duced on a guitar and form the most ac curate method of tuning it.

230. Nodes and Loops in a Bell. Demonstration. - Mount a bell jar as in Fig. 201 and put it in vibration by striking it lightly with a cork hammer, or by drawing a violin bow across its edge. It will give out a belllike tone. If the bow is drawn midway between two of the suspended balls, they will all remain in contact with the rim, showing the existence of nodes; but if one of the balls is raised and the bow drawn at the point where it rested upon the rim, the three other balls will be thrown into vibration, showing the position of the loops.

FIG. 201

231. Vibration of Air Columns. In most musical instruments called wind instruments, the tones are produced by the vibrations of columns of air, of different lengths. There are three classes of mouthpieces, by means of which the air is put into vibration in wind instruments.

In the first class the air is blown across the sharp edge of an opening, as in the whistle, the organ pipe (Fig. 202), and the flute.

FIG. 202

In the second class the air is blown past a thin, flat tongue called a reed, which by its vibration opens and closes the opening into the air column.

B

FIG. 203

The striking reed (Fig. 203, A),

used in the clarinet, closes the opening by striking upon its edges; the free reed (Fig. 203, B), used in the accordion and reed organ, nearly closes the opening by vibrating back and forth through it.

In the third class of wind instruments the lips are generally used as vibrating membranes through which the air is blown

air in a tube is in the direction of its length, but it can give rise to nodes and loops as well as a vibrating cord.

A

B

C

D

N

N

L

L

In this case, however, the node must be understood to mean a point where the particles of air remain at rest, but where there are rapid changes from condensation to rarefaction, and vice versa. A loop means a point where there is the greatest motion, but no change of density. From this it will be seen that the end of a closed pipe must form a node, and the end of an open pipe a loop. In A (Fig. 205), a node N" would be at the upper end and a loop at the mouth; conseL'quently the length of a closed pipe is one fourth the wave length of its fundamental tone, as is the case in the resonator tube in §§ 207, 209. If the pipe is blown strongly, it will give out a tone higher in pitch,

L'

N'

FIG. 205

N

N'

L

but a node will still be at the closed end and a loop at the mouth. In this case (B) there will be an intermediate node and loop at N' and L', and the length of the pipe will be three fourths the wave length of the tone produced.

In the open pipe, C (Fig. 205), there will be a loop at each end, and a node in the middle, and the length of the pipe

will be half the wave length of the fundamental tone. If the next higher tone is produced, there will be two nodes, N' and N", and an additional loop L' and the length of the

pipe will be equal to the wave length of the tone. Comparing A and C it will be seen that the fundamental tone given out by an open pipe is the octave of the tone produced by a closed pipe of the same length.

Demonstration.-Procure an organ pipe, one side of which is glass, and lower into it, by a thread, a light ring over which is stretched a membrane with fine sand sprinkled over it, as shown in Fig. 206. When the fundamental tone is sounded and the ring is lowered, the sand will show by its movements that the amount of the vibration is decreasing until the middle of the tube is reached, where it will come to rest. Increase the force of the bellows that blow the pipe, so as to produce the higher tone; the middle point becomes a loop, as is shown by the dancing of the sand.

If an opening is made in the side of a pipe, this becomes a loop and changes the pitch of the tone produced. In this way the different tones of a flute are made by the fingers of the player stopping and unstopping holes along the side.

FIG. 206

233. The Vibration of Rods and Tubes. A rod fixed at one end may be put in transverse vibration by being struck or plucked at the free end - as in the music box. The longer the rod, the lower the tone produced.

Rods may be made to vibrate longitudinally as well as transversely.

Demonstrations. - Hold a glass rod, a meter long or more, by the middle with one hand, while with the other you draw a moist

cloth lightly from the middle to the end. The rod will be thrown into longitudinal vibrations, and the fundamental tone will be produced. Do the same with a wooden rod, a brass rod, and a brass tube of the same length and diameter, using a rosined cloth for a rubber. Does the pitch of the tone depend upon the material of the rod? Repeat the above demonstration with two glass tubes of different diameters, but of the same length. Does the pitch of the tone depend upon the diameter of the tube? Repeat with one of these tubes and another of the same diameter but only half as long. Does the pitch depend on the length of the tube? How do the two tones compare?

The sound caused by rubbing the tubes and rods in the above demonstrations is due to longitudinal vibrations. That such vibrations exist may be shown as follows:

Demonstration. Clamp a brass rod firmly to a block upon a

will cause the rod to give out a high tone, and will repel the ball from the end of the rod.

The mechanical effect of vibrations in tubes is sometimes very great. It is not uncommon for a test tube to be cracked into a spiral ribbon running from end to end, on being wiped with a damp towel. If a glass bell jar is bowed vigorously a few times with a violin bow, it may be shattered even if the walls are a quarter of an inch thick.

234. The Vibration of Plates. If a thin plate of metal or glass is clamped to a support at the middle, and a bow is drawn across its edge, it will be thrown into vibration

and will produce sound. The positions of the nodal lines

of the plate can be shown very readily as follows:

Demonstrations.

Sift sand evenly over the surface of a brass plate fastened by the middle, as the first one in Fig. 208. Place a finger at one corner and draw a bow across the middle of one side. The sand will be thrown violently about, and will finally come to rest on those parts of the plate that do not vibrate, so that the lines of sand indicate the nodal lines. Figure 208 shows a number of plates

differing in form, size, and thickness, and a few of the many interesting figures that can be produced by them. If the plates are clamped by the corner or at one side, a new set of figures will be obtained.

Scatter a little lycopodium powder on the plate with the sand, and it will be found, on vibrating the plate, that the powder will collect over the places of greatest vibration instead of at the nodal lines as the sand does. Examine carefully and explain why this happens.

235. Graphical Method of Combining Vibrations. It is frequently desirable to represent graphically the relation that exists between the vibrations of tones of different pitches. The method usually adopted is to consider the vibrations of the two bodies to be made at right angles with each other, and to construct curve that shall be the result of the two vibrations combined. If the vibrations producing the tones c and ƒ are to be combined, the curve can be made graphically as follows: