per second.
- Longitudinal wave
—The case where the motion of the vibrating body is in the wave propagation direction.
- Loudspeaker
—A device to produce sounds from an electric current, by electrical and mechanical means, in the range of frequencies around the sonic range (that is produced by humans).
- Medium
—A material body that carries the acoustic vibrations away from the body producing them.
- Microphone
—A device to change sound waves (pressure waves), by electrical and mechanical means, into an electric current having the same frequencies as the sound, in the range of frequencies around the sonic range (that is produced by humans).
- Nodes
—Places where the amplitude of vibration is zero.
- Overtones
—The set of harmonics, beyond the first, of a soundproducing body.
- Period
—The length of time for one cycle to be completed; the reciprocal of the frequency.
- Propagation direction
—The direction in which the wave is traveling.
- Rarefactions
—When air is the vibrating medium there are alternate small increases and decreases of the density of the air; the decreases are called rarefactions.
- Sonar
—A device utilizing sound to determine the range and direction to an underwater object.
- Supersonic
—Refers to bodies moving at speeds greater than the speed of sound (not normally involved in the study of acoustics).
- Transverse wave
—The case where the motion of the vibrating body is perpendicular to the wave propagation direction.
- Ultrasonic vibrations
—When the rate of vibration is above the range of human hearing, e.g., above about 20,000 cycles per second.
- Wave
—A motion, in which energy changes are propagated, is carried away from some source, which repeats itself in space and time with little or no change.
- Wavelength
—The distance, at any instant of time, between parts of a vibrating body having the identical motion, denoted here by L.
Acoustics
Acoustics
Acoustics is the science that deals with the production, transmission, and reception of sound. The first scientist to study sound scientifically was German physicist Ernst Florens Friedrich Chladni (1756–1827). Chladni was an amateur musician who became interested in finding mathematical equations to describe musical sounds. Because of his work, he is often called the father of acoustics.
Acoustics has many applications in the everyday world. When you have your hearing checked by a technician, that person makes use of the principles of acoustics. Those same principles are also used in the architectural design of concert halls.
The study of sound can be subdivided into three parts: production, transmission, and reception. All three elements are necessary in order for sound to occur. For example, a ringing alarm clock cannot be heard if it
is placed inside a jar from which all air has been removed. Without air, sound produced by the clock has no medium through which it can travel.
Words to Know
Amplitude: The maximum displacement (difference between an original position and a later position) of the material that is vibrating. Amplitude can be thought of visually as the highest and lowest points of a wave.
Condensations: Regions of high density in a sound wave traveling through a gas such as air.
Cycle: A single complete vibration.
Cycles per second: The number of complete vibrations per second.
Frequency: The rate at which vibrations take place (number of times per second the motion is repeated), given in cycles per second or in hertz (Hz).
Fundamental: The lowest frequency of vibration of a sound-producing body (also called the first harmonic).
Harmonics (first, second, etc.): The various frequencies of vibration of a sound-producing body, numbered from the one of lowest frequency to higher frequencies.
Hertz (Hz): The unit of frequency; a measure of the number of waves that pass a given point per second of time.
Infrasonic vibrations: A rate of vibration below the range of human hearing, that is, below about 10 cycles per second.
Longitudinal wave: A wave whose motion of vibration is in the direction of the wave's advancement—the same direction in which the wave is traveling.
Loudspeaker: A device to produce sounds from an electric current—by electrical and mechanical means—in the range of frequencies around the sonic range (that is produced by humans).
Medium: A material that carries the acoustic vibrations away from the body producing them.
Microphone: A device to change sounds—by electrical and mechanical means—into an electric current having the same frequencies as the sound, in the range of frequencies around the sonic range (that is produced by humans).
Node: A place where the amplitude of vibration is zero.
Overtones: The set of harmonics, beyond the first, of a sound-producing body.
Rarefactions: Regions of low density in a sound wave traveling through a gas such as air.
Sonar: A device utilizing sound to determine the range and direction of an underwater object.
Transverse wave: A wave traveling in a direction perpendicular to (at right angles to, or like an upside-down T) the motion of the vibrating body.
Ultrasonic vibrations: Vibrations greater than those that can be detected by the human ear (above about 20,000 cycles per second).
Wave: A motion in which energy and momentum is carried away from some source; a wave repeats itself in space and time with little or no change.
Wavelength: The distance, at any instant of time, between parts of a vibrating body having the identical motion.
Production of sound in a string
Sound is produced by a vibrating body. The vibrating body can be a string on a violin or piano, a column of air in an organ pipe or clarinet, an animal skin or piece of plastic stretched over a drum, or the vocal cords in a person's throat, to name but a few. A simple way to illustrate the production of sound is by studying the vibration of a string, as shown in the acoustics diagram (shown on page 20).
