218 Lord Ravleiob on out 



© 



of intensities on the two sides of a sphere of 2 feet circum- 

 ference only about 2 parts per thousand. 



Observation in the open air showed that there was no 

 difficulty whatever in deciding whether this low sound was 

 on the right or the left. Several observers agreed that 

 the discrimination was quite as easy as in the case of forks of 

 pitch 128. On the other hand, as was to be expected, the 

 front and back situations could not be discriminated. 



At this stage a reconsideration of theoretical possibilities 

 seemed called for. There could be no doubt but that relative 

 intensities at the two ears play an important part in the locali- 

 zation of sound. Thus if a fork of whatever pitch be held 

 close to one ear, it is heard much the louder by that ear, and 

 is at once referred instinctively to that side of the head. It 

 is impossible to doubt that this is a question of relative 

 intensities. On the other hand, as we have seen, there are 

 cases where this explanation breaks down. When a pure 

 tone of low pitch is recognized as being on the right or the 

 left, the only alternative to the intensity theory is to suppose 

 that the judgement is founded upon the difference of phases 

 at the two ears. But even if we admit, as for many years * 

 I have been rather reluctant to do, that this difference of 

 phase can be taken into account, we must, I think, limit our 

 explanation upon these lines to the cases of not very high 

 pitch. For what is the difference of phase at the two ears 

 wh^n a sound reaches the observer — say from the right? It 

 is easy to see that the retardation of distance at the left ear 

 is of the order of the semi-circumference of the head, say 

 one foot. At this rate the retardation for middle c (c / = 256) 

 is nearly one quarter of a period ; for c" (512) nearly half a 

 period ; for c'" (1024) nearly a whole period, and so on. Now 

 it is certain that a phase-retardation of half a period affords 

 no material for a decision that the source is on the right 

 rather than on the left, seeing that there is no difference 

 between a retardation and an acceleration of half a period. 

 It is even more evident that a retardation of a whole period, 

 or of any number of whole periods, would be of no avail. In 

 the region of somewhat high pitch a judgement dependent 

 upon phase would seem to be hardly possible, especially when 

 we reflect that the phase-differences enter by degrees, rising 

 from zero when a sound is directly in front or behind to 

 a maximum or minimum in the extreme right and left 

 positions. 



As to whether there is any difficulty in localizing to the 

 rioht or left a tone of pitch 512, an early observation, 

 * Conf. ' Theory of Sound/ § 385. 



