Page:The American Cyclopædia (1879) Volume XV.djvu/187

SOUND 179 large audience. "We have also succeeded with the following experiment. Forcibly sound the reed pipe and place around its mouth eight or more forks of the harmonic series of the sound given by the reed, with the mouths of their resonant boxes toward the reed pipe. After the reed has sounded for a few seconds, stop it, and we shall find that all of the forks are in vibration; and thus singing together, they approximately reproduce the sound of the reed. This experiment requires the reso- nant boxes, the forks, and the harmonics of the reed to be in exquisite unison. The reader may convince himself of the composite nature of the sound given by a piano string, by the following simple experiments. If we sound on the piano the C below the middle or treble 0, if we call this note C 2 , the harmonics of this sound will be C 3 , G 3 , C 4 , E 4 , G 4 , B[, 4 , C 5 , &c. But the seventh harmonic, or B^, is want- ing, because the hammers of the piano strike the strings at points about one seventh of their length, and hence this harmonic cannot appear. If it did, it would cause harshness of timbre, for the seventh harmonic forms dis- sonant combinations with the other harmon- ics of the series. To show that all of the re- maining harmonics exist in the sound of C 2 , depress slowly and firmly the key of C 3 ; the hammer will rise, press against the string, and fall from it, but the damper of this string will remain raised. Now strike strongly the key of Ca, and after holding it for a few seconds stop its sound. We shall now hear the sound of C 3 very distinctly, showing that it has been set into vibration by the vibrations of C 3 which exist in the compound sound designated as C 2 . In like manner one can show that G 3 , 4 , E 4 , G 4 , C 6 , <fec., exist as components of the com- posite sound of the string of Ca. The reader who desires further information on the subject of sonorous analysis will find descriptions of six experimental methods in "Researches in Acoustics," paper No. 5, "American Journal of Science " for August and September, 1874. Reproduction of Sonorous Vibrations from the Curves made ~by Vibrating Bodies. Experi- ment has established that the sensation of a simple sound is alone produced when the aerial molecules vibrate with the same reciprocating motion as pertains to a freely swinging pendu- lum. If we obtain the sinuous trace of a vi- brating tuning fork or of a long elastic rod on a plate of smoked glass, fig. 10, we shall find, on making measures on these curves, that they are sinusoids or curves of sines, and hence can alone be produced by pendulum motions. But the curve produced by the fork can be made to reproduce the motions of the fork, only much slower, in the following manner: Cut a fine slit in a piece of paper, and slide it over the curve from right to left, as shown in fig. 10 ; then we shall see the portion of the curve ex- posed in the slit vibrating upward and down- ward with the same kind of motion as rules the oscillations of a pendulum. The aerial molecules and a point on the membrane of the drum of the ear vibrate thus when we experience the sensation of a simple sound. The majority FIG. 10. of sounds, however, are composite. It is evi- dent that a molecule of air or a point on the tympanic membrane can have only one direc- tion of motion at one and the same instant, and therefore that a composite sonorous vibra- tion will give to the molecule of air a motion which must be the resultant of the combined motions of all the pendulum motions of its simple sonorous components. Hence we may suppose a molecule of air, animated with a re- sultant motion like the above, to trace a curve which evidently will be the resultant of all the simple sinusoidal curves belonging to the sonorous elements of the composite sonorous vibration. "We can obtain this resultant curve as follows, and then we can reproduce from it the motions of a molecule of air, or of a point on the tympanic membrane, when these points are acted on by a compound sonorous vibra- tion. Draw on the axis a 5, fig. 11, sinusoidal curves having lengths related to each other as 1:2:3:4:5:6. These curves will then be the separate traces of the first six harmon- ics contained in a composite vibration which causes a musical sound, such as the sound of a piano string. Another axis c d is now drawn below a Z>, and 500 equidistant lines, perpen- dicular to a b and c d, are drawn through the curves on a 5 and extended below the line FIG. 11. c d. The algebraic sums of the ordinates of the curves on a & are now transferred to the corresponding ordinates on c d, and through