Imagine that the string in this diagram is stretched tightly and then plucked. The way in which the string vibrates depends on a number of factors, including the material from which the string is made, the object with which it is plucked, and the force exerted when plucking on the string. The simplest type of vibration, shown in Figure 1, is called the fundamental or first harmonic.
Real strings do not vibrate with the simple pattern shown in Figure 1. Instead, they vibrate in a complex pattern that consists of vibrations within vibrations. Figure 2 illustrates another kind of vibration in the string called the second harmonic. Notice that the vibration occurs in two sections of the string separated by a point where no vibration occurs. That point is called a node.
Other vibrations may occur at the same time. Figure 3 shows the third harmonic in the string. Harmonics above the first are also known as overtones. This diagram shows the first harmonic and two overtones.
As with all forms of wave motion, a vibrating string can be described completely with only a few variables. The rate at which the string vibrates up and down is known as its frequency. Frequency is usually measured in cycles (vibrations) per second. The unit used to measure frequency is the hertz (abbreviation: Hz). A string might be vibrating, for example, at 1,000 Hz, or 1,000 cycles per second.
The distance between two identical parts of a wave is called the wavelength. Notice that the upward motion of the wave starts at the far left of the string in Figure 2 and is not repeated until the far right of the string. The letter L in the figure shows the wavelength of this wave. The highest point reached by a wave above its average height is the amplitude. The amplitude in the figures is represented by the letter A.
When a musician plays a stringed instrument, he or she can control the way in which the string vibrates by varying the points at which the string is held and the way in which the string is bowed or plucked.
Other ways of producing sound
Sound produced in a vibrating column of air can be analyzed in much the same way as sound produced by a vibrating string. Look at Figure 4 and imagine that a musician has blown into the column of air from the left, as shown by the arrow. Air within the column is pushed from left to right, producing waves similar to those in the vibrating string. The main difference is that the waves of air are longitudinal waves (meaning they travel in the direction of the column) while the waves in the string are transverse waves (meaning they travel at right angles to the string).
The waves in the air column consist of two distinct types: regions where air piles up and becomes more dense, and regions where air spreads out and becomes less dense. More dense regions of air are known as condensations and less dense regions as rarefactions. The pattern of condensation and rarefaction differ depending on whether the column in which they occur is open or closed at one or both ends. As with a stringed instrument, overtones produced by an oboe, clarinet, bassoon, or other wind instrument are determined by the points at which the air column is blocked off and by the force with which air is pushed through the column.
One of the most complex wind instruments is the human voice. Sound is produced by humans when they force air across the vocal cords, causing them to vibrate. The various overtones produced by this process are determined by a number of factors, including the size and shape of various cavities in the head (such as the sinuses), as well as the placement of the tongue and the shape of the mouth. With so many factors involved, it is hardly surprising that each human voice has a distinctive sound.
Detectable and undetectable sounds
Objects can be made to vibrate with a great range of frequencies, from only a few cycles (or vibrations) per second to millions of times per second. However, the human ear is able to detect only a limited range of those vibrations, generally those between 20 to 18,000 Hz. When the rate of vibration is less than 20 Hz, the sound is said to be infrasonic; when the rate is above 18,000 Hz, it is said to be ultrasonic. Although ultrasonic vibrations cannot be heard, they do have a number of research and industrial applications.
Transmission of sound
Since light and sound both consist of waves, they are transmitted in similar ways. The most important difference between the two is their wavelengths. Visible light has wavelengths between about 400 and 700 nanometers (billionths of a meter), while sound has wavelengths between about 3.3 centimeters and 3.3 meters. This difference shows up in the way light and sound are affected by objects placed in their paths.
In general, a wave is blocked by any object in its path if the object is has dimensions greater than its wavelength. In the case of light, then, any object larger than 700 nanometers will block the path of light. You know this from everyday life. If you place a book in front of a beam of light, you can no longer see the light. The book casts a shadow because it is much larger than the wavelength of light.
But placing a book in the path of a sound wave does not block out the sound. The size of the book (less than a meter) is much less than the wavelength of the sound wave. The sound wave acts as if the book is not even there.
This principle has some important practical applications. Many communities are building walls to block off the sound of nearby freeway traffic. In order for this type of construction to work, the wall must have dimensions that are larger than the sound waves coming from the freeway, that is, dimensions greater than 3.3 meters. When a wall is large enough, it casts an acoustical shadow, similar to the light shadow cast by a book.
