waves also vary greatly in magnitude, though to each rate of vibration there corresponds a definite length of wave. Knowing the rate of vibration per second, and the velocity of sound per second, lengths of waves are easily calculated. Take, for example, a tuning-fork that sounds the lowest note of the common D-flute, and it gives 288 vibrations per second. If, now, it be struck in still air, at the freezing-point, the foremost wave will reach a distance of 1,090 feet, at the end of a second, while the chain of waves which connects it with the vibrating fork will be 288 in number: each wave-link will therefore be about 3 feet 9 inches long. With few vibrations and deep tones, waves are long, while, with rapid vibrations and shrill tones, waves are correspondingly short. Within the limits of hearing, sound-waves vary in length, from 70 feet to a half an inch. "The waves generated by a man's organs of voice in common conversation are from 8 to 1 2 feet; those of a woman are from 2 to 4 feet in length. Hence, a woman's ordinary pitch, in the lower sounds of conversation, is more than an octave above a man's; in the higher sounds it is two octaves."
But, because the numbers of their oscillations are exactly determined, we must not suppose that the motions are so simple, for, as Prof. Rood remarks, smooth and clean-cut waves but seldom reach the ear. There are compound vibrations which give complexity to wave-figures. The large waves at sea are often covered by smaller waves, so that the water-particles obey double impulses, and swing in double oscillations. It was illustrated, in Fig. 1, that a string may vibrate as a whole, or in various subdivisions. When a string or any other body vibrates as a whole, it produces its lowest note, which is called the fundamental note. But the fundamental note is never perfectly pure. It is not possible to sound the string as a whole, without at the same time causing the vibrations of its parts. But, as these shorter vibrations are quicker, they yield notes of a higher pitch, which mingle with the fundamental note, and alter its quality. These accompanying higher notes may be in harmony with the fundamental note (when they are called harmonics), or they may not harmonize with it. The sounds emitted by the parts of a vibrating body are called overtones, and it is possible for a string to furnish as many as 20 or 30 of these. The mingling of the overtones with the fundamental one determines the timbre of sound. It is this which gives their peculiar character to different musical instruments, and enables us to distinguish them. A clarinet and a violin may give the same fundamental note, but their overtones are so different that the instruments are never confounded.
Sound-waves are not only transmitted by the air, but also by liquids and solids. That water will convey musical sounds is shown by the following experiment: Fig. 8 represents a tube a yard long, set upon the wooden tray A B, with a funnel at the top, and filled with water. A tuning-fork is attached to a little wooden foot, set into vibration, and the foot is then dipped into the water without touching the sides