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360

Transverse and Longitudinal Vibrations.

the lowest or fundamental note, and the sand collects in the two straight lines joining the middle points of the opposite sides, as in A. if we draw the bow down the middle of one side, while we lightly touch one corner, the sand heaps itself along the diagonals of the square, B, while the note given forth by the plate is a fifth higher than the former. With a few trials, drawing the bow across different parts of the edge of the plate, and touching other parts of the edge, so as to induce the formation of stationary lines, we may obtain an endless variety (C, D) of beautiful symmetrical patterns.

Some very interesting sonorous figures are obtained with round, three-cornered, &c., plates treated in the same way. A common hand-saw may be made to produce a figure appropriate to the note it gives forth.

As a bent rod becomes a tuning-fork, so a bent plate becomes a beil, or goblet, or glass, which is subject to the same laws of vibration as a plate.

If a bell-shaped glass, or a metal bell such as is used in the construction of clocks, be mounted mouth up, and some sand strewed inside, it will be found to arrange itself in nodal lines just as on the square plate, when we sound the bell with a fiddle bow. If water be poured inside, the surface will be thrown into ripples, separated by smooth furrows, according to a similar law.

A common tumbler or a finger-glass partly filled with water, or a large wine-glass partly filled with wine, may be made to sound, and throw the liquid surface into ripples by merely wetting the finger and moving it round the edge with some pressure. If the surface divides into four sections, then the deepest note of the glass is being sounded.

543. The sonorous vibrations of metal wires and rods, which we have just been detailing, take place transversely or across the line of their length. But they may also be made to sound by rubbing (with the wet, or resined, fingers) longitudinally, or in the line of their length. The laws of vibration are akin to those for crossvibration; with half the length of wire or rod we obtain the octave to the original note; with one-third of the original length we get the fifth, and so on. The number of longitudinal vibrations per second increases in exact proportion as the wire or rod is shortened. It is to be remarked, however, that the longitudinal note given forth by any length of wire or rod is, as a general rule, much higher than the transversal note emitted by the same length; the reason being that the elastic force in the direction of the length is much greater than

Determination of the Velocity of Sounds.

361

across the length, and the rapidity of vibration increases with increase of elasticity. When a short piece of wire is briskly rubbed the note is extremely piercing, almost painful.

Difference of tension, unless it be so great as to affect the molecular structure of the wire, does not alter the pitch of the sound; but different metals will for the same length of wire give different notes, simply because their degree of elasticity is different.

An iron wire, for example, gives a higher note than a brass wire of the same length and thickness, the elasticity being greater; and therefore the rapidity of vibration and the velocity of transmission of the sound pulse being correspondingly greater. Hence it follows that by comparing the lengths of iron and brass wire which give the same note, we get the comparative rates of sound transmission through these metals. We should find that an iron wire 23 feet long, and a brass wire 15 feet long, would give the same note when we rub them with a wet cloth; and we conclude from this fact that sound travels through these metals in the same proportion, that is, in the proportion of 46 to 31. Thus, since in the former it is found to be about 17,000 feet per second, in the latter it is about 11,000 feet per second.

Similar experiments enable us to determine the comparative velocities of sound through different kinds of wood (see Art. 486). A glass, wooden, or metal rod fixed or clamped at one end, or clamped at the middle and left free at both ends, may be thrown into sonorous longitudinal vibrations, and obey somewhat similar laws. The longitudinal vibrations of a glass or wooden rod may be easily shown by experiment in the following way :-Fix the rod by one end in a vice or suitable wooden clamp, and hang against the free end a small bead or ball by means of a silk thread: on rubbing the rod lengthwise with the wet fingers or a resined cloth, the small bead will be shot away to a considerable distance.

Kundt's experiments.

544. A glass tube, closed at the ends, may be considered a hollow glass rod enclosing a rod of air. The wave-lengths of glass and of air will be very different; in other words, the lengths of a rod of glass and of air vibrating together or sounding the same note, will be proportioned to the velocities in glass and air respectively. Just as we obtained the comparative velocities of sound in iron and brass by comparing the lengths of iron and brass rods, which gave the same note, we have only to find what length of an air-rod vibrates in unison with any given length of glass rod to determine

362

Kundt's Experiments.

this relation. The invisible nature of air renders the direct comparison in this respect apparently impossible. But we owe to M. Kundt, of Berlin, a very simple solution of the difficulty.

A small quantity of lycopodium dust (the dust of the club-moss or puff-ball) is placed inside the tube, so as to line it through its whole length. This light powder reveals the condensations and rarefactions of the air within, when the tube is sounded by the wet fingers or a wet cloth. It collects into heaps, separated by clean spots, or spots of no vibration, corresponding to the nodes. The distance between any two nodes or spots of no vibration is, of course, half a pulse-length of the internal air; if the tube be fixed or clamped by its

Fig. 156.

middle, the length of the tube is half the pulse-length of the fundamental note which it sounds; for the middle is a node, and each free end is the centre of a ventral segment, so that the two halves together only make the length of one ventral segment. Each of the short air-pulses is made in the same time as the tube itself takes to pulse, or lengthen and contract; and the length of a pulse is the distance travelled by the sound during the time of formation of the pulse. Thus, the velocity of sound in glass will be as many times greater than that in air as the number of dust heaps within the tube. This will be found to be sixteen, if the conditions of the experiment be properly attended to. If the velocity in air be 1120 feet per second, that in glass will be 16 times 1120 feet, or 17,920 feet, a little over 3 miles per second.

