ACOUSTICS, is a branch of physics that deals with the production, propagation, reception, and use of sound. It is one of the oldest of the physical sciences. Its historical roots go back to the ancient Greeks and earlier cultures. The term “acoustics” comes from the Greek word akoustikos, meaning “related to hearing.”

The design of Greek and Roman amphitheaters attests to the acoustical insights of builders and scientists of ancient times. For centuries, man has used sounds to make music, which depends on relationships between sounds. One of the best-known musical scales is the Pythagorean, named after its reputed inventor, Pythagoras, the Greek philosopher and mathematician, who lived in the 6th century b.c. During the Middle Ages, acoustics, like most other sciences, was dormant. It was revived in the upsurge of science following the Renaissance.

Modern Acoustics. Acoustics now comprises a wide variety of fields: physical acoustics and ultrasonics ( the study of matter by using sound waves); architectural acoustics (the study of sound waves in auditoriums and concert halis); psychoacoustics and physiological acoustics (the study of hearing); speech communication (the study of the human speaking apparatus and verbal communication); underwater sound; noise control; mechanical vibrations and shock waves; and many other disciplines.

Acoustics can be divided roughly into two large areas of study: the interaction of sound waves with physical matter, and the interaction of sound waves with living organisms. Another useful distinction is between information-bearing sound waves (such as human speech and bird-calls) and noise, sometimes loosely called “unwanted sound.”

The science of acoustics is progressing on many fronts, most of which are related to important needs of human society. The design of concert halis and auditoriums with better listening conditions and the specification of office and apartment buildings with better sound insulation are well-known examples of acoustics research that affect the well-being of many persons. Noise control, including the reduction of sonic boom, is of great importance in modern transportation. Communications between persons and between persons and machines are areas of rapidly increasing eonsequence in which acoustics plays a decisive role. Machines that are capable of “understanding” speech and executing verbal instructions will play a large part in a society that relies increasingly on automation. Automatic speaker verification will be useful in such applications as banking and access to restricted information where verification of personal identity is crucial.

Speaking machines that can produce intelligible speech also will have many useful applications. Automatic answering and information services (for weather, stock prices, inventories, and the like) and book-reading machines for the blind are some of the many instances in which speaking machines will be applied. At present, many of these applications for communication acoustics are but hopes for the future. Much painstaking research in speech and hearing will be required to bring these dreams to fruition.

Sound waves of extremely high frequencies are an important tool in probing basic properties of matter and in gaining a better understanding of important physical phenomena, such as thermal vibrations and superconductivity. The frequencies of the sound waves that are used for such purposes often exceed the audible range (ultrasound) and may be as high as several billion cycles per second (hypersound). At such high frequencies, sound, like light, is transmitted in little packets of energy called phonons. The study of the interaction of phonons and electrons is giving new insights into the structure of metals and other materials, including superconductors.

Inaudible, extremely low-frequency sound waves stemming from earthquakes and underground explosions are useful for studying the composition of the earth’s mantle. Nuclear explosions above ground generate low-frequency sound waves of such high intensity that they stili can be detected after they have traveled around the entire globe.

In more practical applications, ultrasonic waves are used to locate faults in component parts used in construction, such as spacecraft, where the utmost reliability is required. Ultrasonic waves also are used to facilitate chemical reactions and to clean, dye, and mix different substances. In medicine, ultrasonic waves have found wide applicatiou for therapeutic purposes. Strongly focused ultrasonic pulses can be used to guide the blind. Waterborne sound waves of lower frequency are used to guide and locate ships, including submarines.

A particularly important area of acoustics research is the exploration of structural vibrations and fatigue of metals and other materials used in designing aircraft and rockets.

These applications and a myriad other applications serve to emphasize the importance of sound to man in his modern world.

Physics of Sound. Sound waves are the regular movements of atoms and molecules superimposed on their irregular thermal movements.

In the case of sound waves in solid materials, the sound waves can be interpreted in terms of the model shown in the drawing below. The individual atoms are represented by the identical masses, M. The forces between the atoms are represented by the identical springs, F, which connect adjacent masses. If the masses are equidistant, then no net forces are exerted bythe springs on the masses. In the uppermost diagram (represented by time t„) the masses are in their rest positions. Thi.s condition corresponds to the absence of sound in a solid material. If the end mass begins to be displaced in an oscillatory fashion about its rest position, then the spring that is attached to it exerts a force on the neighboring mass. This force, in turn, is exerted by the connecting spring on the next mass, and the effect propagates down the chain. The action is shown for several successive instants in time (tı, t2, . . . t«) in Fig. 1. After a delay, which is determined by the size of the masses, the spring stiffness, and the distance along the chain, each mass will begin to perform an oscillatory motion about its rest position. The maximum displacement is called the amplitude of the motion. The time of the maximum displacement determines the phase of the motion.

