Sound

Sound. The sensation of sound is produced in the brain when the auditory nerve is affected in a particular way. Sound is transmitted through the air by means of waves; an original impulse given to certain gaseous molecules causes these to start outwards and, after hitting others, to rebound. These latter, in their turn, give up their motion to fresh ones, and so a series of to and fro movements is set up, the effect travelling outwards as a wave. As each particle starts forward it causes a condensation of air in front, and a rarefaction behind; while the wave travels onward in the same direction as that in which the molecules are moving. The faster the particles move to and fro the more quickly does the wave travel onwards, and, as the rate of rebound of the particles depends on the elasticity of the air, it follows that the velocity of sound also varies with this property. [ACOUSTICS.] The loudness of a sound diminishes as we recede from its source, and in such a way that the intensity is inversely proportional to the square of the distance; this is true if the sound be free to travel in all directions, but if the sound be forced to limit its direction this law does not hold. This limitation of direction is obtained when a person speaks into a tube: the sound as heard by a person some distance away is almost as loud as it is near the speaker.

A continuous sound may appear to us as music or as noise. If the sound-waves travel sufficiently rapidly, and follow each other with perfect regularity, we obtain a musical note, but directly the regularity ceases the music descends to noise. It might seem that the method of production would determine whether a sound were musical or not, but this is not the case; regularity is the one essential. Savart's wheel is provided with a number of small cogs or teeth, regularly placed round its circumference. If the wheel be made to strike against a card as it rotates, a quick succession of taps is obtained, which gives a note when the speed of rotation is sufficiently high. In the siren (q.v.) air or steam is made to issue in quick, regular puffs, and so produce a note. In many other ways can musical notes be produced: by the vibrations of a stretched string, by the rapid oscillation of a clamped rod, or by the lightning strokes of an insects wing. One of the commonest methods of getting a pure note is to throw a tuning-fork into vibration by drawing a bow across it. Although it is impossible to count the number of vibrations made by such a fork by merely watching it, yet the fork may be made to register its movements in a very simple way. A fine style is attached to one prong, and this is made to just touch a piece of smoked glass (Fig. 1). When the fork is sounding the smoked glass is quickly moved downwards with constant velocity. A series of tiny waves then appears on the glass. By counting the number of waves in any length, and knowing the velocity of motion of the glass, the number of vibrations can be found. It will be noticed that, as time goes on, the sound, although remaining the same note, gets less and less intense. This effect is shown on the blackened glass by the decreasing amplitude of the waves. The vibrations of a tuning-fork may also be exhibited by means of Lissajou's figures (q.v.). rhese vibrations set up a succession of rarefactions and condensations in the air which may be thus exhibited, and the length of a sound-wave is the distance between points of the greatest condensation or rarefaction. The actual wave-length of any note in air is found by dividing the distance traveled by the sound per second by the number of vibrations per second of the tuning-fork. Taking the velocity of sound to be 1,120 feet a second at ordinary temperature, a fork giving 320 vibrations per second will generate waves 3-1/2 feet long. Since the pitch of a note rises with the increase in number of vibrations, it follows that in the same medium a high note is produced by shorter waves than a low note. The wave-length of a note is twice as much as that of its octave higher, and the waves produced by a woman's voice are only about a quarter the length of those produced by a man's. Temperature exerts its effects on the wave length: the wave-length increases with rise of temperature when the rate of vibration is the same. The use of vibrating strings as a source of sound is exhibited in the violin and other musical instruments, but the vibration of the string itself has to be taken up by a sound-board to make it produce an audible sound. The laws of vibrating strings can be experimentally found by means of the monochord (q.v.). It is then found that the rate of vibration varies - (1) inversely as the length of the string; (2) inversely as the thickness; (3) directly as the square root of the tension; (4) inversely as the square root of the density. If suoh a stretched string be touched at a point half-way along it and a bow be drawn across one segment the string vibrates in two halves. If held at a point one-third of its length from one end, and the shorter part be agitated, it will vibrate in three parts (Fig. 3). The same sort of thing happens if the string be touched at points. 1/4, 1/5, etc., of its length along it, the string vibrating in 4, 5, etc., equal segments. These segments are separated from each other by points at which there is no motion, and these points are called nodes (q.v.). When the string is halved, it follows that the rate of vibration is doubled, and the pitch of the note is raised, and we have, in fact, the octave; when the string vibrates in three parts we have the twelfth. Those notes which can be produced by dividing the string into any aliquot parts are known as the overtones or harmonics of the string. When it vibrates as a whole, the note is known as the fundamental; but when apparently vibrating as a whole, the smaller vibrations occur as well as the others, and the overtones are mingled with the fundamental; it is the presence of these overtones which gives quality to the sound produced. Some overtones are not a pleasant addition to the note; so in the piano, for instance, one of these discordant harmonies is avoided by making the hammer strike the wire at a point (about 1/7 the length of the wire from its end) which would naturally be a node of that overtone, but which is now set in active motion.

