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Fig. 1. High frequencies pass by an observer's far ear. Low frequencies readily curve around the cranial obstruction to the far ear.
The average human-ear phase-sensitivity range is from some very low frequency up to approximately 800 to 1000 cycles/sec, which thus allows a perception of directivity by binaural phase comparison over this range. The amplitude sensitivity range of the individual ear is from the lowest frequency perception point up to the highest frequency perception limit within the dynamic volume range of the ear. This dynamic volume range is defined by the standard Fletcher-Munson hearing curves modified by the room masking noise level.1
By simple amplitude comparison a mental computation of directivity may be obtained, except as limited by the physics of sound propagation. This means that due to the lack of directivity of low-frequency sounds below, say, 800 to 1000 cycles, the ear's amplitudedetection ability is of no avail, since a
low-frequency sound wave curves around the head without appreciable amplitude loss. Therefore, the amplitude-derived directional sensitivity of the binaural ear arrangement falls off rapidly. This is exemplified by the fact that a 1000cycle/sec tone directed toward a listener from one side of his head produces only a 3-db level difference at his far ear compared with the near ear; a 10,000cycle/sec tone under the same conditions produces a 30-db level difference (Fig. 1).
It may be shown that the portion of normal auditory perspective due to phase sensitivity is related to the lineal distance between the human ears. Let us assume that a theoretical observer has a between-the-ears distance of, say, 6.78 in. Under certain environmental conditions the speed of sound in air is, say, 1130 ft/sec. The maximum frequency, /, that the ears may compare
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August 1952 Journal of the SMPTE Vol. 59