Waves in which the particles move along the line of the direction of wave propagation are called longitudinal ıvaves. In solids and certain liquids the particles also can move at right angles to the direction of wave propagation. Such waves are called transversal, or shear, toaves.

In gases the forces between atoms and molecules cannot easily be represented by springs because the forces are caused by collisions between the individual particles. The forces resulting from these collisions are called gas pressure. Because pressure is a longitudinal force, only longitudinal waves can exist in gases.

The number of oscillations per second is called the frequency, which is measured in cycles per second or Hertz (Hz). The shortest distance between particles oscillating in equal phase is called the ıvavelength of the wave. The product of frequency and wavelength equals the velocity with which the wave propagates.

For an observer who moves with respect to the source of the waves, the apparent frequency differs from the frequency for a stationary observer.

If observer and source move toward each other, the apparent frequency is increased. If observer and source move away from each other, the apparent frequency is decreased. This phenomenon is called the Doppler effect. It can be heard, for example, as a sudden drop in frequency, or pitch, when a whistling train passes an observer at high speed.

When two waves of different frequencies are perceived simultaneously, a pitch corresponcling to the difference of the two frequencies is sometimes heard. This pitch is known as a beat note.

When two waves of equal frequency and equal amplitude travel in opposite directions, they produce a standing wave. In a standing wave ali particles move in equal or opposite phase; that is, they reach their extreme amplitudes at identical times. Standing waves are very common. For example, the air in an organ pipe or the string of a violin moves as a standing wave.

Sound Transmission. Sound propagates as waves. In contrast to light, which can travel through empty space, sound waves require some kind of elastic matter for their propagation. The propagation medium can be a gas, such as air; a liquid, such as water; or a solid, such as the walls of a building. The sounds we hear reach our ears by way of the air surrounding us. Fish “listen” to sound waves propagating in water. The vibrations of the walls of a noisy building are called “solid-borne” sound.

The speed of sound is determined by the pressure, temperature, and other properties of the material through which it travels. The speed of sound in air, at a temperature of 77° F (25° C) and at normal atmospheric pressure, is 1,055 feet (322 meters) per second. Thus, a sound wave requires almost one second to traverse a distance of 1,000 feet (305 meters). A light wave travels the same distance in less than a millionth of a second. It is because of this large difference between the velocities of sound and light that we hear thunder after we see the lightning.

The velocity of sound in liquids and solids usually is considerably greater than in gases. This is so because the atoms and molecules in liquids and solids are much closer to each other than in gases, and the forces between them are much greater. At 70° F (21° C), the velocity of sound in pure water is 5,100 feet (1,555 meters) per second; in steel it is 17,200 feet (5,243 meters) per second.

The transmission of sound always is accompanied by an attenuation of its intensity. In homogeneous and isotropic media, sound spreads in spherical waves. This spreading causes a progressive decrease in the intensity of sound as it travels farther and farther from its source. This behavior is much like circular water waves on the surface of a pond; the waves become weaker and weaker with increasing distance from their origin. The intensity of a spherical wave is reduced fourfold for every doubling of distance because the same total energy is spread over four times the original areas ($\displaystyle A=\pi {{r}^{2}}$).

Relative sound intensity often is expressed in decibels. The decibel is defined as “10 times the logarithm to the base 10 of the ratio of intensities.” In mathematical form, the definition of the decibel looks as follows: attenuation in decibels

$\displaystyle =10{{\log }_{{10}}}\frac{{({{I}_{0}})}}{{(I)}}$

where I is tje later intensity of the sound, and $\displaystyle {{{I}_{0}}}$ is the original intensity. For a doubling of distance, $\displaystyle \frac{{{{I}_{0}}}}{I}=4$. In this case, the attenuation of a spherical wave is:

$\displaystyle 10{{\log }_{{10}}}(4)=6$ decibels.

Because the intensity of a sound wave is proportional to the square of the sound pressure amplitude associated with the wave, the definil tion of a decibel also can be rendered in the following form:

attenuation in decibels =

$\displaystyle 10{{\log }_{{10}}}\frac{{(p_{0}^{2})}}{{({{p}^{2}})}}=20{{\log }_{{10}}}\frac{{(p_{0}^{{}})}}{{({{p}^{{}}})}}$

where p is the actual sound pressure amplitude, and $\displaystyle {p_{0}^{{}}}$ is the reference sound pressure amplitude.

The attenuation of sound waves due to spreading can be avoided by confining the waves to a narrow region. In the case of airborne and liquid-borne sound, this confmement can be accomplished by using hollow tubes. In the case of solid-borne sound, the spreading can be avoided, for example, by transmitting the sound through thin rods.

In addition to attenuation caused by spreading, sound is attenuated by the internal friction that occurs between the atoms and molecules in a viscous medium. This kind of attenuation is called sound absorption. However, the energy of the sound wave is not completely lost. As in ali friction processes, energy is converted into heat. The heat generated may be imperceptibly snıall, but it may represent a substantial fraction of the energy of the sound wave.

In general, there is more friction in gases and liquids than in hard solids, especially metals and certain crystals. At normal temperatures and pressures the attenuation of audible sound waves in steel is about 100 times smaller than in air. The low sound absorption of steel, together with the lack of spreading, accounts for the fact that one can hear a distant railroad train by putting an ear to the track, even though the airborne sound is much too weak to be heard.

In general, sound absorption increases with frequency. Quartz is a material that has particularly low sound absorption, even at very high frequencies. Therefore, quartz crystals are used in many industrial applications when sound has to be transmitted with a minimum of loss. Because nature’s supply of quartz is insufRcient, quartz crystals now are grown artificially in many laboratories.

Sound Sources: The Human Voice. An important source of sound is the human voice. From the elemental sounds that the respiratory and oral systems can produce, humans have developed a highly sophisticated tool: speech. Although human speech is weak in physical energy, it is a most powerful means of communicating. It can be informative, persuasive, edifying, destructive, boring, or simply unintelligible.

All speech sounds are generated by the air escaping from the lungs. There are two kinds of speech sounds: voiced, and unvoiced. For voiced speech sounds, such as the vowels and diphthongs (a, e, oo, a, i, o), the air stream from the lungs is chopped into short pulses of air by the vocal cords. The rate at which this chopping occurs determines the fundamental frequency, or pitch, of the voice. The pitch is low for males (about 100 pulses per second), higher for female voices (about 200 pulses per second), and higher stili for children. The pulses of air enter the space within the vocal tract. Like any hollow pipe, the space has resonances that impart a characteristic tone quality, or timbre, to the air pulses. Each speech sound is distinguished by a different timbre. The resonance frequencies, and therefore the timbre, depend on the position and shape of the articulators (the tongue, the lips, the palate). By varying the position and shape of the articulators, one produces continuous speech.

For unvoiced speech sounds the vocal cords remain inactive. For these speech sounds, the audible sound is generated by sudden release of pressure (pops) or by turbulence caused by friction of the air stream in narrow passages. Examples of plosive speech sounds are p, t, and k. Examples of fricative sounds are f, s, and th (as in thin). Some speech sounds, like z and t), are neither purely voiced nor purely unvoiced. They are called voiced fricatives. For other speecjh sounds (m, n, ng) the air escapes from the nostrils. These sounds are nasals.

Many questions concerning the production and perception of speech by humans are stili unanswered. Much research is devoted to these problems both for the sake of a better basic understanding of these processes and because of the many applications that would become possible as a result of such an understanding. Among the applications are automatic speech recognizers and speaking machines that produce intelligible speech from written text. Automatic speech recognizers for a small number of carefully pronounced words have been developed. Speaking machines that produce synthetic speech from a phonetic symbol input have been simulated on digital computers, but the artificial “computer speech” does not yet sound very human.

An important application of synthetic speech for communication is the vocoder (a word coined from voice and coder). Vocoders analyze speech into its individual frequency components. After transmission, vocoders resynthesize artificial speech at some distant receiving point. Information concerning the frequency components of several speech signals can be transmitted over a single telephone circuit. Thus, long-distance communication will become more economical when the artificial speech of a vocoder can be made to sound natura!

