Page:The New International Encyclopædia 1st ed. v. 01.djvu/124

pressional (i.e., longitudinal) waves, the pro- duction of the sound-sensation is due to waves of this kind. The ditl'erence between the longitu- dinal and the transverse wave can be appreciated by reference to the accompanying diagram. Fig. 1.

In this illustration 1 represents a row of par- ticles at rest; these particles displaced to form a simple transverse wave are shown in 2, while a longitudinal wave is shown in 3. Here each particle moves to and fro in the direction of the line of propagation of the wave, and the ampli- tude of the wave is the distance that each par- ticle moves from its position of rest, while the wave-length is the distance between similar points of condensation and rarefaction, as from 4 to 4. Although sound is produced by longi- tudinal waves, there is no reason for believ- ing that all compressional waves will produce soimds : some may be too long or too short to affect the nerves of the ear.

Our sense of hearing distinguishes between two great classes of sounds: noises and musical notes. A noise is recognized as being abrupt, discontinuous, and exeeedinglj' complex; a musi- cal note is smooth, continuous, and with a definite, regular character. We distinguish, further, be- tween different musical notes as being simple or complex, meaning, by the latter, a note in which we can recognize the presence of several simple tones. Thus, if a piece of paper is torn, or two blocks of wood struck together, we call the re- sulting sound a noise. The viltrations of a tun- ing-fork cause a simple musical note; while if a banjo string is plucked we hear a complex note. Complex notes differ greatly in their character. They are said to have "quality" or "timbre;" thus, a sound produced by an organ- pipe has a quality entirely different from one produced by a piano or by a drum. Simple notes may differ in loudness and in shrillness or "pitch;" thus, a note of a definite pitch may be loud or feeble, and the pitcli of a piccolo note is quite different from that of a note produced by a flute.

Waves and Vibrations. Since the direct cause of a sound is the reception into the ear of waves in the air, it is necessary to analyze the nature of these waves. We may have an irregu- lar, isolated disturbance, which is analogous to a "hump" passing along a stretched rope, or to the effect of <lropping several stones at random intervals into a pool of water; or we may have a regular continuous succession of waves identical in all respects, which is called a "train of waves." The simplest kind of train of waves is what is called a "simple harmonic" train, such as is produced in any medium by a simple harmonic vibration of the body which is causing the waves. (Vibrations of a pendulum are simple harmonic.) Such a train of waves is character- ized by its "wave-number" and "amplitude;" the wave-number being the number of individual waves which pass a given fixed point in one second, while the amplitude is the extent of the path of vibration of any particle of the medium through which the waves are passing. The velocity of waves of a definite character, e.g., compressional ones, in any definite homogeneous medium depends upon the properties of the me- dium itself, not on the wave-number or ampli- tude of the waves. So, if A is the wave-length, i.e., the distance from one point in the medium to the next point, measured in the direction of advance of the waves, where the conditions arc identical with tho.se at the first point, and if . is the wave-niunlier. the velocity of the waves V is given by the formula V=N I

Consequently, if A' is known, A can be calculated, and vice versa : and the characteristics of the simple harmonic train of waves may be said to be its wave-length and its amplitude. If sev- eral trains of waves are passing through the same medium at the same time, the resulting waves — called a "complex" train — is simply the sum of the individual waves, the motion of any particle of the medium being the geometrical sum of the motions which it would have, owing to each of the separate trains of waves. (This is rigidly true only if the amplitudes of these separate trains are very small compared with their wave-lengths, as in general they are.) This is shown in Fig, 2, where A and B are two sets of simple harmonic waves which form the resultant wave C. This wave is olitained by taking the algebraic sum of the motion of the particles. The point b" is obtained by taking n"h", equal to the sum of a 6 and a'b', c" d" is the sum of c d and c'd', the latter, as it occurs be- low the axis, considered as having a negative sign. Conversely, it may be shown that any com- plex train of waves may be analyzed into simple harmonic trains. Therefore, complex trains of waves may differ in several ways; 1. The num- ber of the component simple harmonic trains. 2. Their wave-numbers and amplitudes. 3. Their relative "phases," for two waves are in different phase if the maximum displacement due to one train does not coincide in position with that due to the other ; or, looked at in another way, the component trains may have been started at irregular intervals. Since waves are due to the vibrations of some elastic body (e.g., a tuning-fork, the air in an organ-pipe or horn), it is necessary next to analyze the nature of vibrations. We may have an irregular vibra- tion, consisting of only a few to and fro motions, then a sudden change into another viln'ation of a different character, the whole motion lasting only a short time, e.g., when a piece of stiff paper is torn or when a scratching pen is used in writing; or we may have a regular continuotis