8 THE POPULAR SCIENCE MONTHLY. 



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 mu- 

 sical 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 sec- 

 ond octave with 64 vibrations per second. By thus ascending through 

 11 octaves, the number of vibrations reached would be 32,768 per sec- 

 ond ; but all the notes comprised within these limits cannot be em- 

 ployed in music. Tyndall states that the practical range of musical 



Fig. 7. 



SaVABT'8 APPARATUS FOE NUMBERING VIBRATIONS. 



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|- 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- 