Other gases introduced within the tube will give a different number of dust heaps: carbonic acid gas will give twenty heaps instead of sixteen, while coal gas will only give ten heaps, and purc hydrogen about five heaps. These numbers represent the comparative velocities of sound through these gaseous media.

545. By an extension of the same experimental method the comparative velocities of sound in air and in metal rods may be readily

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found. A brass or iron rod, B D (fig. 157), has fitted at its middle, C, a cork which just fits the end of the glass tube, A C, and on the end, B, a cork which will pass through A C with very little friction, and the rod is fitted in the figure so that A B is of the same length

as B D.

Laws of Sounding Pipes.

363

Some lycopodium powder is put into A B, and B D is made to sound by briskly rubbing with a resined cloth. The vibrations of the rod, B D, are communicated to the air-column, A B, by B acting as a piston. It divides itself into segments (shown by the lycopodium heaps) which vibrate in unison with the rod, B D. The num

ber of these segments will give the number of times by which the velocity of sound in the brass rod, B D, exceeds that in air. Thus, brass gives a sound-velocity of nearly eleven times that in air; strel, 15 times, and copper 12 times. The relative velocities of any solids capable of heing formed into rods, may thus be determined.

Sounding air-columns; organ-pipes.

546. When we blow across the mouth of a pipe or tube, every one knows that by properly modulating the blast, a musical note is obtained; and the shorter the tube the harder we must blow to get it to sound. A railway whistle is a wide short tube, which only a powerful blast of steam can suffice to sound. In understanding the cause why a whistle sounds, we have to remember that an air-column of a given length and pressure takes a definite time to vibrate or pulse, just as a string of a given length or tension, or a pendulum of a given length takes a definite time to vibrate. Double, triple, &c., a length of air-column just takes double, triple, &c., time of vibration. When we blow against the edge of an organ-pipe we set up small pulses of the adjacent air; and when these have the same periodicity as the vibrations of the air-column, they induce pulsations of the latter which gradually swell into a sonorous scream.

When a tube is closed at one end, the theory of its vibrations is analogous to that of a vibrating rod fixed at one end; the closed end of the pipe, like the fixed end of the rod, forms a node, and the open end, like the free end of the rod, forms the middle of a ventral segment. For the lowest tone of such a pipe, then, its length must be just the fourth part of the pulse-length of that tone. By blowing harder we may obtain higher tones or overtones, but there will obviously be, in every instance, an odd half of a ventral segment. Thus, the number of vibrations being in proportion to the number of ventral segments, the pulse numbers of the lower and higher tones will stand in the relations of to 1, 2, 3, &c., that as I to 3, 5, 7, &c. This is easily confirmed by trial with different lengths of glass or metal tubing.

547. But, again, a pipe open at both ends will also give a musical note; it is like a rod fixed at the middle and free at both ends. Each end will be the middle of a ventral segment with a node

364

Theory of Organ-Pipes.

between, and consequently the length of the pipe will be half the length of the corresponding sound-pulse.

Hence, if we blow at one end of a piece of glass tube, say six inches long, the length of sound-pulse generated will be twelve inches when the tube is open at both ends, but twenty-four inches when we stop one end with the finger. The ear will easily confirm this, by declaring the latter note to be an octave below the former. Hence, a 3-inch closed pipe would give the same note as a 6 inch open pipe.

548. It matters little how the air-pulses are set up in a tube or pipe. A tuning-fork, of the same pitch as the pipe, held at its mouth, will be enough to make the interior column resound the

same note.

In an ordinary organ-pipe, the primitive action of the lips, which is employed in the flute, is replaced by the arrangement seen in the

d

figure. The wind entering at b (fig. 158), issues in a flat sheet through the bass slit at d, and breaking into a flutter upon the edge, e, induces the pulsations proper to the aircolumn, a, in the pipe. The principle of a common whistle is very much the same; only in the whistle there is no cavity before the sheet formation of the air.

In what are called reed-pipes, an elastic flap, or valve, induces by its vibrations the sonorous pulsations of the tube. The notes of the clarionet, hautboy, and bassoon are thus created. In the child's trumpet, the French horn, the harmonium, concertina, &c., the elastic tongue does not thus act as a complete flap, but vibrates to and fro within the aperture, practically opening and shutting it, but not absolutely so. In any case the note will depend on the elasticity, length, stiffness, &c., of this governing vibrator. In the trumpet, trombone, cornet-a-piston, &c., the quivering of the lips takes the place of this elastic tongue of the reed. The fingering of a flute or whistle produces variations of pitch by simply varying Fig. 158. the length of the vibrating pipe, or by altering the position of the internal nodes; for where a hole is opened the air inside the tube will be in the same condition as at the open end of the pipe—that is, will be the middle of a ventral segment. Thus, if a node was there when the hole was closed, it can no longer be there, and the note will be altered in pitch according to the rule already explained.

549. In large organs there are several thousands of pipes, with

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