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Music is the art of producing pleasing, expressive, or intelligible combinations of tones. The sounds of original music are produced by the human voice or instruments actuated by musicians. Most music is recorded and translated into sound from a symbolic notation on paper. The ultimate objective destination of all music is the human hearing mechanism. Thus the production of music consists of the following processes: the symbolic notation on paper by the composer, the translation of the notation into musical sounds by a musician employing his own voice or an instrument or both, and the actuation of the human hearing mechanism by the musical sounds.
The evolution and production of combinations of tones by composers and musicians, which have been accepted by the listeners as pleasant and expressive, have gone on through all the ages of man. Some of the musical developments have withstood the rigors of time and are in evidence at the present time. Others enjoyed a short-lived popularity and, as a consequence, were lost in the oblivion of the past. The evolution, development, and production of music through all the past epochs has been a very slow process, because the number of persons that could listen first hand to music as it was rendered was obviously limited. The advent of sound reproduction changed all this and made it possible for people in the millions to hear famous actors, artists, and musical aggregations where only the order of a thousand had been able to hear them first hand. As a result of sound reproduction, music entered upon a new era which made the musical past seem rather insignificant in comparison.
The reproduction of sound is the process of picking up sound at one point and reproducing it either at the same point or at some other point either at the same time or at some subsequent time. The most common sound-reproducing systems are the telephone, the phonograph, the radio, the sound motion picture, and television.
The telephone is the oldest sound-reproducing system. There is an average of more than one telephone instrument for each family in this country. This means that any person can talk to any other person in the matter of seconds.
The phonograph was the first sound-reproducing system which made it possible for all the people of the world to hear statesmen, orators, actors, orchestras, and bands when, previously, only a relatively few could hear them at first hand. The phonograph is used in every country and clime. There is an average of at least one phonograph per family in this country. For the past decade the sale of records has averaged three per year for every man, woman and child. The popularity of the phonograph is due to the fact that the individual can select any type of information or entertainment and reproduce it whenever he wants it.
The radio, like the phonograph, is a consumer-type instrument. Practically every family owns several radio receivers from the personal to the high-quality types. More than half of the automobiles are equipped with radio receivers. As a result, practically every person can select almost any desired program for listening.
The addition of sound to motion pictures made this type of expression complete. This was the first system in which picture and sound were synchronized and reproduced at the same time. Practically one-half of the population sees a motion picture once a week.
Television is the latest system in which picture and sound are reproduced at the same time. Sound is, of course, important to television because without it the result would be the same as the silent motion picture. On the average, every family owns a television receiver and has the opportunity to select from a myriad of varied programs.
The radio, phonograph, sound motion picture, and television have made it possible for all the people of the world to hear famous statesmen, artists, actors, and musical aggregations where only a relatively small number had been able to hear them at first hand. It is evident that the reproduction of sound has produced in a relatively short time a great change in the education and entertainment of this and other countries. The impact of the telephone, phonograph, radio broadcasting, sound motion pictures, and television upon the dissemination of information, art, and culture has been tremendous. The reproduction of sound in these fields has been as important to the advancement of knowledge as the invention of the printing press.
The science of music has been advanced along with acoustics, mathematics, electrical engineering, electronics, psychology, and physiology. The findings in these fields have made it possible to use a scientific approach in the study of speech and music. As a result, great advances have been made in reducing speech and music to a scientific basis. These advances have been hastened by the advent of the reproduction of sound, because the maximum exploitation of this medium requires a scientific understanding of speech and music. The studies in speech, music, hearing, and sound reproduction have advanced to the point where the fundamental aspects dealing with speech, music, musical instruments, hearing, and sound reproduction are reasonably well established. This implies that the science of music and the related subjects have advanced to the stage where they can be classed as engineering. In view of the importance and status of the science of speech, music, and the related subjects, it seems logical and timely to devote a book to the exposition of the scientific aspects of these subjects. Accordingly, the book presented herewith was written. In keeping with the treatment outlined above, the book is given the title Musical Engineering. Musical engineering is the theory and practice of the subjects of speech, music, hearing, acoustics, and electronics in the applied-science domain. More specifically, musical engineering involves the following subjects: the nature of an audio sound wave; the fundamental generators for the production of sound waves; musical terminology; musical scales; resonating and radiating systems used in musical instruments; string, wind, percussion, and electrical musical instruments and the human voice; the frequency spectrums, power output, directivity patterns, growth and decay and duration characteristics of musical instruments; the fundamental properties of speech and music; the human hearing mechanism; the acoustics of rooms; and sound-reproducing systems. It is the purpose of this book to present the subject of musical engineering.
