PHYSICAL MEASUREMENTS OE AUDITION 153 



greater cooperation in the future between men in the various branches 

 of science working on this subject, so, in order to avoid misunder- 

 standing, it would be very advantageous for all to use, as far as pos- 

 sible, the same units. With this in mind, I am taking the liberty 

 of suggesting for discussion units for both loudness and pitch. 



In the telephone business, the commodity being delivered to the 

 customers is reproduced speech. One of the most important qualities 

 of this speech is its loudness, so it is very reasonable to use a sensa- 

 tion scale to defin/i the volume of the speech delivered. At the present 

 time, an endeavor is being made to obtain an agreement of all the 

 telephone companies, both in the United States and abroad, to adopt 

 a standard logarithmic unit for defining the efficiency of telephone 

 circuits and the electrical speech levels at various points along the 

 transmission lines. The chief interest in changes in efficiency of trans- 

 mission apparatus is their effects upon the loudness of the speech 

 delivered by the receiver at the end of the telephone circuit. So it 

 would be very advantageous to use this same logarithmic scale for 

 measuring differences in loudness. 



This scale is chosen so that the loudness difference is ten times 

 the common logarithm of the intensity ratio. This means that if the 

 intensity is multiplied by a factor 10, the loudness is increased by 

 ten; if the intensity is multiplied by 100, the loudness is increased by 

 20; if the intensity is multiplied by 1,000, the loudness is increased 

 by 30, etc. It was seen above that under the most favorable cir- 

 cumstances a change in loudness equal to 1/2 on this scale could 

 just be detected. Knudsen's data indicate, however, that when a 

 silent interval of only two seconds intervenes between the two tones 

 being compared, a loudness change greater than unity on this scale 

 is required before it is noticeable. So the smallest loudness change 

 that is ordinarily appreciated is equivalent to one unit on this scale. 

 It is also convenient because of the decimal relation between loudness 

 change and intensity ratio. This relation is expressed by the formula : 



IT al 



AL=L 1 -L 2 = 10 1og 1 oy 1 or^=10 10 



J 2 -12 



where L\ and L 2 are the two loudness values corresponding to the 

 intensities I x and 7 2 - Since intensities of sound are proportional to 

 the square of pressure amplitudes this may also be written : 



AL = 20 1og^ 



The most convenient choice of the intensity or pressure used as a 

 standard for comparison depends upon the problem under consider- 



