Intensity and pitch sensibilities of the ear as functions of loudness and frequency.—Intensity sensibility is defined, as usual, as the ratio of the least perceptible difference of energy to the total energy of that tone, $\frac{\Delta E}{E}$, while pitch sensibility is the ratio of the least perceptible difference of frequency to the frequency of the tone, $\frac{\Delta N}{N}$. There are considerable discrepancies among the results of previous investigators. The author used as a source of sound a telephone receiver actuated by a current from a vacuum tube oscillator. The intensity or the pitch could be changed periodically, once a second or so, by automatically changing the resistance or capacity in the oscillating circuit. The method of observation, then, was to change $\Delta E$ or $\Delta N$ continuously until the threshold of perception of fluctuation was reached. Separate observations usually checked within 10 per cent. As auxiliary experiments, in which the intensity was varied by changing the distance, showed that the acoustical energy of the source was a linear function of the electrical energy input, the latter was used as a convenient measure of the intensity of the sound. The frequency scale was determined by calibration. While the curves for the ears tested show individual differences, the results are in general the same for all. The intensity sensibility was found to be about 0.10 for moderate and high intensities but to increase to the limiting value 1 as the intensity decreases to the threshold. The curves are very similar to those obtained for the eye, and the modification of the Weber-Fechner law proposed by Nutting for light sensation also fits the results for audition satisfactorily: $\frac{\Delta E}{E}=F+(1-F)\mathrm{}{\left(\frac{E_0}{E}\right)}^n$, where $E_0$ is the threshold intensity and $F$ is about 0.10. The exponent $n$ varies somewhat with the frequency, being 1.65 for 200 d.v. and 1.05 for 1,000 d.v.; nevertheless at the same loudness level, for instance 10,000 $E_0$, $\frac{\Delta E}{E}$ is nearly independent of frequency, showing only a 10 per cent. variation from 100 to 3,200 d.v. The results were the same whether harmonics were present or not. It is concluded that for 1,000 d.v. under favorable circumstances the normal ear can distinguish about 400 gradations of loudness between the threshold and a painful intensity ${10}^{12}$ times as loud. The pitch sensibility, $\frac{\Delta N}{N}$, was found to depend on relative loudness in nearly the same way as $\frac{\Delta E}{E}$. For the same loudness level, $\frac{\Delta N}{N}$ decreased from 0.01 at 50 d.v. to 0.003 at 600 d.v. and then remained constant up to 3,200 d.v. The limit of perception of variation of pitch was about the same or trained as for other ears, but training helped in distinguishing which note was higher. Two ears were found more sensitive than one ear to small differences of pitch but not to small differences of loudness.

• Received 16 June 1922

DOI:https://doi.org/10.1103/PhysRev.21.84