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_)).