Sound Waves

Type of physical science: Classical physics

Field of study: Acoustics

Sound waves travel in any elastic medium (air, liquid, or solid) that is set in vibrational motion. Understanding music, human speech, underwater acoustics, medical ultrasonics, noise pollution, or earthquakes requires knowledge of sound waves.

Overview

Sound is commonly described as a wave that travels through the air and strikes the eardrum. It may be conversation, music, or noise. Yet it is a more general phenomenon. Sound travels in air, liquids, and solids. A mechanical disturbance of any material having both mass and elasticity generates sound waves.

Without matter, sound waves do not exist. A wave is transmitted when matter is vibrated. An elastic medium, when disturbed, experiences a force that restores it to its equilibrium position. Elasticity is the tendency to return to an undeformed state. This property enables waves to travel through matter without permanently disturbing it. The velocity of sound depends on the elasticity and the density (mass per unit volume) of a material. Sound travels faster in solids than in either gases or liquids. The velocity in air, at room temperature, is about 340 meters per second; in fresh water, it is about 1,435 meters per second.

There are two types of sound waves: longitudinal and transverse. The transverse wave resembles a water wave, such as one produced by throwing a stone into a quiet pond. As a small bit of floating wood will show, the water does not move with the wave. In transverse waves, matter vibrates in a direction at right angles (or transverse) to the direction the wave travels.

Longitudinal waves travel as a series of compressions and rarefactions, as seen in a stretched spring when several turns are compressed and then released. Sometimes called compressional waves, they differ from transverse waves in that the direction of vibration is parallel to the direction of wave propagation. In air, the vibration of molecules can be measured as changes in air pressure. The ear detects sound as a pressure wave. Water waves, though they appear transverse, are actually surface waves confined to travel only along the interface between air and water.

The elasticity of air and liquids differs from that of solids. In solids, sound can be both a compressional and a transverse wave. The three-dimensional rigid framework of molecules enables solids to exert a transverse (or shear) force, returning the molecules to their undisturbed state. Gases and liquids lack the rigid framework, so no shear force can be exerted and no shear wave can travel. Thus, only compressional waves travel through gases and liquids.

Both compressional and transverse sound waves can be described by their wavelength, frequency, and amplitude. The distance between successive crests or compressions of a wave is its wavelength. Frequency is measured in units of hertz, the number of wave vibrations per second. When heard, frequency is the tone, or pitch, of a note. The reciprocal of the frequency is the period, the time for one vibration. Sound velocity is given by the product of its wavelength and frequency or by its wavelength divided by its period. The amplitude is the size of the vibration (the height of the wave).

The study of sound has many branches. Acoustics is the study of sound heard by the human ear. The average human hears sound frequencies between 20 and 20,000 hertz.

Frequencies greater than 20,000 hertz are ultrasonic, beyond the range of hearing. Sounds less than 20 hertz are known as infrasonic, or below hearing. Within the acoustic range, one can study human speech or music. Architectural acoustics studies conditions for good hearing in any auditorium. Ultrasonics enables one to look into metals to find structural flaws or into humans without surgery. Infrasonics studies sound that cannot be heard but can be felt by the human body. Underwater acoustics deals with the transmission and detection of sound waves in water.

Compressional and shear waves can also travel through the earth and along its surface.

Seismology studies sound waves in the earth, whether generated naturally by earthquakes or artificially by explosions.

Sound exhibits properties common to all waves. They can be reflected and refracted when striking the interface between two media. In air, a reflection of sound is heard as an echo.

The refraction, or bending, of sound waves occurs because of a change in the velocity between the two media. At night, refraction can cause a distant sound, such as a train whistle, which can be heard more easily than in the day. After sunset, warm air often lies above the cool air near the ground. Sound travels faster in the warmer air and is refracted back toward the ground.

Sound waves can also interfere with one another. If the same-frequency tone is generated from two sources and no sound is heard, then the waves interefere destructively. For constructive interference, the wave amplitudes add and the tone is amplified. The interference of two or more waves generally produces a more complicated sound. The French physicist Joseph Fourier was the first to show that any periodic wave pattern is formed by the interference of two or more single-frequency waves. The interference of one frequency with its harmonics (integral multiples of the tone) produces musical sound. Interference of a random combination of tones is noise.

