SOUND 177 executes a known number of vibrations, after which the number of vibrations made by its whole length can readily be calculated by a well known law. 3. The following method of determining the number of vibrations of a sounding body is applicable to all cases, whether the body be solid, liquid, or gaseous. After we have determined, by the method already de- scribed, the precise number of vibrations of a given fork, we make another fork higher in pitch than the former, which makes with the first eight beats a second ; a third fork is then tuned until it gives eight beats with the second fork, or sixteen with the first. Thus a series containing many forks is formed, any fork of which makes eight vibrations more in a second . than the fork next below it in pitch. On each fork is stamped its number of vibrations. To determine with these forks the pitch of a given sound, we find in the series of forks one which makes with this sound eight beats or fewer than eight beats in a second, and we count the number of these beats given during one minute or more. Dividing the number of beats found by the number of seconds during which the observation lasted, we have the number of beats made in one second by the fork and the given sound, and as the number of beats per second is always equal to the difference in the number of vibrations per second of the two sounds, it follows that we at once know how many vibrations per second the fork exceeds or falls short of those of the sound. To ascer- tain whether the fork makes more or less than le sound in a second, we place a small piece of wax on a prong of the fork, and observe whether this causes the number of beats to increase or to diminish. If the number of beats increases, then the fork was lower in pitch than the sound, while if the beats are less frequent the fork was higher in pitch than the given sound. The series of forks just de- scribed is called after its inventor a Scheibler's tonometer. 2. The Intensity of Sound. The intensity of sound depends on the energy of the aerial vibrations contiguous to the ear. For sounds of the same pitch the intensity varies as the square of the amplitude of the aerial oscilla- tions. The plans generally used are unworthy the designation of measures, being only rough comparisons. The writer first succeeded in measuring the relative intensities of sounds of the same pitch, and the reader is referred to the publication on the subject in the " Amer- ican Journal of Science " for February, 1873. The principle of the method depends" on the fact that if two sonorous impulses meet in traversing an elastic medium, and if at their place of meeting the molecules of the medium remain at rest, then at this place of quiescence the two impulses must have opposite phases of vibration and be of equal intensities. By means of an appropriate apparatus the above conditions are brought about in the union of the two sounds whose intensities we would compare. We then measure the distances from the place of meeting of the two sounds to the points of origin of these sounds. The relative intensities of the sounds will be as the inverse ratio of the squares of these distances. But to determine the relative or absolute intensities of sounds of different pitch is one of the most difficult of experimental problems. The writer has recently succeeded in reaching approxi- mate measures of the absolute intensities of sounds by measuring the amounts of heat pro- duced when the sound vibrations are absorbed by India rubber. By knowing the exact frac- tion of the whole energy of the sound absorbed and the specific heat of the rubber, the mechan- ical equivalent of the entire sonorous vibra- tions, in fractions of a Joule's unit, can be cal- culated. It was thus shown that the aerial vi- brations produced by a treble fork, mounted on its resonant box and vibrated during ten seconds, will, if entirely converted into heat, raise the temperature of one pound of water To-V?r?r of a degree ; or, in mechanical effect, will raise 54 grains one foot high. 3. Timbre of Sound, and Analysis of Sounds. Timbre is a term used to designate those special charac- ters by which we distinguish between two or more sounds having the same pitch and equal intensities. Thus, sounding the same note on a flute, a violin, a clarinet, and a piano, the ear at once distinguishes the instrument pro- ducing the note. Some preliminary knowl- edge as to the differences between a simple and a composite sound is necessary before giving an explanation of the cause of timbre. A sim- ple sound is a sound which has only one pitch. Such a sound is produced when a tuning fork, mounted on a resonant box, is gently vibrated by drawing a bow across one of its prongs. All simple sounds are alike in timbre; the only differences existing between them are differences of pitch and of intensity. Thus, if simple sounds alike in pitch and in intensity were produced by four instruments differing even very much in construction, the ear could not give us the information by which we could distinguish one instrument from another. On examining closely into the nature of the aerial vibrations which produce a simple sonorous sensation, we find that this sensation is only experienced when the aerial particles swing to and fro with the same character of reciproca- ting motion as pertains to a freely swinging pendulum. But there are other sounds which are not simple but composite, being formed of the combination of several simple sounds of various pitch and intensities. Thus, by atten- tive listening one can distinguish several sounds of various pitch in the sound of a piano string, or in that of a reed organ pipe. On analyzing these composite sounds, by methods presently to be described, we find that they can always be separated into two or more simple sounds, and that if we call the number of vibrations producing the lowest in pitch unity, then the remaining sounds will, in order of ascending pitch, bear to the first the vibration ratios of
