Obliquely Truncated Simple Horns: Idealized Models for Vertebrate Pinnae

Abstract

The acoustical behaV:iour of simple horns of parabolic, conical and exponential profile is analyzed and explicit expressions are given for the impedance coefficients Zii. Wavefront curvature effects are included and the discussion is extended to investigate the effect of oblique truncation, which gives the horn a shape closely similar to that of a typical vertebrate pinna. The effects of higher modes.are discussed qualitatively and the conditions under which these can be neglected are outlined. All horns are shown to act as efficient pressure transformers over only a restricted bandwidth, the limits of which are determined by flare rate and mouth diameter. For a horn with throat area S1 and mouth area S2 the maximum blocked-throat pressure gain is 10log10 (4 S2/S1) decibels; the gain reduces to 0 dB _at low frequencies and may become negative at very high frequencies. Oblique truncation raises the maximum gain above that of a horn truncated normally with the same minimum throat-to-mouth distance. It also moves the axis of maximum acoustic response away from the geometric axis of the horn towards the normal to the oblique mouth. This shift is large at low frequencies, becomes slightly nega;pefe at mid frequencies, and approaches zero at high frequencies. Use of these results .in the analysis of model auditory systems is outlined.