SOLID TORSIONAL HORNS
HARVARD UNIV CAMBRIDGE MA ACOUSTICS RESEARCH LAB
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The propagation of torsional waves in tapered solid elastic rods has been studied both theoretically and experimentally from the viewpoint of acoustic horn theory. Such tapered rods in torsional vibration have been dubbed torsional horns. Two differential equations are derived which describe the propagation of torsional waves. For purposes of analysis, torsional horns are divided into three categories those having smooth contours fitting separable coordinates, those having smooth contours not fitting separable coordinates, and those having piecewise-smooth contours. Experimental apparatus was devised and built for the measurement of the standing-wave patterns and resonance frequencies of experimental torsional horns made of brass or mild steel. The experimental data are compared with the solutions of the two wave equations for selected horn contours from each category. A quantitative estimate of the error introduced by the plane-wave approximation is obtained for the exponential horn.