CHAPTER IV.

1. MEASURE OF THE NUMBER OF VIBRATIONS; THE GRAPHIC METHOD— 2. CAGNIARD DE LA TOUR'S SIREN-3. PITCH OF SOUNDS; LIMIT OF

AUDIBLE SOUNDS, OF MUSICAL SOUNDS AND OF THE HUMAN VOICE4. THE NORMAL PITCH"-5. LAWS OF THE VIBRATIONS OF A STRING,

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AND OF HARMONICS.

1. THE second characteristic quality of musical sounds is their pitch. Every ear, however little practised, distinguishes a high note from a low one, even when the interval is not large. I propose to demonstrate that the pitch depends on the number of vibrations that a sounding body makes in each second of time, in such a way that the low notes are characterised by the small number, the high notes by the large number of their vibrations per second.

In order to solve this problem, we must first solve another: how the number of vibrations is to be determined? There are many methods in physics used for this purpose.

One method I have already to a great extent indicated— the graphic method, by means of which the vibrations of a tuning-fork were traced in the first chapter. In that experiment use was made of a cylinder, turned by hand. Naturally the motion could not be very regular, but if in

stead of the hand, use is made of one of the many mechani cal equivalents, a perfectly regular motion can easily be obtained; and further, the velocity of this motion may be determined. Suppose, for example, that the cylinder has a velocity of one turn per second; the tuning-fork will then record its vibrations, and to know their number per second we have only to count how many there are in one complete turn of the cylinder. The calculation is equally simple if the cylinder makes any other number of turns in a second. If, for example, the cylinder only makes five, we have only to count the vibrations in five turns, and the determination will be accurate, if the number of turns that the cylinder makes per second is accurately determined. This is often possible, and I will describe later on a very simple counter, by which the number of turns of a rotating apparatus is measured. The problem may then be solved by this means, as far as the vibrations of a tuning-fork are concerned.

2. At this point it becomes necessary to make the reader acquainted with another instrument, which answers this purpose to perfection, and which offers the advantage over the turning cylinder of not requiring for its use a slight change of the note, for a point has to be attached to the vibrating tuning-fork to trace its vibrations. This instrument is Cagniard de la Tour's Siren. Figs. 24, 25, and 26 show the arrangement of the instrument. It consists of a hollow empty cylindrical box BBB, which by means of its neck can be put in communication with a blower capable of

furnishing a constant current of air. In the upper end of the cylinder are a certain number of equidistant holes, disposed on the periphery of a circle concentric to the outline of the rim itself. These holes are all oblique, so

as to form an angle of about 45° with the vertical line. Over these holes is a metal disc C, which covers them entirely, and which is able to turn rapidly on a vertical axis A. This disc carries an equal number of holes, corresponding exactly in position and size with the holes in the disc below. These holes are also oblique, but in a different direction, and form an angle of about 45° with the vertical, but an angle of 90° with the direction of the holes beneath. Fig. 25 shows the section of the two discs, the fixed one and the movable one, as well as the arrangement of the holes. The holes p slope in one direction and the holes p' in the other. Fig. 26 is a drawing in section of the whole apparatus, in which is shown the hollow cylindri

cal box B of the siren, the movable disc CF, and the axis Aa on which it turns. When a current of air is forced into the cylinder by means of the blower, this current passes, it is true, through the holes; but on account of their obliquity, it strikes against their sides. The movable disc thus receives a series of impulses, all in the same direction, and therefore begins to turn. It turns quickly when the current is strong, and slowly when the current is weak; by suitably controlling the blower, the force of the current can be regulated at will, and through it the velocity of rotation of the movable disc.

But the current of air that enters the cylinder in a regular jet, can only pass out through the holes intermittently as soon as the movable disc has begun to turn. The reason for this is very simple. The air only passes out at the moments when the holes in the movable disc coincide with the holes in the fixed disc; it is, on the other hand, intercepted when the holes in the movable disc are over the unperforated parts between the holes in the fixed disc. It follows that the air must come out of the siren in the form of little puffs, which will be more frequent as the number of holes in the two discs is greater, and the velocity of rotation of the movable disc is greater. Suppose, for example, that each disc has twenty-five holes, as is the case in the siren I am now describing [twelve are shown in the drawing, but the number is arbitrary]. Suppose further that the velocity of rotation is one turn per second of time. In this case each hole in the upper

disc will give out twenty-five puffs of air in a second of time. If, however, the movable disc makes 2, 3, 4, &c., turns in a second, I must multiply the number of holes -i.e., 25-by 2, 3, 4, &c., or generally by the number of turns, to find the number of puffs of air produced by each hole per second.

When the siren is set in action, a very pure note is formed, low at first when the disc turns slowly, but higher as the velocity of the disc increases. The note is produced because the external air over the instrument is struck regularly by the puffs of air from the siren. These periodical blows produce vibrations in the external air, the number of which per second evidently corresponds to the number of blows received per second. We can therefore produce at will, by controlling the blower, any note we please, be it high or low; we can at the same time calculate the number of vibrations per second corresponding to it, as there is a means of determining the number of turns that the instrument makes in a second of time.

The very simple counter, which is placed at the top of the instrument, and which is represented in fig. 26, answers this purpose. To the movable disc CF is fixed a vertical steel arbor Aa, which carries at its upper end a few turns S of what is called an endless screw. The teeth of a toothed wheel EH gear into this screw, so that it moves forward one tooth for one turn of the arbor and movable disc. To the axis of the toothed wheel is