Sound Sources: Musical Instruments. Musical instruments are another important class of sound sources. Musical instruments produce their sounds by a variety of physical mechanisms. Some instruments, such as the violin, the çello, the double bass, the guitar, and the harp, produce their sounds by vibrating strings, which are set into motion by plucking or bowing. Other instruments, such as the accordion, use vibrating reeds. Many musical instruments use a combination of mechanisms, such as vibrating reeds and resonating air columns. The clarinet, the bassoon, and the saxophone are in this class. For some musical instruments the performer’s lips play the role of the reed. Well-known examples are the bugle, the trumpet, the trombone, and the tuba. In organ pipes, flutes, and recorders the resonating air column is set into motion by an air reed that periodically interrupts the flow of air.

Drums of all kinds use vibrating membranes to produce sound. In bells, chimes, and glockenspiels the sound is generated by the impact of hammers on variously shaped resonating metal bodies.

In contrast to these purely mechanical instruments, loudspeakers convert a given electrical signal into a corresponding acoustical wave. Loudspeakers play an increasing role for the generation of sounds of ali kinds. A loudspeaker can reproduce, with more or less fidelity, the sounds of other musical instruments. When coupled to an electric organ or other music synthesizer, the loudspeaker becomes an integral part of the instrument.

Sound Receivers: The Human Ear. Among the many receivers for sound the human ear, in many respects, is the most sophisticated and capable.

Unlike human vision, which is limited to a frequency ratio of 2 to 1, or one octave, normal human hearing spans more than 10 octaves: from 16 cycles per second to more than 16,000 cycles per second. In this fr6quency range, humans are able to distinguish a virtually unlimited variety of sounds—the spoken word of a fellow human, the roar of a modern jet, the humming of an insect, and the crescendo sound of a symphony orchestra are examples.

In addition to its great range in frequency the human ear has an almost unbelievable range in sound intensity. For the faintest sounds that the ear can detect, the ear drum moves by less than a billionth of an inch—about the diameter of a hydrogen atom. The loudest sounds that the human ear can tolerate without pain have an intensity of 1,000 billiou times greater than the faintest. The frequency sensitivity of the ear is remarkable too. At 1,000 cycles per second the human ear can detect a frequency difference of only a few cycles, that is, a few parts in 1,000.

One of the astonishing properties of binaural (two-eared) hearing is the capability to localize where the sound comes from. Not only can we distinguish left from right, front from back, and many intermediate directions, but we can also “focus” on a particular source of sound surrounded by other sources. This amazing ability of human hearing sometimes is called the “cocktail party effect.” Without it we would be unable to extract and understand the speech of a single speaker from the surrounding babble. The cocktail party effect is related to the “precedence effect”—the ear can concentrate on the first arriving sound wave and reject later arriving echoes of the same sound wave. Without this ability it would be very diflıcult or even impossible to understand speech in reverberant rooms. In fact, an echo that arrives 0.01 second later can be 10 times as intense as the original sound before it becomes distracting. This extension of the precedence effect is known as the “Haas effect.” The Haas effect is utilized in modern sound reinforcement systems. The amplified sound from the loudspeakers is delayed by approximately 0.01 second with respect to the direct sound from the original source. In this manner an acoustic illusion is created—ali the sound seems to be coming from the original source rather than from the loudspeaker.

The complicated interactions that take place in binaural hearing are not yet fully understood, but they are being investigated by scientists in many laboratories. Concurrent with this research, attempts are being made to duplicate binaural interaction by using electronic circuits. When this duplication is accomplished, it may become much easier to hold conferences between large groups of people by telephone, thereby eliminating much unnecessary traveling.

The Human Hearing Mechanism. The human hearing mechanism may be divided into three parts: the outer ear, the middle ear, and the inner ear. The outer ear consists of the external ear (pinna) and the ear canal, which is terminated in the eardrum (tympanic membrane). Behind the eardrum is the middle ear, a small cavity in which three bones—the hammer, the anvil, and the stirrup—form the elements of a lever system for transmitting vibrations from the eardrum to an aperture (the oval window) of the inner ear.

The inner ear (cochlea) has a form resembling a snail shell. It is divided along its length by a wedgeshaped tunnel, or partition, composed of two membranes: the basilar membrane and Reissner’s membrane. A viscous fluid (endolymph) fllls the partition, and a different fluid (perilymph) fills the outer canals (scalas). inside the partition and situated on the basilar membrane is the organ of Corti, which contains the auditory nerve endings and hair cells. There are about 30,000 nerve fibers running from the cochlea to the brain. Each nerve fiber is enclosed in a sheath like that of an insulated wire. The 30,000 nerve fibers form a single cable, which is a little more than one millimeter in diameter. The cable of nerves passes through the temporal bone to the base of the brain.

