382 BELL SYSTEM TECHNICAL JOURNAL 



observers the electrical power W\ in the receivers which produces the 

 same loudness as a level /3i of the reference tone. The intensity level 

 ^T of an open air reference tone equivalent to that produced in the 

 receiver for any other power Wr in the receivers is then given by 



/3. = |3i + 10 log {WrIW,). (5) 



Or, since the intensity level ^r of the reference tone is its loudness 

 level L, we have 



L = 10 log Wr + Cr, (6) 



where Cr is a constant of the receivers. 



In determining loudness levels by comparison with a reference tone 

 there are two general classes of sound for which measurements are 

 desired: (1) those which are steady, such as a musical tone, or the hum 

 from machinery, (2) those which are varying in loudness such as the 

 noise from the street, conversational speech, music, etc. In this 

 paper we have confined our discussion to sources which are steady and 

 the method of specifying such sources will now be given. 



A steady sound can be represented by a finite number of pure tones 

 called components. Since changes in phase produce only second order 

 effects upon the loudness level it is only necessary to specify the 

 magnitude and frequency of the components.^ The magnitudes of 

 the components at the listening position where the loudness level is 

 desired are given by the intensity levels /3i, 182, • * • jSa-, • * • jS^ of each 

 component at that position. In case the sound is conducted to the 

 ears by telephone receivers or tubes, then a value Wk for each com- 

 ponent must be known such that if this component were acting 

 separately it would produce the same loudness for typical observers as 

 a tone of the same pitch coming from a source at one meter's distance 

 and producing an intensity level of ^k- 



In addition to the frequency and magnitude of the components of 

 a sound it is necessary to know the position and orientation of the head 

 with respect to the source, and also whether one or two ears are used 

 in listening. The monaural type of listening is important in telephone 

 use and the binaural type when listening directly to a sound source in 

 air. Unless otherwise stated, the discussion and data which follow 

 apply to the condition where the listener faces the source and uses 

 both ears, or uses head telephone receivers which produce an equivalent 

 result. 



^ Recent work by Chapin and Firestone indicates that at very high levels these 

 second order effects become large and cannot be neglected. K. E. Chapin and F. A. 

 Firestone, "Interference of Subjective Harmonics," Jour. Acous. Soc. Am. 4, \76A 

 (1933). 



