The usual range of hearing lies between 16 vibrations in a second and about 38,000 vibrations per second. Starting with 16 vibrations per second, as the number is increased we have a series of rising musical notes, until the number is doubled, and an octave is produced with 32 vibrations per second. Increasing them from this point, the notes rise in pitch until they are again doubled, and we have the second octave with 64 vibrations per second. By thus ascending through 11 octaves, the number of vibrations reached would be 32,768 per second; but all the notes comprised within these limits cannot be employed in music. Tyndall states that the practical range of musical
sounds is comprised between 40 and 4,000 vibrations per second, which amounts, in round numbers, to seven octaves. Helmholtz says that the deepest tone of orchestra instruments is the E of the double bass with 41 ¼ vibrations. The new pianos and organs generally go down to 33 vibrations. In height, the piano-forte reaches to 3,520 vibrations, or sometimes to 4,224; while the highest note of the orchestra is that of the piccolo flute, with 4,752 vibrations per second. The limits of hearing vary in different persons. The squeak of the bat, the sound of the cricket, and even the chirrup of the sparrow, cannot be heard by some persons. The limit of sensibility often varies by as much as two octaves.
Waves of water, as everybody knows, vary greatly in magnitude; the riplets of the pool may be not more than an inch in length, while the sea-waves may measure a hundred feet from crest to crest. Sound--
