The input admittanceY(x) of a conical bore is more simply stated than its input impedance. For a conic section truncated at x=x0, the input admittance is
where the pressure wave reflectance C-/C+ is determined by the length of the bore and the boundary conditions at the opposite end, as discussed above.
Equation (13) applies equally well to bores of increasing and decreasing diameter by using either positive or negative values of x.
Equation (13) may be interpreted as a parallel combination of an acoustic inertance and a term reminiscent of the impedance of a cylindrical waveguide (Benade, 1988).
The impedance of the acoustic inertance, which has an equivalent acoustic mass
approaches infinity as
The input admittance seen from the open end (at x=-L) of a complete cone reduces to
where the pressure reflectance at the cone apex (x=0) is negative one.
An open end at x = -L can be approximated by the low-frequency estimate
The resonance frequencies of a complete cone ideally open at its large end are thus found at the infinities of Eq. (14), which are given for
The complete cone with open mouth has a fundamental wavelength equal to two times its length and higher resonances that occur at all integer multiples of the fundamental frequency, as was observed for open-open cylindrical pipes.
The anti-resonances of the complete cone, however, do not fall exactly midway between its resonances, but are influenced by the inertance term in Eq. (14).