A vocal tract model based on a digital waveguide is presented in which the vocal tract has been decomposed into uniform cylindrical segments of variable lengths. We present a model for the real-time numerical solution of the digital waveguide equations in a uniform tube with the temporally varying cross section. In the current work, the uniform cylindrical segments of the vocal tract may have their different lengths, the time taken by the sound wave to propagate through a cylindrical segment in an axial direction may not be an integer multiple of each other. In such a case, the delay in an axial direction is necessarily a fractional delay. For the approximation of fractional-delay filters, Lagrange interpolation is used in the current model. Variable length of the individual segment of the vocal tract enables the model to produce realistic results. These results are validated with accurate benchmark model. The proposed model has been devised to elongate or shorten any arbitrary cylindrical segment by a suitable scaling factor. This model has a single algorithm and there is no need to make section of segments for elongation or shortening of the intermediate segments. The proposed model is about 23% more efficient than the previous model.