Concatenated Acoustic Tube Model of the Vocal Tract

The first step towards a digital model is in representing the tube as a series of $N$ concatenated tubes of constant cross-sectional areas, as in Figure 1.1(b) (where $N$=8). The tubes are assumed to be of equal length $\Delta$; if $L$ is the total length of the vocal tract, we have $N\Delta = L$. In the limit as $\Delta$ becomes small, the shape of the approximation of the series of tubes will converge to that of continuous vocal tract shown in Figure 1.1(a).

Figure 1.1: (a) The vocal tract, modeled as a single one-dimensional acoustic tube of varying cross-sectional area and (b) an eight tube model suitable for discretization.