Transfer matrix of conical waveguides with any geometric parameters for increased precision in computer modeling

The existing formula for the transfer matrix of conical elements assumes constant wave number, which is only valid for sufficiently short conical elements. In acoustic waveguides, the phase velocity, attenuation constant, and hence complex wave number depend on frequency and cross-section radius. As for conical waveguides, the cross-section radius is position dependent, the transfer matrix must allow for a position-dependent wave number. Taking this into account, this letter presents an analytic derivation of the transfer matrix for conical waveguides with any geometric parameters, which can be utilized to improve the method of computer modeling of complex waveguides.