WAVE-ACTION IN NATURE. 9 



waves also vary greatly in magnitude, though to each rate of vibration 

 there corresponds a definite length of wave. Knowing the rate of vi- 

 bration 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 vibra- 

 tions 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 correspond- 

 ingly 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 or- 

 gans 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 deter- 

 mined, 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 vibra- 

 tions 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 