Reception of sound
By far the most important sound receiver in use is the human ear. Although the details of the workings of the ear are complicated, the general principles by which humans hear are fairly simple. When sound waves reach the outer ear, they pass down the ear canal and strike the eardrum. The eardrum consists of a thin membrane that vibrates with the same frequency as the sound wave. The vibrating membrane of the eardrum, in turn, causes three small bones in the middle ear—the malleus, incus, and stapes—to vibrate, too. (These three bones are more commonly called the hammer, anvil, and stirrup because of their shapes.)
The last of the three bones, the stapes, is connected to a fluid-filled chamber called the cochlea. Vibrations from the stapes are passed to the cochleal fluid and then on to tiny hairs that line the cochlea. These hairs change the wave motion of sound into an electrical signal that is transmitted along the auditory (hearing) nerve to the brain. Finally, the brain interprets the meaning of the sound/electrical wave, allowing a person to perceive the sound.
Applications
The many applications of acoustical devices are easy to find in the world around you: telephones, radios and television sets, compact disc players and tape recorders, and even clocks that "speak" the time are common examples. One of the most important acoustical devices from the human point of view is the hearing aid. The hearing aid is a system consisting of miniature microphones, amplifiers, and loudspeakers that make it easier for people with hearing difficulties to understand sounds.
One of the first large-scale industrial applications of acoustics was sonar. Sonar stands for the phrase so und na vigation r anging. It was developed by the U.S. military during World War I (1914–18) for the detection of submarines and continues to be an invaluable device for navies throughout the world. The sonar system is based on readings of sent and received sound waves. A ship looking for underwater objects (such as a submarine) sends out a sound signal. If that sound signal strikes an object, such as the hull of a submarine, it is reflected back to the detecting ship in an echo. The nature of the echo tells an observer the direction and distance of the object (in this case, the submarine hull) that was hit by the wave.
Listening devices can also be used to study sounds emitted by an underwater object. Each type of submarine and each type of engine emit distinctive sound patterns that can be picked up and analyzed by listening devices on other ships.
Sonar has uses other than in military applications. For example, fishing fleets can use sonar to locate schools of fish, determine their size, and track their movement.
Acoustical principles are now used widely in the construction of concert halls and auditoriums. For many years, scientists have known that music and the spoken word can be more clearly and easily heard in certain types of rooms. Only recently, however, have the scientific principles of acoustics been understood well enough to apply them to the actual construction of halls and auditoriums.
The field of ultrasonics has become an important subspecialty in the science of acoustics. Ultrasonic sources with frequencies of millions of cycles per second are now used for inspecting metals for flaws. These waves reflect off tiny imperfections in a metal, indicating where it is weak or likely to fail. Some of the structures that are now routinely inspected by ultrasonic techniques are bridges, airplanes, and pipelines.
acoustics
Sound is due to the vibrations of a source, such as a mus. instr., which are transmitted through the air to the ear-drum where they set up vibrations at the same rate. The pitch of a sound depends on the speed of those vibrations, which if rapid produce a ‘high’ pitch and if slow a ‘low’ pitch. The rate of vibration per second is known as the ‘frequency’ of the note.
The loudness of a sound depends on the ‘amplitude’ of the vibrations; for instance, a vn. str. violently bowed will oscillate for a considerable distance on either side of its line of repose, thereby producing strong vibrations and a loud sound, whereas one gently bowed will only oscillate a short distance on each side and so produce small vibrations and a soft sound.
Smaller instr. produce more rapid vibrations and larger ones slower vibrations: thus the ob. is pitched higher than its relative the bn., likewise a vn. than a vc., a stopped str. than an ‘open’ str., a boy's v. than a man's v., etc. But other factors enter into the control of pitch. For instance, mass (the thinner str. of a vn. vibrate more quickly than the thicker ones and so possess a higher general pitch) and tension (a vn. str. tightened by turning the peg rises in pitch).
The varying quality of the sound produced by different instr. and vv. is explained as follows. Almost all vibrations are compound, e.g. a sounding vn. str. may be vibrating not only as a whole but also at the same time in various fractions which produce notes according to their varying lengths. These notes are not easily identifiable by the ear but are nevertheless present as factors in the tonal ens. Taking any particular note of the harmonic series (as G, D, or B), the numbers of its harmonics double with each octave as the series ascends. The numbers attached to the harmonics represent also the ratios of the frequencies of the various harmonics to the fundamental. Thus if the frequency of the low G is 96 vibrations per second, that of the B in the treble stave (5th harmonic) is 5×96 = 480 vibrations per second.