When a sound wave enters the ear canal, it impinges on the eardrum. The eardrum vibrates with a motion corresponding to the undulatıons in the sound wave. The motion of the eardrum is transmitted to the oval window of the cochlea by the lever system of the middle ear. The vibrations of the oval window are transmitted into the fluid of the cochlea back of the oval window. The sound waves in the cochlea cause a relative motion between the basilar membrane and another membrane (the tectorial membrane) located inside the cochlea partition. This motion causes the hair cells to stimulate the endings of the auditory nerve.

The cochlea is a frequeney-selective mechanism. The portion of the cochlea nearest the oval window is most sensitive to high frequencies; the midportion of the cochlea is excited predominantly by medium frequencies; and the portion farthest from the oval window is excited by low frequencies. The various frequencies in a complex sound wave are sorted out by the frequency-selective properties of the cochlea. Thus, the cochlea is, in effect, a sound analyzer.

The nerve fibers transmit short electrical impulses. The intensity of the sound determines the number of impulses that are transmitted along a nerve fiber in one second. The greater the intensity, the greater is the excitation of the hair cells, and a correspondingly greater number of nerve impulses are sent to the brain.

Loudspeakers and Microphones. Because signals, such as speech and music, can be transmitted effectively as electrical signals, the transformation of sound waves into corresponding electrical signals and vice versa is of great practical importance. Devices that accomplish these transformations are called electromechanical transducers. The best known examples of electromechanical transducers are loudspeakers, which convert electrical energy into sound, and microphones, which convert sound into electrical energy.

In the electrodynamic loudspeaker, the most common type, an electrical current that is proportional to the signal is sent through a coil attached to a paper membrane. The coil moves inside a permanent magnet; the magnetic field exerts a force on the coil that is proportional to the electrical current. The resulting movement of the coil and the attached membrane sets up sound waves in the surrounding air.

The most common microphone is the carbon-button microphone, which is used in most telephone handsets. In a carbon-button microphone the sound wave impinging on the microphone membrane varies the electrical resistance between the small carbon granules enclosed in a space behind the membrane. If a voltage is applied to the electrical terminals of the microphone, the resulting current varies in proportion to the amplitude of the second wave.

Recording of Sound. Since Thomas Edison’s invention of the phonograph, the recording of sound for later playback has made great strides. The modern long-playing record can store almost the entire frequency range of audible sound with little distortion. In many cases the quality of the reproduced sound is very similar to that of the original signal. By modulating both edges of the disc groove, stereophonic sound signals can be stored in a single groove and picked up separately by a stereophonic cartridge, which is a special kind of electromechanical transducer. The resulting two electrical signals are amplified separately and are reproduced by two or more loudspeakers. From a good stereophonic recording, the reproduced sound can be heard in any direction between the loudspeakers.

Recording of sound on magnetic tape provides even higher fidelity than disc recordings. On a magnetic tape the sound signal is stored as a variable spot of magnetization that is detected by a magnetic playback head and reconverted into an electrical signal.

Architectural Acoustics. An important branch of acoustics deals with the transmission of sound waves inside reverberant rooms, such as auditoriums, theaters, and concert halis. In a reverberant room the sound reaches a listener’s ears not only directly (in a straight line from the source) but also by way of reflections from the ceiling, the floor, and the walls. If these reflections are sufficiently strong and arrive after a delay greater than 0.05 second, they are heard as echoes. Otherwise, they are heard as reverberation. The time interval in which the reverberation is attenuated to one millionth of its original intensity is called the reverberation time. Typically, living rooms have reverberation times of 0.5 second or less. Lecture halis have reverberation times of approximately one second. Good concert halis have reverberation times of about two seconds. Large churches, railroad stations, and indor swimming pools can have reverberation times as long as 10 seconds or more.

The acoustical quality of a concert hail is determined in part by its reverberation time. But there are many other factors that influence acoustical quality. Many of these factors are not yet fully understood, and much basic research is required to elucidate the complex problems of sound transmission and perception in reverberant spaces.

A related subject is the study of sound transmission in buildings and through walls. Ordinarily, the sound insulating efficiency of a wall is proportional to its mass per unit area. An important practical problem is to obtain good sound insulation for lightweight construction, which is particularly important for better sound insulation in apartment buildings and airplanes. Much progress has been made by using a sandwich type of construction in which a sound-absorbing material is inserted between the two surfaces of the wall.