No abstract

An empirical formula for calculating the loudness of any steady sound from an analysis of the intensity and frequency of its components is developed in this article. The development is based on fundamental properties of the hearing mechanism in such a way that a scale of loudness values results. In order to determine the form of the function representing this loudness scale and of the other factors entering into the loudness formula, measurements were made of the loudness levels of many sounds, both of pure tones and of complex wave forms. These tests are described and the method of measuring loudness levels is discussed in detail. Definitions are given endeavoring to clarify the terms used and the measurement of the physical quantities which determine the characteristics of a sound wave stimulating the auditory mechanism.

The integration of sensation with respect to time was studied experimentally by means of tones of short duration. Loudness tests were made on sounds persisting from .005 to 0.2 second and covering a wide range of levels. The observed increase in magnitude of a sensation as the duration time is increased is attributed to the properties of nerve conduction in the central nervous system, and an equivalent electrical circuit is derived. The circuit analogy is then used in the computation of loudness as a function of the duration time of the stimulus.

An understanding of the over-all process of hearing depends upon proper interpretation of the results of many individual experiments. In the field of subjective experimentation the problem has been complicated by the wide variety of test procedures that characterize available data. If a common technique could be applied to the many different types of auditory tests, such as thresholds of acuity, masking tests, difference limens, etc., the organization of these data would be facilitated. The purpose of the present paper is to describe a test procedure which has shown promise in this direction and to give descriptions of equipment which have been found helpful in minimizing the variability of the test results. The procedure, which we have called the “ABX” test, is a modification of the method of paired comparisons. An observer is presented with a time sequence of three signals for each judgment he is asked to make. During the first time interval he hears signal A, during the second, signal B, and finally signal X. His task is to indicate whether the sound heard during the X interval was more like that during the A interval or more like that during the B interval. For a threshold test, the A interval is quiet, the B interval is signal, and the X interval is either quiet or signal. For a masking test, A is the masking signal, B is the masking signal plus the signal being masked, and X is either A or B repeated. The apparatus for the ABX test is mechanized so all details of the method can be duplicated for each observer, and the variability of manual operation eliminated. The entire test is coded on teletype tape to reduce the time and effort of collecting large quantities of data.

The unexplained difference in sound pressure in the ear canal which appears to exist when equally loud low frequency tones are presented alternately from an earphone and from a loudspeaker has bedeviled acousticians for many years and, unfortunately, still continues to do so. There are presented here the results of some of the measurements carried out at the Bell Telephone Laboratories which show the magnitude of the effect and various attempts at explaining it. While no satisfactory explanation has been found, it is hoped that publication of these results will stimulate interest in the problem.