170 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 32 



may accordingly be defined as the intensity in decibels above the 

 threshold of audibility of that frequency. 



On this basis experiment shows that for pure sounds of medium 

 frequency the range of audibility between the thresholds of hearing 

 and feeling is covered by about 130 decibels. This figure is rather 

 less for high and low frequencies. 



The position, however, is not so straightforward when we come to 

 the broader question of comparing the loudness of pure sounds of 

 different frequencies. We find at once that there is no simple rela- 

 tion of wide application between physical intensity and loudness. 

 Two pure sounds of different frequencies do not in general pro- 

 duce the same loudness sensation, even if (a) their phj^sical inten- 

 sities are equal, or (b) their physical intensities bear the same ratio to 

 their respective threshold values, i. e., if the sounds have equal sensa- 

 tion levels. Further, if the intensity levels of two pure sounds of 

 different frequencies which appear equally loud are increased by the 

 same amount, the sounds will not in general remain equally loud. 



It follows that in the case of sounds of different or mixed fre- 

 quencies neither the physical intensity level nor the sensation level 

 can be used as a measure of loudness. In the circumstances we 

 have to adopt an arbitrary scale as a practical standard, and a suit- 

 able one for the purpose is the sensation scale of a pure note having 

 a frequency in the region of 1,000 cycles per second. Then the loud- 

 ness of any sound, whether pure or a mixture such as noise, is de- 

 fined as the sensation level (expressed in decibels above the threshold 

 value) of the standard note which appears equally loud to the ear. 

 It may be mentioned that zero or threshold value of a 1,000-cycle 

 scale corresponds to a pressure of about a millidyne per square 

 centimeter. 



It should be reiterated that such a standard scale is quite arbi- 

 trary and that equal increments on the scale do not in general ap- 

 proximate very closely to an equal number of sensation steps. For 

 instance, in the case of the 1,000-cycle scale, the step from to 10 

 decibels corresponds roughly to about 1 i^erceptible gradation of 

 loudness under average conditions, the step from 50 to GO contains 

 about 10 gradations, and the step from 100 to 110 about 15. In other 

 words, we may ascend the range of physical intensity lying between 

 the two thresholds either by the decibel ladder, with equally spaced 

 rungs, or by the sensation-step ladder, with rungs first widely spaced 

 and afterwards more narrowly, though more evenly, spaced (fig. 3). 



It may be added that, in adopting a practical scale of loudness, 

 some latitude is possible in the choice of the standard frequency, 

 in view of the fact that for medium frequencies above 700 cycles 

 per second there is a constant relation between loudness and sensa- 



