MEASUREMENTS OF THE MINIMUM AUDIBLE IN- 
TENSITY OF SOUND FOR TONES OF 
HIGH FREQUENCY 
C. E. LANE 
Many investigators have worked on the problem of determining 
the minimum amount of sound energy necessary for audible per- 
ception, but most of the investigations have been concerned with 
sounds of ordinary frequency and very little attempt has been 
made to make such a determination in absolute units near the up- 
per limit of the range of audition. The mechanical difficulty of 
securing tones of sufficient intensity at these high frequencies is 
great, and, furthermore, it is not so easy to ascertain the amount 
of sound energy given out from the sounding apparatus at these 
values of frequency as at lower values. 
In this investigation the Hewlett tone generator was used as a 
source of sound and the amount of sound energy given off was 
computed from the amplitude of vibration of the diaphragm of 
the instrument. (See preceding article.) 
From the equations for sound waves derived in terms of dis- 
placement, it follows that the amplitude of the air wave near the 
diaphragm has the same value as the amplitude of the diaphragm 
and the total amount of sound energy passing out from the instru- 
ment is given by 
where S is the area of each side of the diaphragm, d is the density 
of the air, A is the amplitude, f is the frequency, and V is the ve- 
locity of sound. 
If the observer is stationed at a given distance from the sound- 
ing apparatus and the amplitude is reduced until he is just able to 
hear the tone, one could calculate from the amplitude the total 
amount of energy given off at this intensity, and, if the fractional 
part of this total energy flowing through a square centimeter at 
the observer is determined, the problem is solved. If the sound 
energy leaving the tone generator passed out with equal intensity 
in every direction it would only be necessary, in order to deter- 
mine the flux of energy necessary for audition, to divide the total 
energy given off when the tone is just audible by the area of a 