Sound is an alteration in pressure, particle displacement, or particle velocity which is propagated in an elastic medium, or the superposition of such propagated alterations.
Sound is also the auditory sensation produced through the ear by the alterations described above.
From these definitions it will be seen that sound is produced when the air or other medium is set into motion by any means whatsoever. Sound may be produced by a vibrating body as, for example, the sounding board of a piano, the body of a violin, or the diaphragm of a loudspeaker. Sound may be produced by the intermittent throttling of an air stream as, for example, the siren, the human voice, the trumpet and other lip-reed instruments, and the clarinet and other reed instruments. Sound may also be produced by the explosion of an inflammable-gas mixture or by the sudden release of a compressed gas from bursting tanks or balloons. Sound may be produced by the impact of the wind against certain objects in which the nonlinear properties of the medium convert a steady air stream into a pulsating one.
The properties of sound waves and the most common ways of producing sound waves will be described in this chapter in the sections which follow.
1.3 NATURE OF A SOUND WAVE
An explosion of a small balloon of compressed air produces one of the simplest forms of sound wave. A small balloon filled with compressed air is shown in Fig. 1.1 A. The air surrounding the balloon is in repose. In Fig. 1.1 B, the balloon has burst and the air which has been confined under pressure is transmitted outward in all directions as a pulse of pressure. In equalization, the pressure or condensation pulse is followed by a rarefaction pulse. In the rarefaction pulse the pressure is below the normal undisturbed atmospheric pressure, and in the condensation pulse the pressure is above the normal undisturbed atmospheric pressure, as shown in C, D, and E of Fig. 1.1. Following the definition of a sound wave, given in Sec. 1.2, it will be seen from the foregoing description that the disturbance produced by the bursting balloon constitutes a sound wave, consisting of a condensation or high-pressure pulse followed by a rarefaction or low-pressure pulse. The sound wave travels outward in all directions at the velocity of sound, that is, 1,100 feet per second. The magnitude of the condensation and corresponding rarefaction falls off inversely as the distance from the point of explosion of the balloon. The sound wave depicted in Fig. 1.1 is one of the simplest types. More complex sound waves consist of more than one condensation and rarefaction, usually of different values. These sound waves are produced by a vibrating body or a throttled air stream.
The sound wave described above is termed a spherical wave. The wavefront in a spherical wave is a continuous spherical surface in which the sound variations for all parts of the surface have the same phase. Phase is the fraction of the whole period or time interval which has elapsed with reference to some fixed origin of time. If a relatively small volume, at a large distance from the source, in a spherical sound wave is examined, the waves will be found to be plane. The wavefront in a plane wave is a continuous plane surface in which the sound vibrations for all parts of the surface have the same phase. For example, in Fig. 1.1 E, the simple sound wave approximates a plane wave. This sound wave is shown in greater detail in Fig. 1.2. The sound pressure and particle velocity are shown for equal time intervals over a complete cycle of events. The pressure p is depicted by the pointer of the small pressure gauge. The magnitude and direction of the flow of the air molecules, termed particle velocity, is depicted by the arrow marked u. It will be seen that the instantaneous value of the pressure corresponds to and is proportional to the particle velocity.
