Sound

A

Three Important Types of Ordinary Sound

In speech, music, and noise, pure tones are seldom heard. A musical note contains, in addition to a fundamental frequency, higher tones that are harmonics of the fundamental frequency. Speech contains a complex mixture of sounds, some (but not all) of which are in harmonic relation to one another. Noise consists of a mixture of many different frequencies within a certain range; it is thus comparable to white light, which consists of a mixture of light of all different colors. Different noises are distinguished by different distributions of energy in the various frequency ranges.

When a musical tone containing some harmonics of a fundamental tone, but missing other harmonics or the fundamental itself, is transmitted to the ear, the ear forms various beats in the form of sum and difference frequencies, thus producing the missing harmonics or the fundamental not present in the original sound. These notes are also harmonics of the original fundamental note. This incorrect response of the ear may be valuable. Sound-reproducing equipment without a large speaker, for example, cannot generally produce sounds of pitch lower than two octaves below middle C; nonetheless, a human ear listening to such equipment can resupply the fundamental note by resolving beat frequencies from its harmonics. Another imperfection of the ear in the presence of ordinary sounds is the inability to hear high-frequency notes when low-frequency sound of considerable intensity is present. This phenomenon is called masking.

In general, reproductions of speech and musical themes are recognizable even if only a portion of the frequencies contained in the originals are copied. Frequencies between 250 and 3,000 Hz, the frequency range of ordinary telephones, are normally sufficient. A few speech sounds, such as th, require frequencies as high as 6,000 Hz. For high quality reproduction, however, the range of about 100 to 10,000 Hz is necessary. Sounds produced by a few musical instruments can be accurately reproduced only by adding even lower frequencies, and a few noises can be reproduced only at somewhat higher frequencies.

For information on the conversion of sound waves into electrical waves and electrical waves into sound waves, see Microphone; Telephone.

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IV

Historical Development

The elementary phenomena of sound were the subject of much speculation among ancient peoples; however, with the exception of a few lucky guesses, little was known about the science of sound until about 1600. Starting at that time, the knowledge of sound increased more rapidly than knowledge of the corresponding phenomena of light, because the latter are more difficult to observe and measure.

The ancient Greeks cared little for the scientific study of sound, but they had a great interest in music, and considered music to represent “applied number,” in contrast to “pure number,” the science of arithmetic. Greek philosopher Pythagoras discovered that an octave represents a two-to-one frequency ratio and enunciated the law connecting consonance with numerical ratios.

Aristotle, in brief remarks on sound, made a fairly accurate guess concerning the nature of the generation and transmission of sound, but no scientifically valid experimental studies were made until about 1600, when Galileo made a scientific study of sound and enunciated many of its fundamental laws. Galileo stated the relationship between pitch and frequency and the laws of musical harmony and dissonance, essentially as stated in this article. He also explained theoretically how the natural frequency of vibration of a stretched string, and hence the frequency of sound produced by a string instrument, depends on the length, weight, and tension of the string.

A

The 16th, 17th, and 18th Centuries

During the early 17th century, French mathematician Marin Mersenne determined the speed of sound by measuring the time of return of an echo. He arrived at a figure that was in error by less than 10 percent. Mersenne also made the first crude determination of the actual frequency of a note of a given pitch. He measured the frequency of vibration of a long, heavy wire that moved so slowly that its motion could be followed by the eye. Then, from theoretical considerations, he calculated the frequency of a short, light wire that produced an audible sound.

In 1660 the dependence of sound on a gaseous, liquid, or solid medium for transmission was demonstrated by Anglo-Irish scientist Robert Boyle, who suspended a bell in a vacuum by means of a string and showed that, although the clapper could be seen to strike the bell, no sound was heard.

The mathematical treatment of the theory of sound was begun by English mathematician and physicist Sir Isaac Newton in his Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy, 1687). The propagation of sound through any fluid was shown to depend only on measurable physical properties of the fluid, such as elasticity and density, and Newton calculated from theoretical considerations the speed of sound in air.

The 18th century was primarily a period of theoretical development. Calculus provided a powerful new tool to scientists in many fields, and mathematicians such as the French Jean le Rond d'Alembert and Joseph Louis Lagrange, the Dutch Johann Bernoulli, and the Swiss Leonhard Euler contributed to the knowledge of subjects including the pitch and quality of sound produced by a particular musical instrument and the speed and nature of transmission of sound in various media. The complete mathematical treatment of sound, however, depends on harmonic analysis, which was discovered by French mathematician Baron Jean Baptiste Joseph Fourier in 1822 and applied to sound by German physicist Georg Simon Ohm.

Variations in sound, called beats, inherent in sound waves, were discovered about 1740 by Italian violinist Giuseppe Tartini and German organist Georg Sorge. German physicist Ernst Chladni made numerous discoveries in acoustics at the close of the 18th century, notably concerning the vibration of strings and rods.

B

The 19th and 20th Centuries

The 19th century was primarily a period of experimental development. The first accurate measurements of the speed of sound in water were made in 1826 by French mathematician Jacques Sturm, and throughout the century numerous experiments were made determining the speed of sound of various frequencies in various media with extreme accuracy. The fundamental law that the speed is the same for sounds of different frequencies and depends on the density and elasticity of the medium was determined in these experiments. The stroboscope, the stethoscope, and the siren were all used in the study of sound during the 19th century.

The standardization of pitch occupied much attention in the 19th century. The first suggestion for a standard had been made about 1700 by French physicist Joseph Sauveur, who proposed C equals 256, a convenient standard for mathematical purposes. German physicist Johann Heinrich Scheibler made the first accurate determination of pitch corresponding to frequency and proposed the standard A equals 440 in 1834. In 1859 the French government decreed that the standard should be A equals 435, based on the research of French physicist Jules Antoine Lissajous. This standard was accepted in many parts of the world, including the United States, until well into the 20th century.

During the 19th century the telephone, the microphone, and the phonograph, all of which were useful for further study of sound, were invented. In the 20th century, physicists for the first time had instruments that made possible simple, accurate, quantitative study of sound. By means of electronic oscillators, waves of any type may be produced electronically, then converted into sounds by electromagnetic or piezoelectric means (see Electronics). Conversely, sounds may be converted into electrical currents by means of a microphone, amplified electronically without distortion, and then analyzed by means of a cathode-ray oscilloscope. Modern techniques permit extremely high-fidelity recording and reproduction of sound. See also Phonograph; Sound Recording and Reproduction.

Military necessity in World War I (1914-1918) led to the first use of sound for underwater detection of vessels; sound is now also used for studies of ocean currents and layers, and for sea-bottom mapping (see Sonar). In addition, ultrahigh-frequency (ultrasonic) sound waves are now used in a wide range of technical and medical applications.

See also Light.

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