The modes of division of a rod fixed at both ends, and made to vibrate transversely, are the same as those of a stretched string, but the rates of vibration are not the same. When the number of nodes is 0, 1, 2, 3, etc., the rates of vibration are proportional to the numbers 3², 5², 7², 9²2; etc.

A rod fixed at one end may also vibrate as a whole or in segments, and the rates of vibration of the overtones are thus related (Fig. 4). If the rate of vibration of the fundamental be considered as proportionate to 2² that of the first overtone is proportional to 5², and the rates of the first, second, third, etc., overtones are proportional to the numbers 3², 5², 7², etc. With rods of different lengths the rates of vibration vary inversely as the square of the length. This is the basis on which the musical box is constructed.

A rod free at both ends will vibrate in its simplest manner when possessing two nodes (Fig. 5). With 2, 3, 4, 5, etc. nodes, the rates of vibration are nearly proportional to 3², 5², 7², 9², etc. This system is used in the claquebois, but only the simplest method of vibration, viz. with two nodes, is employed. The vibrations of a tuning-fork are comparable with those of a rod free at both ends (Fig. 6). The fundamental has 2 nodes, the first overtone has 4; there is no division of a tuning fork by three nodes. Chladni investigated the vibrations of plates and obtained beautiful figures-known as Chladni's figures - by strewing sand on the vibrating body, the sand distributing itself on the nodal lines. The overtones of plates and also those of cells are not simply related to the fundamental, so these bodies are not greatly employed in music.

The vibration of columns of air is made use of in organ-pipes. Pipes may be of two kinds, open at both ends or closed at one. In the tube closed at one end that end is necessarily a node, while the open tube possesses a node at the centre. The note from an open pipe is therefore the octave of a closed pipe whose length is the same. In an open pipe the rates of vibration of the fundamental and overtones are proportional to the numbers 1, 2, 3, 4, etc., while in the stopped pipe they are proportional to 1, 3, 5, 7, etc. Reeds are often connected to columns of air and set up the vibrations [REED], and the choral chords of the human throatthroat act like the reed of an instrument. Sounds often occur which are made up of a number of componcomponent notes. These can be sifted by means of resof resonators (q.v.), or by sensitive flames.

Simple sounds may be arranged in scales, the notes of the scale being related in a simple way; the rates of vibration are proportional to 24, 27, 30, 32, 36, 40, 45, 48, the number 24 representing the fundamental, and 48 the octave. Between any consecutive two of these numbers there are only 3 ratios or intervals, these are 8/9 a major tone, 10/9 a minor tone, and 16/15 a limmar. To use this in practice would be inconvenient, so the octave is divided into 12 parts, the interval between two consecutive notes being the twelfth root of 2; this is known as a scale of equal temperament. Discord is produced when many notes are struck together, and if two consecutive low notes be sounded at once, that sort of discord is obtained which gives rise to audible beats (q.v.). Sound is propagated by waves in the same way as light. The laws of reflection and refraction are the same in both cases. Reflection is illustrated in the case of echoes, and refraction is exhibited when sound is concentrated by means of a lens containing a gas (e.g. carbonic dioxide) denser than air.