An experimental study of the open end correction coefficient for side branches within an acoustic tube

The open end correction coefficient (OECC) of acoustic tubes has been widely investigated under a free-field condition. This study examines OECCs in confined regions, such as side branches within the vocal tract. To do this, a number of mechanical acoustic models are used to examine the effects of the angle of the branch axis and the proximity of the walls of the main tract to the open end of the branch. The OECC is estimated by matching both the peaks and troughs (i.e., spectral maxima and minima) of the computed and measured transfer functions for each model. The results indicate that the OECC of a side branch depends on L/D, where L is the cross dimension of the main tract at the branching point, and D is the branch diameter. For side branches connected to the main tract through a narrow neck, the OECC of each end of the neck is determined using the ratio of the radius of the neck to that of the adjacent section. Two empirical equations for evaluating the OECC within a tract are derived from the present study. Finally, the range of appropriate OECC values for estimating an accurate vocal tract transfer function is discussed, based on the results presented here and morphologic measurements reported previously.