RESUMO
A progressive spherical or spheroidal wavefront approximation has previously been found to be a necessary step for a more accurate application of Webster's wave equation to rapidly flaring horns. This leads to a necessary transformation of the horn area function, from the usual flat cross-sectional area in terms of the axial coordinate, into a curved cap-like wavefront area as a function of either the axial coordinate, the arc-length coordinate along the horn profile, the leading curved wavefront coordinate, or still other possible longitudinal coordinates. In this article, horn functions, and related frequency potential functions are calculated from the measured horn profiles of a trombone and a trumpet for several of the above parameterizations. From them, cutoff frequencies and effective lengths are determined. A comparison is drawn between theoretical results using different parameterizations, results calculated via transfer-matrix models, and experimental measurements of the acoustical input impedance and reflection function of both instruments. Results indicate that one-dimensional models accurately predict the effective lengths, and consequently the fundamental resonance frequency of the instruments within ±25 cents, but fail noticeably in predicting cutoff frequencies, leading to what is probably an inaccurate representation of perceived timbre.
RESUMO
Current techniques for measuring normal incidence sound transmission loss with a modified impedance tube, or transmission tube, require setting up two different absorbing termination loads at the end of the downstream tube [ASTM E2611-09, Standard Test Method for Measurement of Normal Incidence Sound Transmission of Acoustical Materials Based on the Transfer Matrix Method (American Society for Testing and Materials, West Conshohocken, 2009)]. The process of physically handling the two required passive absorbing loads is a possible source of measurement errors, which are mainly due to changes in sample test position, or in test setup re-assembly, between measurements. In this paper, a modified transmission tube apparatus is proposed for non-intrusively changing the downstream acoustic load by means of a combined passive-active termination. It provides a controlled variable sound absorption which simplifies the setup of standard two-load techniques, without the need of physically handling the apparatus during the tests. This virtually eliminates the risk of errors associated with the physical manipulation of the two passive terminations. Transmission loss measurements in some representative test conditions are reported, showing improvements over current implementations, in reducing by approximately 50% the measurement variations associated with the setup of the two required absorbing terminations. Measurement results agree within 0.4 dB (maximum difference in high resolution broadband), and 0.04 dB (mean difference in 1/3-octave bands), with those obtained using standard passive two-load methods.