1.4 SOUND GENERATORS
A vibrating body in contact with the atmosphere will produce sound waves. One of the simplest vibrating bodies suitable for the production of sound is the vibrating piston, depicted in Fig. 1.3. The piston is moved back and forth by the crank and connecting-rod arrangement. In Fig. 1.3 A, the entire system including the piston and atmosphere is in repose. In Fig. 1.3B, the piston has moved forward, causing a compression of the air in front of the piston. For reasons of simplicity, the conditions existing on the back of the piston are not shown. In Fig. 1.3C, the pressure wave has now advanced one-half cycle. The air pressure next to the piston is the same as that in the free or undisturbed atmosphere. In Fig. 1.3D, the air next to the piston is below that of the undisturbed atmosphere. In Fig. 1.3E, the pressure next to the piston is the same as that in the free atmosphere. Now a cycle has been covered which includes a complete condensation and rarefaction, that is, a pressure above and a pressure below the undisturbed atmosphere. In Fig. 1.3F, two cycles have been completed. In Fig. 1.3 G, six cycles have been completed. Examples of this type of sound generator are the soundboards of the piano and harp, the bodies of the instruments of the violin family, the stretched membranes of drums, the surfaces of cymbals, and the diaphragms of loudspeakers.
Another common type of sound generator employs a means for throttling an air stream and thereby converts a steady or constant stream of air into a pulsating one. The throttled air-stream sound generator shown in Fig. 1.4 consists of a valve in the form of a motor-driven eccentric disk covering an aperture and a source of air under pressure. In Fig. 1.4 A, the entire system is in repose. In Fig. 1.4B, the aperture is partially open and a pulse of air under pressure is released. In Fig. 1.4C, the aperture is wide open and the pressure is a maximum. In Fig. 1.4D, the aperture is partially closed and the pressure is less than the maximum. In Fig. 1.4E, the aperture is closed and the pressure at the aperture is the same as that in the undisturbed atmosphere and a full cycle has been completed. In Fig. 1.4F, four completed cycles have been emitted. It will be seen that equalization takes place with a result that ultimately the rarefactions are equal to the condensations. Examples of this type of sound generator are the human voice, the trumpet, trombone and other lip-modulated instruments, the clarinet, saxophone, bassoon, organ and other reed-modulated instruments, and sirens.
1.5 VELOCITY OF PROPAGATION OF A SOUND WAVE
The preceding examples have shown that a sound wave travels with a definite finite velocity. The velocity of propagation, in centimeters per second, of a sound wave in a gas is given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.1)
where γ = ratio of specific heats for a gas, 1.4 for air
p0 = static pressure in the gas, in dynes per square centimeter
ρ = density of the gas, in grams per square centimeter
If the pressure is increased, the density is also increased. Therefore, there is no change in velocity due to a change in pressure. But this is true only if the temperature remains constant. Therefore, the velocity can be expressed in terms of the temperature. The velocity of sound, in centimeters per second, in air is given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.2)
where t = the temperature in degrees centigrade.
1.6 FREQUENCY OF A SOUND WAVE
Referring to the Sec. 1.4 on Sound Generators, it will be seen that these generators produce similar recurrent waves. A complete set of these recurrent waves constitute a cycle. These recurrent waves are propagated at a definite velocity. The number of recurrent waves or cycles which pass a certain observation point per second is termed the frequency of the sound wave.
1.7 WAVELENGTH OF A SOUND WAVE
The wavelength of a sound wave is the distance the sound travels to complete one cycle. The frequency of a sound wave is the number of cycles which pass a certain observation point per second. Thus it will be seen that the velocity of propagation of a sound wave is the product of the wavelength and the frequency, which may be expressed as follows:
c = λf (1.3)0
where c = velocity of propagation, in centimeters per second
λ = wavelength, in centimeters
f = frequency, in cycles per second
1.8 PRESSURE IN A SOUND WAVE
A sound wave consists of pressures above and below the normal undisturbed pressure in the gas (see Secs. 1.3 and 1.4).
The instantaneous sound pressure at a point is the total instantaneous pressure at that point minus the static pressure, the static pressure being the normal atmospheric pressure in the absence of sound.
The effective sound pressure at a point is the root-mean-square value of the instantaneous sound pressure over a complete cycle at that point. The unit is the dyne per square centimeter. The term "effective sound pressure" is frequently shortened to "sound pressure."
The sound pressure in a spherical sound wave falls off inversely as the distance from the sound source.
Excerpted from Music, Physics and Engineering by Harry F. Olson. Copyright © 1967 Dover Publications, Inc.. Excerpted by permission of Dover Publications, Inc..
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