Phonograph Monthly Review, Vol. 1, No. 10 (1927-07)

The Phonograph Monthly Review 417 F^- Sound waves are longitudinal vibrations in air. Each complete wave consists of a compression or condensation and expansion or rarefaction. If we regard the air as being composed of a number of equally distributed particles, we shall readily understand that the forward movement of, say, the prong of a vibrating tuning fork causes the particle nearest to it to move towards the next one, giving rise to a congestion of these units, or a condensation in the air. This compression causes the next particle to move forward in an attempt to re-establish a state of equal distribu- tion. In this way, with the advance of succes- sive units, the condensation travels forward. Meanwhile the prong of the fork returns to its neutral position, and then passes beyond it in the opposite direction, pulling the first particle back with it. This sets up a rarefaction, which fol- lows after the condensation. A sound wave has three very important charac- teristics, viz: length, amplitude, and form. These will be better understood after a consideration of the sine curve, or curve of simple harmonic mo- tion. For the present we may say that wave length determines pitch, amplitude loudness, and form quality or timbre. It is this third charac- teristic with which we are more particularly con- cerned. Longitudinal vibrations in air may produce, through the agency of the ear, the impression either of a musical note, or merely of a noise. No hard and fast distinction can be drawn between these impressions. The sound of the tuned drums (i.e. the kettle-drums) of the orchestra may be taken as a combination of the two. Periodicity, or the regular succession of waves which are exactly similar in form, is a necessary character- istic of a train of waves corresponding to a purely musical note. If the motions of the vibrating source are irregular, so will be the train of waves to which it gives rise, and a noise will Be pro- duced. A knowledge of periodic vibration is, therefore, an essential to the understanding of the scientific theory of tone-color in music. The simplest form of periodic vibration is that of which the displacement diagram is a simple harmonic or sine curve; that is to say, it is the curve of the equation:— y = sin (-) in which values of the angle (-) are plotted against the corresponding values of y. The data for the plotting of such a curve may, however, be ob- tained by means of a simple geometrical con- struction, without the use of trigonometrical tables. Fig. (3) should make this quite clear. The point P moves round the circle A B C at a constant speed. This point, as viewed from a position I in the same plane as the circle ABC, but at an infinite distance from it, appears to be traveling forwards and backwards along the diameter A B, not at a constant speed, but in simple harmonic motion. The wave-form corre- sponding to this motion may be represented dia- grammatically by the curve C D E F G. Here the units actually used along the axis C G are equal angles (30°), but since the point P moves round the circle at a constant speed, the scale may be taken as one of current time. At right angles to this axis is marked off the displacement of the point p (that is, the projection of P on A B) from its mean position 0, corresponding to the par- ticular value of the angle (-). Since radius 0 P is a constant, these values of 0 p are proportional to sin (-), and give a curve of the same form as that obtained when the sines themselves are plotted. The curve is therefore the displacement curve of a point in the air through which a har- monic wave of condensation and rarefaction is passing. As a representation of a longitudinal wave it is only diagrammatic, since the displace- ment is shown as being at right angles to the direction C G in which the wave is traveling, but it affords a useful method of representing wave- form. In this diagram C G is the wave length, and X D the amplitude of vibration. A pure musical note, according to the scientific definition, is one which has a simple harmonic curve for its wave-form. Fourier has shown that the wave-forms of all other musical notes can be resolved into components, each of which is, it- self, a curve of this type. The dull character of the sustained note of a tuning-fork, mounted on a resonator, is due to the fact that the form of its wave is very nearly a sine curve. The wave- forms of many musical instruments are, how- ever, very complex—they are rich in “upper par- tials.” It is on the presence or absence of the different partial tones, and their relative intensi- ties, that musical quality or timbre depends. The formation of overtones follows a definite law. If we have a wave of x feet in length, the wave-length of the first possible “upper partial” will be x/2 feet; this gives the octave of the fun- damental tone. The second possible “upper par- tial” will have a wave-length of x/3, correspond- ing to a note a fifth above the last, that is a twelfth above the fundamental. In some instru- ments, the oboe for example, many of these har- monics are present; in others only a few are suf- ficiently strong to have any appreciable effect on