If one will but put his hand upon a table or a chair-back in any room where a piano or an organ is being played, or where voices are singing, especially in church, he cannot fail to feel the sound; and if he notices carefully he will perceive that some sounds make such table or seat to shake much more vigorously than others,—a genuine case of sympathetic vibrations.
It is for this reason that special materials and shapes are given to parts of musical instruments, so that they may respond to the various vibrations of the strings or reeds. For instance, the piano has an extensive thin board of spruce underneath all the strings, which is called the sounding-board. This board takes up the vibrations of the strings; but, unlike the rubber, gives them all out to the air, greatly re-enforcing their strength, and changing somewhat their quality. But the air itself may act in like manner. In almost any room or hall not more than fifteen or twenty feet long, a person can find some tone of the voice that will seem to meet some response from the room. Some short tunnels will from certain positions yield very powerful, responsive, resonant tones. There is certainly one such in Central Park, New York. It is forty or fifty feet long. To a person standing in the middle of this, and speaking or making any kind of a noise on a certain pitch, the resonance is almost deafening. It is easy to understand. When a column of air enclosed in a tube is made to vibrate by any sound whose wave-length is twice the length of the tube, we have such column of air now filled with the condensed part of the wave, and now with the rarefied part; and as these motions cannot be conducted laterally, but must move in the direction of the length of the tube, the air has a very great amplitude of motion, and the sound is very loud. If one end of the tube be closed, then the length must be but one-fourth of the wave-length of the sound. Take a tuning-fork of any convenient pitch, say a C of 512 vibrations per second: hold it while vibrating over a vertical test-tube about eight inches long. No response will be heard; but, if a little water be carefully poured into the tube to the depth of about two inches, the tube will respond loudly, so that it might be heard over a large hall. In this case the length of the air-column that was responding, being one-fourth the wave-length, would give twenty-four inches as the wave-length of that fork.
It is easy in this way to measure approximately the number of vibrations made by a fork.
| Letting | l | = | depth of tube, |
| d | = | diameter of tube, | |
| v | = | velocity of sound reduced for temperature, | |
| N | = | number of vibrations, | |
| Then | N | = | v . (4(l+d)) |
When a vibrating tuning-fork is placed opposite the embouchure of an organ-pipe of the same pitch, the pipe will resound to it, giving quite a volume of sound. In 1872 it occurred to me, that the action of an organ-pipe might be quite like that of a vibrating reed in front of the embouchure. As the air is driven past it from the bellows, the form of the escaping air will evidently be like a thin, elastic strip; and, having considerable velocity, it will carry off by friction a little of the air in the tube: this will of course rarefy the air in the tube somewhat, and a wave of condensation will travel down the tube. At the bottom, being suddenly stopped, its re-action will be partly outwards, and so will drive the strip of air away from the tube. After this will follow, for a like reason, the other phase of the wave, the rarefaction, which will swing the strip of air towards the tube. This theory I verified by filling the bellows with smoke, and watching the motion of the escaping air and smoke with a stroboscope. This view is now advocated by an organ-builder in England, Herman Smith; but whether he discovered it before or after me, I do not know.
When a membrane vibrates, its motion is generally perceptible to the eye; and it may have a very great amplitude of motion, as in the case of the drum; and various instruments have been devised for the study of vibrations, using membranes like rubber, gold-beater's skin, or even tissue paper, to receive the vibrations. One of the musical instruments of a former generation of boys was the comb. A strip of paper was placed in front of it, and placed at the mouth, and sung through, the paper responding to the pitch with a loose nasal sound. Köenig fixed a membrane across a small capsule, one side of which was connected by a tube to any source of sound, and the other side to a gas-pipe and a small burner. A sound made in the tube would shake the flame, and a mirror moving in front of the flame would show a zigzag outline corresponding to the sound vibrations.
In like manner if a thin rubber be stretched over the end of a tube one or two inches in diameter and four or five inches long, and a bit of looking-glass one-fourth of an inch square be made fast to the middle of the membrane, the motions of the latter can be seen by letting a beam of sunlight fall upon the mirror so as to be reflected upon a white wall or screen a few feet away. (Fig. [8].)