Resonance occurs when a system is forced to vibrate at its natural, or resonating, frequency. Constructive interference greatly amplifies the vibrations. In 1989, sediments in the San Francisco area (forced to vibrate at their resonance frequency by earthquake waves) produced large enough amplitudes to cause the collapse of homes and businesses. Yet, resonance is not always undesirable; it is important in the creation of musical sound.

Musical instruments produce sound by vibrating some medium that, in turn, vibrates the air. The sound wave then travels to the ear and is heard. The vibrating medium may be a thin wire (violin or guitar), a flexible membrane (drum), or a stiff solid (cymbals). For an instrument such as a pipe organ or clarinet, air vibrates inside a hollow tube. All wind musical instruments are based on a resonating air column. The air at one end of a hollow tube is set in motion. It may be by the lips (in a trumpet), by blowing across a reed (in a clarinet), or by an air jet (in a pipe organ). Continued reflection of the waves sets up a resonating interference pattern. The fundamental resonating frequency of the tube depends on its length and whether the second end is open or closed. The first end is always open. The air at the open end of the pipe vibrates freely.

Thus, open and closed pipes of the same length have different interference patterns, giving different fundamental and harmonic frequencies. By opening and closing valves on a musical instrument, different notes can be produced. The different timbre, or quality, of the same note produced by two different instruments depends on the harmonics produced. Each instrument has its own range of musical tones and its own harmonic structure.

The frequency (pitch) changes if the sound source and listener are in relative motion.

As a train approaches, its whistle is heard at an increasingly higher pitch, and as the train moves away, the sound decreases in pitch. The sound waves ahead of a moving source are pushed together, while behind the waves are spread out, resulting in the changes heard in the frequency of the wave. The phenomenon is the Doppler effect, first studied and explained by Christian Johann Doppler.

Noise is defined as unwanted sound of a nonrepeating, or inharmonic, nature. It may be irritating or soothing, a subjective reaction. Nevertheless, the loudness of sound--music or noise--can be damaging to the human ear. The ear does not perceive changes in loudness but changes in intensity, the sound energy flowing through an area per second. Sound level, measured in decibels, is a relative scale of sound intensity. The threshold of human hearing is defined as 0 decibels. A sound ten times more powerful has a sound level of 10 decibels; one hundred times more powerful, a level of 20 decibels. Normal conversation takes place at about 60 decibels. A lawn mower has a sound level of 80 decibels. Sound levels above 120 decibels can cause pain. Prolonged exposure to sound at these levels can cause permanent ear damage.

Applications

Knowledge of sound waves is used in a wide range of areas. The ancient Greeks knew that sound was a vibration detected by the ear. Only in modern times, however, has science begun to learn how these mechanical vibrations are translated by the ear as sound. Learning how the ear detects and transmits sound through its various parts can lead to an understanding of the causes of deafness. One out of every twenty Americans has some degree of hearing loss. Some people cannot hear the very high or low frequencies, while others cannot detect the complex harmonics of sound. Legal deafness, defined as the inability to hear sounds below the level of ordinary speech, can pose great difficulties to young and old. The increased understanding of sound transmission in the ear has enabled some to be helped by corrective surgery and others to be helped by hearing aids.

Sound also exists at frequencies undetectable to the human ear. It was not until the 1930's that scientists were able to build a device to detect ultrasonic frequencies. It was then discovered that bats "see" in the dark by producing and hearing sounds at frequencies up to 50,000 hertz. By analyzing the echoes reflected from various objects, bats determine the distances to walls, food, and other bats. The process, called echolocation, is also used by porpoises to avoid obstacles and find food under water. Porpoises produce and hear a wide range of sonic and ultrasonic sounds (up to 170,000 hertz). Echolocation was first used by humans during World War I to detect submarines. Refined sonar devices (for sound navigation ranging) use sound echoes to detect fish, submarines, and wrecks on the ocean floor.

The construction of musical instruments requires a knowledge of the production of harmonic sounds. Yet, even the best-designed and best-manufactured instruments played by expert musicians cannot be heard and enjoyed if the interference of reflected sounds is excessive.

Reverberation, excessive echoing of sound waves in a room, was first studied by Wallace Clement Sabine at Harvard University. His studies led to the development of the science of architectural acoustics, which is concerned with conditions for good hearing in any auditorium.

Sabine's work found that certain materials absorbed sound and reduced excessive reverberations.

While all matter absorbs sound energy, some absorbs better than others by allowing more energy to be transmitted into the material than is reflected. A proper combination of resonance (so that music is loud enough to be heard), interference (so areas of destructive interference, or "dead" spots, are minimized), and reverberation (to carry musical harmonics throughout the room) is needed for good hearing conditions. The design of modern auditoriums incorporates this knowledge to provide the best conditions for the enjoyment of music.

Ultrasound (frequencies above human hearing) is of great value in medicine for diagnosis and surgery. Focused beams of ultrasonic waves penetrate the body and are reflected by internal organs. The reflections are detected and processed electronically to produce a "picture" of the internal organs. Ultrasound is especially useful in the fields of obstetrics and gynecology. Multiple births can be detected early in a pregnancy, and fetal development can be followed without danger to mother or infant. Ultrasound echolocation has its most dramatic use in eye surgery. A miniaturized sonar device and probe was first used successfully in 1964 to locate and remove a 0.6-centimeter brass sliver from the eye of an eleven-year-old boy. Using the Doppler effect at ultrasonic frequencies allows study of active body functions, such as blood flowing through arteries or the beating of the heart.

Some sounds are pleasing, while others disturb and irritate. The latter type is unwanted sound or, scientifically speaking, noise. Though noise is sometimes classified as sound that is nonperiodic and inharmonic, even pleasing sounds, such as music, can be irritating if played too loud. The sound level (loudness) of noise is of increasing importance in human lives. Long-term exposure to loud noise can result in permanent hearing loss. Noise pollution is an increasing problem in the home and workplace from the ever-growing sources of noise, such as jet aircraft, dishwashers, or computer printers. The Occupational Safety and Health Administration (OSHA) of the U.S. Department of Labor has set maximum decibel levels and noise exposure limits for many industrial workers and has mandated use of hearing-protection devices, such as earplugs.

The use of sound-absorbing materials on ceiling, floors, and walls can reduce noise levels in the home and workplace. It is still a matter of scientific debate, however, as to what constitutes a hazardous level of noise.

Context

The study of sound and music began with the ancient Greeks. In the sixth century B.C., the mathematician Pythagoras first recognized that sound is a vibration. In his studies of vibrating strings, he discovered the relationship between string length and harmonic tones. About 350 B.C., Aristotle observed that air is necessary for sound to travel through and suggested that it would not travel through a vacuum. It was not until 1660, however, that English scientist Robert Boyle confirmed the absence of sound in a vacuum with a simple experiment. He pumped the air from a jar that held a watch with a loud alarm. The alarm rang, but no sound was heard.

The seventeenth and eighteenth centuries brought great advancements in the design of musical instruments, particularly in violins by Antonio Stradivari. The knowledge, however, was more intuitive than theoretical. Understanding also advanced as general principles of acoustics were discovered by scientists such as Galileo, who described the phenomenon of resonance, and Robert Hooke, who connected the frequency of vibration to musical pitch. The complex nature of sound waves was shown by Joseph Fourier in 1807, who explained that any sound was a combination of two or more single frequency waves. In 1842, Doppler explained the changing pitch of a moving sound source. It was not until 1878, however, that the theoretical foundation for modern acoustics was provided by Lord Rayleigh (John William Strutt) with the publication of THE THEORY OF SOUND. Practical applications of these theories soon followed: the development of architectural acoustics, the invention of the telephone, underwater acoustics and the use of sonar, and medical uses of sound.

