MEASUREMENT OP NOISE KAYE 167 



the dotted portions being those which are difficult to determine. We 

 see that the range of audibihty passes through a maximum (at about 

 1,000 cycles per second) as the frequency is varied, and is greatly 

 reduced toward each end of the musical scale. This maximum range 

 corresponds to about a million millionfold variation in power, or a 

 millionfold variation of acoustical pressure from about, say, 0.0005 

 to 3,000 dynes per square centimeter. We note also in the case of 

 very high and very low notes the great intensity that is essential for 

 audibility and how restricted the range of audibility is. A familiar 

 illustration is the sound from a 32-foot organ pipe which one feels 

 rather than hears. 



As will presently appear, the matching and masking of sounds 

 form the basis respectively of two aural methods of measuring the 

 loudness of noise ; and it will be of interest, therefore, to examine the 

 basic physical facts of each method. 



THE MATCHING OF SOUNDS 



As regards the matching of sounds, it is found that the average 

 ear can recognize under very favorable conditions a 10 per cent ^ 

 difference of energy when two pure notes of medium loudness are 

 sounded alternately without break. Under ordinary conditions, 

 however, the smallest average change in energy level detectable by 

 the normal ear is of the order of 26 per cent for sounds of medium 

 intensity and frequency. The figure is greater for feeble sounds 

 and less for very loud sounds. The value is also greater for very 

 high or low frequencies than for the roiddle of the range. 



From the fact that it is a percentage increase rather than an 

 additive increase of energy which the ear associates with a change 

 of loudness, it is evident that, while the steps in the scale of sensation 

 of loudness advance arithmetically, the physical intensities advance 

 geometrically, the relation thus resembling the logarithmic scale of 

 powers of a slide rule. Here is, then, another illustration of the 

 Weber-Fechner law — the physiological effect is roughly proportional 

 to the logarithm of the energy producing the stimulus. 



Kingsbury (Fletcher's Speech and Hearing, p. 230) has carried 

 out experiments on the matching of pure tones to determine the 

 relation between the physical intensity and the aural loudness for 

 different frequencies. These experiments indicated that for fre- 

 quencies between about 700 and 4,000 cycles per second, the relation 

 between loudness and intensity is independent of the frequency. For 

 notes of lower frequency the loudness increases proportionately more 



''This figure is more than doubled if there is an interval of silence between the two 

 notes of as little as half a second. 



