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THE MINIMUM AUDIBLE INTENSITY OF SOUND. 



By Clifford M. Swan. 



Received January 2, 1923. Presented by Theodore Lyman. 



The absolute energy value at the threshold of audibility has en- 

 gaged the attention of experimenters for a number of years. It is of 

 interest in the domain of experimental psychology, and of late has 

 figured in researches in telephone engineering. It is also of importance 

 in the work of architectural acoustics, since the laws governing reverber- 

 ation as laid down by W. C. Sabine l make use of the minimum 

 audible sound as the unit of intensity. Previous researches having 

 shown wide discrepancies and uncertainties in results, the investiga- 

 tion here reported was undertaken several years ago to establish more 

 reliable values if possible. The author is indebted to the late Professor 

 Sabine for his assistance in making check observations in all of the 

 determinations. 



Previous Work. 



In reviewing previous work in this field, we find that the first 

 quantitative determination was made by Toepler & Boltzmann 2 in 

 1870. The variation in density at the node at the end of a closed 

 organ pipe, blown at constant pressure, was measured by an optical 

 interference method, with a stroboscopic device to slow down the 

 rapidly shifting interference pattern and render it visible to the eye. 

 The amplitude of vibration at any distance outside the pipe was de- 

 duced theoretically in terms of the density variation within, and the 

 distance measured to the point at which the sound became inaudible. 

 No attempt was made to reach an exact result, the experiment being 

 supplementary to another piece of work, and made only to determine 

 the order of magnitude of the quantity sought. 



In 1877, Rayleigh 3 attempted to solve the problem from the 

 theoretical amount of energy consumed and the distance at which the 

 sound became inaudible when a whistle of high pitch was blown at 

 constant pressure. 



1 Contributions, Jeff. Phys. Lab., Harvard Univ., 1906, Vol. 4, pp. 1-74. 

 Also, Collected Papers on Acoustics, W. C. Sabine, Harvard Univ. Press, 1922. 



2 Pogg. Ann., 1870, Vol. 141, p. 349. 



3 Proc. Roy. Soc, 1877, Vol. 26, p. 248. 



