The upper frequency limit for the binaural localization of a pure tone by phase difference

It is well known that if a pure tone is presented binaurally so that its intensity is the same in each ear, and there is no phase difference between the notes at the ears, the resulting sensation is that of a source of sound located in the median plane and situated is that of a source of sound located in the median plane and situated either within the skull or outside it. If a difference of phase between the notes is gradually introduced without altering their intensities, and the frequency of the tone is, say, 800 cyc. /sec., then the source appears to move laterally towards the side of the ear in which the phase is made to lead. According to some observers, the movement is on a horizontal circular arc centred between the ears, while others consider it to be along a line joining the ears. There is general agreement among workers on localization that considerable difficulty exists in the detection of such movements at frequencies above 800 cyc. /sec., and that their extent is more limited, but they disagree as to the frequency above which the lateral motion ceases to be noted. Stewart (1920) obtained movement at 1280 cyc. /sec., but not 1536 cyc. /sec.; Banister (1925) found movements at 1040 and 1345 cyc. /sec., but anomalous in character. On the other hand, von Hornbostel and Wertheimer (1920) state that at about 800 cyc. /sec., the lateral movement no longer extends 90° left and right, but decreases as the frequency increases, and should reach zero at 17,000 cyc. /sec. Halverson (1927) found that observable right and left effects appear to be present up to the upper auditory limit. Below 1400 cyc. /sec. judgments of direction are fairly consistent, between 1400 and 3000 cyc. /sec. there is no particular difficulty if allowance is made for the more rapid onset of fatigue at these frequencies. Above 3000 cyc. /sec. lateral effects are still observable, though median localization is extremely difficult to achieve. Hartley (1919) gave theoretical curves showing the phase difference produced at the ears by sources of various frequencies at different distances from the head. According to these, above 650 cyc. /sec. the maximum movement of the apparent source would be less than 90°, though at 1860 cyc. /sec. there should still be about 27° of movement on either side of the median plane. These curves have been checked experimentally by Firestone (1930), who found for three frequencies the phase difference and amplitude ratio of the sounds entering the ears of a man-shaped wax dummy from a source at varying azimuths around the head and at different distances from it. The phase differences found were in good agreement with the values calculated by Hartley. Various methods have been used to present the notes to the ears and to vary the phase difference between them. In the experiments of Halverson the sounds were produced by a tuning fork and led to the ears through tubes, in one of which was incorporated a sliding section to vary its length and thus the phase difference at the ears. An objection to this is the possibility of resonances in the tubes, different on both sides on account of their different lengths, so that intensity changes might occur as well as changes oh phase. Stewart, and Banister, used notes generated electrically and presented to the ears by telephones. Continuous phase changes could be made with their generators, but the purity of the resulting notes was doubtful.