Continued study and understanding of sound and the human ear promise to lead to the development of an artificial ear, enabling some people to regain lost hearing and others to hear for the first time. In a related field, scientists seek to learn how humans produce the sounds called speech in order to develop speech-recognition devices. These devices eventually will enable one to communicate directly with computers, using ordinary sentences.

The use of artificially produced sound is providing a detailed look at the structure of the earth's continents and, under water, of the ocean floor. This could uncover areas of untapped natural resources, such as oil or metal ores. Whales are believed to communicate by sound over vast distances in the ocean. Understanding the phenomenon could lead to a better understanding of sound waves in water and, perhaps, lead to communication between species.

The need to determine the effects of noise on human hearing and health is of increasing importance. The setting of hazardous sound levels and the reduction of noise in homes and businesses will protect the hearing ability of people and provide a healthier environment.

Principal terms

AMPLITUDE: the maximum displacement of a vibrating medium from its rest or equilibrium position

ELASTICITY: the property of an elastic medium that, when disturbed, experiences a force that restores it to its equilibrium position

FREQUENCY: the number of vibrations in any given time; in units of hertz, the number of vibrations per second

LONGITUDINAL WAVE: a wave in which the vibrational direction of the medium is parallel to the direction of wave motion; also called compressional wave

PERIOD: the time for one complete vibration; the reciprocal of frequency

RESONANCE: the forced vibration of a system at its natural, or preferred, frequency, resulting in relatively large amplitudes

SOUND LEVEL: a relative measure of the intensity of sound (subjectively called loudness), in units of decibels, where the threshold of human hearing is defined as 0 decibels

TRANSVERSE WAVE: a wave in which the vibrational direction of the medium is at right angles to the direction of wave motion; also called shear wave

WAVELENGTH: the distance between successive crests or compressions of a wave

Bibliography

Asimov, Isaac. UNDERSTANDING PHYSICS: MOTION, SOUND, AND HEAT. 3 vols. New York: Walker, 1966. An easy-to-understand book about physics for the general reader. The chapters "Sound" and "Pitch" explain the basic principles of sound and provide an overview of discoveries in the field.

Chedd, Graham. SOUND: FROM COMMUNICATION TO NOISE POLLUTION. Garden City, N.Y.: Doubleday, 1970. A book for the general reader covering principles of sound and their application in such fields as music, speech, medicine, and noise pollution.

Dixon, Robert T. THE DYNAMIC WORLD OF PHYSICS. Westerville, Ohio: Charles E. Merrill, 1984. Introductory text, for college students not majoring in science, on principles of physics. The chapters "Vibrations and Waves" and "Sound and Music" provide well-illustrated explanations of the basics of waves and sound. Suggested readings and home experiments are also included.

Fletcher, Neville H. PHYSICS AND MUSIC. Victoria: Heinemann Educational Australia, 1976. A book for the high school or college student interested in both physics and music. Principles of sound and vibration are applied to musical instruments with a minimum of mathematics. Experiments supplement the text.

Moravcsik, M. J. MUSICAL SOUND. New York: Paragon House, 1987. An introduction to the physics of music at any level using elementary mathematics. Thorough treatment of sound, music, and musical instruments. Includes problems, solutions, and bibliography.

THE PHYSICS OF MUSIC. San Francisco: W. H. Freeman, 1978. A series of articles, reprinted from SCIENTIFIC AMERICAN, on the application of physics principles to music, musical instruments, and architectural acoustics. Written for the general reader by knowledgeable authors. Includes a bibliography for each article.

Rayleigh, J. W. S. THE THEORY OF SOUND. 2 vols. New York: Dover, 1945. The two volumes form a reprinting of the classic work on the theory of sound. This edition of the 1877 text includes a historical introduction by R. B. Lindsay. Covers all aspects of sound, experimental and theoretical. Recommended for the more advanced reader because of the mathematics involved. Nevertheless, the text portions of the work can be readily understood by the informed reader.

Stevens, S. S., and F. Warchofsky. SOUND AND HEARING. Alexandria, Va.: Time-Life Books, 1980. A well-illustrated book for the general reader, covering the nature of sound and how it is perceived as music, information, or noise by the ear and brain.

Producing and Detecting Sounds

Waves on Strings