Whilst these harmonics are normally heard in combination some of them may, on some instr., be separately obtained. By a certain method of blowing, a brass tube, instead of producing its first harmonic, or fundamental, can be made to produce other harmonics. By lightly touching a str. (i.e. a stopped str.), at its centre and then bowing it, it can be made to produce (in a peculiar silvery tone-quality) its 2nd harmonic; by touching it at a 3rd of its length it will similarly produce its 3rd harmonic, etc. (Harmonics are notated in str. parts as an ‘o’ above the note. ‘Natural’ harmonics are those produced from an open str.; ‘artificial’ harmonics those produced from a stopped str.)
The normal transmission of sound is through the air. The vibrations of a str., a drum-head, the vocal cords, etc. set up similar vibrations in the nearest particles of air; these communicate them to other particles, and so on, until the initial energy is gradually exhausted. This process of transmission of pressure to adjacent units of air creates what are known as sound waves: unlike waves created by water-motion, there is no forward movement, but each particle of air oscillates, setting up alternate pressure and relaxation of pressure which in turn produce similar effects on the human or animal eardrum (= vibrations), so causing the subjective effect of ‘sound’.
To judge pitch differences, or intervals, the human ear obeys a law of perception called the Weber–Fechner law, which states that equal increments of perception are associated with equal ratios of stimulus. Perception of the octave pitch is a 2:1 frequency ratio. In judging the loudness of sound there are 2 ‘thresholds’, those of hearing and of pain. If the intensity of sound at the threshold of hearing is regarded as 1, the intensity at the pain threshold is 1 million million. Acousticians' scale of loudness, following the Weber-Fechner law, is logarithmic and based on a ratio of intensities 10:1. This is known as a bel. The range of loudness perception is divided into 12 large units. Each increment of a bel is divided into 10 smaller increments known as decibels, i.e. 1 bel = 10 decibels. A difference in loudness of 1 decibel in the middle range of hearing is about the smallest increment of change which the ear can gauge.
When 2 notes near to one another in vibration frequency are heard together their vibrations necessarily coincide at regular intervals and thus reinforce one another in the effect produced.
This is called a beat. When the pf. tuner is tuning a str. of a certain note to another str. of the same note the beat may be heard to diminish in frequency until it gradually disappears with correct adjustment. When the rate of beating exceeds 20 per second, the sensation of a low bass note is perceived.
When 2 loud notes are heard together they give rise to a 3rd sound, a combination or resultant tone, corresponding to the difference between the 2 vibration numbers: this low-pitched note is called a difference tone. They also give rise to a 4th sound (another combination tone—high and faint) corresponding to the sum of the 2 vibration numbers: this is called a summation tone.
There is reflection of sound, as of light, as we experience on hearing an echo. Similarly there are sound shadows, caused by some obstruction which impedes the passage of vibrations which reach it. However, unlike light vibrations, sound vibrations tend to ‘diffract’ round an obstruction, and not every solid object will create a complete ‘shadow’: most solids will transmit sound vibrations to a greater or lesser extent, whereas only a few (e.g. glass) will transmit light vibrations.
The term resonance is applied to the response of an object to the sound of a given note, i.e. its taking up the vibrations of that note. Thus if 2 identical tuning-forks are placed in close proximity and one is sounded, the other will set up sympathetic vibrations and will also produce the note. The 1st fork is then a generator of sound and the 2nd a resonator. It is often found that a particular church window will vibrate in response to a particular organ note, and that a metal or glass object in a room will similarly respond to a certain vocal or instr. note.
This phenomenon is true resonance (‘re-sounding’) in the strict scientific sense of the word. There is also a less strict use of the word, which is sometimes applied to the vibration of floor, walls, and ceiling of a hall, not limited to a particular note, but in response to any note played or sung. A hall may either be too resonant for the comfort of performers and audience, or too little so—too ‘dead’ (a hall with echo is often described as ‘too resonant’, but there is an obvious clear distinction to be made between the mere reflection of sounds and the sympathetic reinforcements of them). Reverberation time is defined as the time it takes for sound to fall 60 decibels (1 millionth of original intensity).
Materials of walls and ceiling should be neither too reverberatory nor too absorbent (‘dead’). Acoustical engineers have worked out co-efficients of absorption for building materials, but absorption is rarely uniform throughout the whole spectrum of pitch. Only wood and certain special acoustic materials show nearly even absorption in the total frequency range. Amplifiers and loudspeakers can be used (as they nowadays often are) to overcome difficulties caused by original faulty design. Most modern halls can be electronically ‘tuned’ and have movable panels, canopies, and reverberation chambers which can be adapted to whatever type of music is being performed.