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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.

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The intelligibility of the speech received over a communication system is usually expressed in terms of one or another measure such as the vowel or the consonant articulation, the average speech sound articulation, the syllable articulation,' the word articulation, or the sentence intelligibility. The present paper establishes relationships among several of these measures and the articulation index. Relationships based upon statistical considerations are compared with the results of observations. Functions are developed which permit the calculation of articulation index and hence of articulation for communication systems which include a wide variety of response versus frequency characteristics and of noise conditions, as well as several special types of distortion. Although the treatment is predominantly empirical, the functions and processes are closely related to various fundamental properties of speech and hearing. Four principal series of articulation tests are cited in detail, some of which have been described in published articles by various persons. The response and the noise, if any, are given for each of these cases and the observed articulations are compared with values calculated by the method here presented.The application of •:he computational method to the perception of speech by deafened persons is reserved for a subsequent paper.

This paper deals with the normal modes of vibration of a stiff piano string. The equations that govern the vibration of a solid string are developed along traditional lines. They are modified to apply to strings having a solid-steel core upon which are wrapped one or two copper windings. The bass strings of most pianos are made this way. Two boundary conditions are considered: namely, (1) pinned by sharp knife edges at both ends and (2) clamped at both ends. Formulas for the partial frequencies for both of these conditions are developed. The partial frequencies that are calculated by these formulas are compared to the experimental values obtained on an upright Hamilton piano. The experimental values appear to agree somewhat better with the pinned boundary condition rather than the clamped boundary condition, although the differences are not much greater than the observational error. It was found that the formula fn = nf1[(1 plus; Bn2)/(1 + B)]12 gives values of the partial frequencies that agree with the experimental ones where n is the number of the partial, f the fundamental frequency, and B a constant that can be calculated from the dimensions of the wire.