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, Koeenig 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.