PHYSICAL FACTORS 



253 



500 1000 5000 



FREQUENCY IN CYCLES PER SECOND 



20,000 



Fig. 4 — Loudness difference produced in the right ear when a source of pure tone is 

 moved from the right to the left of an observer. 



Loudness Theory of Localization 

 Upon this assumption the apparent angle of the source as a function 

 of the difference in decibels between the speech levels emitted by the 

 loud speakers of the 2- and 3-channel systems has been calculated. 

 Each loud speaker contributes an amount of direct sound loudness to 

 each ear, depending upon its distance from, and its angular position 

 with respect to, the observer. These contributions were combined on 

 a power basis to give a resultant loudness of direct sound at each ear, 

 from which the difference in loudness between the two ears was deter- 

 mined. The calculated results for the 2- and 3-channel systems are 

 shown by the solid lines in Fig. 5. The y axis shows the apparent 

 angle, positive angle being measured in a clockwise direction. The 

 X axis shows the difference in decibels between the speech levels from 

 the right and left loud speakers. The points are observed values 

 taken from Fig. 1. The observed apparent angles were obtained 

 directly from the average observer's location and the average apparent 

 positions shown in Fig. L The speech levels from each of the loud 

 speakers were calculated for each position on the pick-up stage. This 

 was done by assuming that the waves arriving at the microphone had 

 relative levels inversely proportional to the squares of the distances 

 traversed. By correcting for the angle of incidence and for the known 

 relative gains of the systems, the speech levels from the loud speakers 

 were obtained. 



A comparison of the observed and calculated results seems to indi- 

 cate that the loudness difference at the two ears accounts for the greater 

 part of the apparent angle of the reproduced sounds. If this is true. 



