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 colours. Different noises are distinguished by different distributions of energy in the various frequency ranges (see Spectrum).

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 supply the fundamental note by resolving beat frequencies from its harmonics. Another imperfection of the ear in the presence of ordinary sounds is the inability to hear high-frequency notes when low-frequency sound of considerable intensity is present. This phenomenon is called masking.

In general, speech is understandable and musical themes can be satisfactorily understood if only the frequencies between 250 and 3,000 hertz, the frequency range of ordinary telephones, are reproduced, although a few speech sounds, such as th, require frequencies as high as 6,000 hertz. For naturalness, however, the range of about 100 to 10,000 hertz must be reproduced. Sounds produced by a few musical instruments can be reproduced naturally only at somewhat lower frequencies, and a few noises can be reproduced at somewhat higher frequencies.

For the conversion of sound waves and electrical waves into each other, see Microphone; Telephone.

IV

Historical Development

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

The ancient Greeks cared little for the scientific study of sound, but they had a great interest in music, and considered music to represent “applied number”, in contrast to “pure number”, the science of arithmetic. The philosopher Pythagoras discovered that an octave represents a two-to-one frequency ratio and enunciated the law connecting consonance with numerical ratios; on this law, he built an edifice of mystical speculation. Aristotle, in brief remarks on sound, made a fairly accurate guess concerning the nature of its generation and transmission, 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 described in this article, above. He also explained theoretically how the natural frequency of vibration of a stretched string, and hence the frequency of sound produced by a stringed instrument, depend on the length, weight, and tension of the string.

A

The 16th, 17th, and 18th Centuries

Quantitative measurements of sound were made by the French mathematician Marin Mersenne, who measured the time of return of an echo, and arrived at a figure for the speed of sound that was in error by less than 10 per cent. Mersenne also made the first crude determination of the frequency of a note of a given pitch. He measured the frequency of vibration of a long, heavy wire that moved so slowly that its motion could be followed by the eye; then, from theoretical considerations, he calculated the frequency of a short, light wire that produced an audible sound.

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

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

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

Variations in sound called beats, a consequence of the wave nature of sound, were discovered about 1740 by the Italian violinist Giuseppe Tartini and the German organist Georg Sorge. The German physicist Ernst Chladni made numerous discoveries in sound 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 the French mathematician Jacques Sturm, and throughout the century numerous experiments were made determining the speed of sound of various frequencies in various media with extreme accuracy. The fundamental law that the speed is the same for sounds of different frequencies and depends on the density and elasticity of the medium was established in these experiments. The stroboscope, the stethoscope, and the siren were all used in the study of sound during the 19th century.

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

During the 19th century the telephone, the microphone, and various kinds of record-player, 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 analysed by means of a cathode-ray oscilloscope. Modern techniques permit extremely high-fidelity sound recording and reproduction.

Military necessity led in World War I to the first use of sonar for underwater detection of vessels; it is now also used for studies of ocean currents and layers, and for sea-bottom mapping. In addition, ultra-high-frequency sound waves are now used in a wide range of technical and medical applications.