Page:Encyclopædia Britannica, Ninth Edition, v. 1.djvu/126

forated plates and perforated rings, both the moveable plates being driven by the same current and revolving about a common axis. Annexed is a figure of this instrument (fig. 11).

Fig. 11.

52.The relation between the pitch of a note and the frequency of the corresponding vibrations has also been studied by graphic methods. Thus, if an elastic metal slip or a pig's bristle be attached to one prong of a tuning-fork, and if the fork, while in vibration, is moved rapidly over a glass plate coated with lamp black, the attached slip touching the plate lightly, a wavy line will be traced on the plate answering to the vibrations to and fro of the fork. The same result will be obtained with a stationary fork and a movable glass plate; and, if the time occupied by the plate in moving through a given distance can be ascertained, and the number of complete undulations exhibited on the plate for that distance, which is evidently the number of vibrations of the fork in that time, is reckoned, we shall have determined the numerical vibration-value of the note yielded by the fork. Or, if the same plate be moved in contact with two tuning-forks, we shall, by comparing the number of sinuosities in the one trace with that in the other, be enabled to assign the ratio of the corresponding numbers of vibrations per second. Thus, if the one note be an octave higher than the other, it will give double the number of waves in the same distance. The motion of the plate may be simply produced by dropping it between two vertical grooves, the tuning-forks being properly fixed to a frame above.

53.Greater accuracy may be attained with the so-called Vibrograph or Phonautograph (Duhamel's or Kœnig's), consisting of a glass cylinder coated with lamp-black, or, better still, a metallic cylinder round which a blackened sheet of paper is. wrapped. The cylinder is mounted on a horizontal axis and turned round, while the pointer attached to the vibrating body is in light contact with it, and traces therefore a wavy circle, which, on taking off the paper and flattening it, becomes a wavy straight line. The superiority of this arrangement arises from the comparative facility with which the number of revolutions of the cylinder in a given time may be ascertained. In Kœnig's phonautograph, the axis of the cylinder is fashioned as a screw, which works in fixed nuts at the ends, causing a sliding as well as a rotatory motion of the cylinder. The lines traced out by the vibrating pointer are thus prevented from over lapping when more than one turn is given to the cylinder.

Any sound whatever may be made to record its trace on the paper by means of a large parabolic cavity resembling a speaking-trumpet, which is freely open at the wider extremity, but is closed at the other end by a thin stretched membrane. To the centre of this membrane is attached a email feather-fibre, which, when the reflector is suitably placed, touches lightly the surface of the revolving cylinder. Any sound (such as that of the human voice) transmitting its rays into the reflector, and communicating vibratory motion to the membrane, will cause the feather to trace a sinuous line on the paper. If, at the same time, a tuning-fork of known number of vibrations per second be made to trace its own line close to the other, a comparison of the two lines gives the number corresponding to the sound under consideration.

Part V.
Stationary Waves.

54.We have hitherto, in treating of the propagation of waves of sound, assumed that the medium through which it took place was unlimited in all directions, and that the source of sound was single. In order, however, to understand the principles of the production of sound by musical instruments, we must now direct our attention to the case of two waves from different sources travelling through the same medium in opposite directions. Any particle of the medium being then affected by two different vibrations at the same instant will necessarily exhibit a different state of motion from that due to either wave acting separately from the other, and we have to inquire what is the result of this mutual interference (as it is termed) of the two given waves.

Fig. 12.

Supposing, as sufficient for our purpose, that the given waves are of equal lengths and of equal amplitudes, in other words, that the corresponding notes are of the same pitch and equally loud; and supposing, further, that they are advancing in exactly opposite directions, we shall now show that the result of the mutual interference of two such waves is the production of a stationary wave, that is, taking any line of particles of the medium along the direction of motion of the component waves, certain of them, such as $a$, $c$, $e\ldots$ at intervals each $={\tfrac {\lambda }{2}}$, will remain constantly in their usual undisturbed positions. All the particles situated between $a$ and $c$ will vibrate (transversely or longitudinally, as the case may be) to and fro in the same direction as they would if affected by only one of the interfering waves, but with different amplitudes of vibration, ranging from zero at $a$ to a maximum at $b$ and thence to zero at $c$. Those between $c$ and $e$ will vibrate in like manner, but always in an opposite direction to the similarly placed particles in $ac$, and so on alternately.

Fig. 13.

The annexed figures will represent to the eye the states of motion at intervals of time $={\tfrac {1}{4}}$ of the time ${\text{T}}$ of a complete vibration of the particles. In fig. 13, 1, the particles in ac are at their greatest distances from their undisturbed positions (above or to the right, according as the motion is transversal or longitudinal). In fig. 13, 2, they are all in their undisturbed positions. In fig. 13, 3, the displacements are all reversed relatively to fig. 13, 1. In fig. 13, 4, the particles are again passing through their equilibrium positions, resuming the positions indicated, in fig. 13, 1, after the time ${\text{T}}$.

The points $ace$, &c., which remain stationary are termed nodes, and the vibrating parts between them ventral segments.

54a. Proof.In fig. 14, 1, the full curved line represents the two interfering waves at an instant of time such that,