The common A and C tuning-forks to be had in music stores, often vary a great deal from the accepted concert pitch. Such as the writer has measured have been generally too high; sometimes being ten or more vibrations per second beyond the proper number. The tuning-forks made by M. Köenig of Paris are accurate within the tenth of one vibration, the C making 256 vibrations in one second.
LIMITS OF AUDIBILITY.
Numerous experiments have been made to determine the limits of audible sounds; and here it is found that there is a very great difference in individuals in their ability to perceive sounds. Helmholtz states that about 23 vibrations per second is the fewest in number that can be heard as continuous sound; if they are fewer in number than that, the vibrations are heard as separate distinct noises, as when one knocks upon a door four or five times a second. If one could knock evenly 23 times per second, he would be making a continuous musical sound of a very low pitch. But this limit of 23 is not the limit for all: some can hear a continuous sound with as few as 16 or 18 vibrations per second, while others are as far above the medium as this is below it. The limits of sound in musical instruments are about all included in the range of a 7-octave pianoforte from F to F, say from 42 to 5,460 vibrations per second. But this high number is not anywhere near the upper limit of audible sounds for man.
Very many of the familiar sounds of insects, such as crickets and mosquitoes, have a much higher pitch. Helmholtz puts this upper limit at 38,000 vibrations per second, and Despraetz at 36,850. The discrepancy of results is due solely to the marked difference in individuals as to acoustic perception.
For the production of high musical tones, Köenig of Paris makes a set of steel rods. A steel rod of a certain length, diameter, and temper, will give a musical sound which may be determined. The proper length for other rods for giving higher tones may be determined by the rule that the number of vibrations is inversely proportional to the square of the length of the rod.
The dimensions of these rods when made 2 c. m. in diameter are as follows:—
| Length. | Vibrations. |
| 66.2 m. m. | 20,000 |
| 59.1 " " | 25,000 |
| 53.8 " " | 30,000 |
| 50.1 " " | 35,000 |
| 47.5 " " | 40,000 |
These rods need to be suspended upon loops of silk, and they are struck with a piece of steel so short as to be wholly beyond the ability of any ear to hear its ring. Nothing but a short thud is to be heard from it when it strikes, while from the others comes a distinct ringing sound. In experimenting with such a set of steel rods I have not found any one yet who could hear as many as 25,000 per second, my own limit being about 21,000. But it has been experimentally found that children and youth have a perceptive power for high sounds considerably above adults. Dr. Clarence Blake of Boston reports a case in his aural practice, of a woman whose hearing had been gradually diminishing for some years until she could not hear at all with one ear, and the ticking of a watch could only be heard with the other when the watch was held against the ear. After treatment it was discovered that the sensibility to high sounds was very great, and that she could hear the steel rod having a tone of 40,000 vibrations.
Last year Mr. F. Galton, F.R.S., exhibited before the Science Conference an instrument in the shape of a very small whistle, which he had devised for producing a very high sound. The whistle had a diameter less than the one twenty-fifth of an inch. The length could be varied by moving a plug at the end of the whistle. It was easy to make a sound upon such an instrument that was altogether out of hearing-range of any person. Mr. Galton tried some very interesting experiments upon animals, by using these whistles. He went through the Zoölogical Gardens, and produced such high sounds near the ears of all the animals. Some of them would prick up their ears, showing that they heard the sound; while others apparently could not hear it. He declares that among all the animals the cat was found to hear the sharpest sound. Small dogs can also hear very shrill notes, while larger ones can not. Cattle were found to hear higher sounds than horses. The squeak of bats and of mice cannot be heard by many persons who can hear ordinary sounds as well as any; sharpness of hearing having nothing to do with the limits of hearing.