118 ACOUSTICS 103. The phenomena of beats may be easily observed with two organ-pipes put slightly out of tune by placing the hand near the open end of one of them, with two musical strings on a resonant chest, or with two tuning- forks of same pitch held over a resonant cavity (such as a glass jar, vid. 97), one of the forks being put out of tune by loading one prong with a small lump of bees -wax. In the last instance, if the forks are fixed on one solid piece of wood which can be grasped with the hand, the beats will be actually felt by the hand. If one prong of each fork be furnished with a small plain mirror, and a beam of light from a luminous point be reflected successively by the two mirrors, so as to form an image on a distant screen, when one fork alone is put in vibration, the image will move on the screen and be seen as a line of a certain length. If both forks are in vibration, and are perfectly in tune, this line may either be increased or diminished permanently in length, according to the difference of phase between the two sets of vibrations. But if the forks be not quite in tune, then the length of the image will be found to fluc tuate between a maximum and a minimum, thus making the beats sensible to the eye. The vibrograph ( 52, 53) is also well suited for the same purpose, and so in an especial manner is Helmholtz double syren ( 51), in which, by continually turning round the upper box, a note is pro duced by it more or less out of tune with the note formed by the lower chest, according as the handle is moved more or less rapidly, and most audible beats ensue. The gas harmonica and the flame manometer also afford excellent illustrations of the laws of beats. 104. Advantage has been taken of these laws for the purpose of determining the absolute number of vibrations per second corresponding to any given note in music, whence may be derived the number for all the other notes ( 45). The human ear maybe regarded as most correctly appreciating two notes differing by an octave. Two tuning- forks then are taken, giving respectively the note A and its lower octave, and a number of other forks are prepared intermediate in pitch to these, say 54, and by means of bees -wax these are so tuned, that the first gives four beats with the A fork, the second four beats with the fourth, and so on up to the last, which also gives four beats with the A_j fork. Now, if re = the unknown number of vibrations for the note A, n 4, n 8 . . . n - 55 x 4, will be the numbers for all the successive forks down to the A_ a fork, which being an octave below A, we have = | and 71 consequently n = 440. 105. Beats also afford an excellent practical guide in the tuning of instruments, but more so for the higher notes of the register, inasmuch as the same niimber of beats, that is, the same difference between the numbers of vibrations, for two notes of high pitch, indicates greater deviation from perfect unison, than it does for two notes of low pitch. Thus, two low notes of 32 and 30 vibrations respectively, whose interval is therefore or i.e., a semi- o) Lo tone, give two beats per second, while the same number of beats are given by notes of 32 x 16 (four octaves higher than the first of the preceding) or 512 and 514 vibrations, which are only slightly out of tune. 106. As the interval between two notes, and con sequently the number of beats increases, the effect on th ear becomes more and more unpleasant, and degenerates at last into an irritating rattle. With the middle notes of the musical register, this result occurs when the number of beats comes up to 20 or 30 per second, the musical interval between the two interfering notes being then between half and a whole tone. Helmholtz attributes the disagreeable im pression of beats on the ear. to the same physiological cause to which is due the painful effect on the eye of a faint flickering light, as, for instance, the light streaming through a wooden paling with intervening openings when the individual affected is passing alongside. In this case, the retina, which, when continuously receiving the same amount of light, thereby loses its sensitiveness in a great degree, is unable to do so. It is, however, remarked by the above-mentioned author that the same number of beats, which has so irritating an effect when due to two notes in the middle of the register, is not attended by the same result when due to notes of much lower pitch. Thus, the notes C, D forming a tone give together 33 beats per second, while a note two octaves lower than C also gives 33 beats with its fifth; yet the former combination forms a discord, the latter a most pleasing concord. 107. When the number of beats reaches to 132 or upwards per second, the result is a continuous and not unpleasing impression on the ear, and it was formerly held that the effect was always equivalent to that of a note having that number of vibrations. Helmholtz has shown that this opinion is inaccurate, except when the interfering tones are very loud, and consequently accompanied by very considerable displacements of the particles of the vibrating medium. These resultant tones being, as to their vibration-number, equal to the difference between the numbers corresponding to the two primaries, are termed difference-tones, and may be best observed with the double syren. The same author was led also, on theoretical grounds, to surmise the formation of summation-tones by the interference of two loud primaries, the number of resultant vibrations being then equal to the sum of the numbers for the two components, and appealed for experi mental proof to his syren. But, at the last meeting of the British Association (1872), Koenig, the celebrated Parisian acoustician, maintained that the notes of the syren, thus held to be summation-tones, were in reality the difference- tones of the harmonics. 108. By reference to the laws of the interference of vibrations, Hebnholtz has been enabled to offer a highly satisfactory explanation of the cause whence arises dif ference of quality or timbre or acoustic colour between different sounds. He has shown conclusively that there are but few sounds which are of a perfectly simple character, that is, in which the fundamental is not accompanied by one or more overtones. Now, when a note is si aple, there can be no jarring on the ear, because there is : x> room for interference of sound. Hence, the softness of the tuning- fork when its fundamental is reinforced by a resonant cavity, and also of the flute. The same character of soft ness belongs also to those instruments in which the powerful harmonics are limited to the vibration ratios 2, 3 ... G ( 57, 80); because the mutual interference of the funda mental and their harmonics give rise to concords only. The piano, the open organ pipe, the violin, and the softer tones of the human voice, are of this class. But if the odd harmonics alone are present, as in the narrow stopped organ pipe, and in the clarionet, then the sound is poor, and even nasal; and if the higher harmonics beyond the sixth or seventh are very marked, the result is very harsh (as in reed-pipes). 109. The human voice (for a description of the organ in which it originates, we refer to Art. Physiology Voice and Speech) is regarded by the best authorities as being analogous to a reed-pipe, the vocal chords forming the reed, and the cavity of the mouth the pipe, and, like the reed, is rich in harmonics, as many as sixteen having been detected in a bass voice. But their number and relative intensities differ much in different individuals, or even in the same person at dif ferent times ; and it is on this variety that, agreeably to Hclrn- Differeiici tones. Summa tion-tone Ilelm- lioltz s ej planation of acoust colour.
Voice,
