The linear stability of a hypersonic boundary-layer is investigated for an almost sharp flared cone at Mach 6. Towards this end, a short-duration pulse through a small hole on the surface of the cone is utilized to excite a broad spectrum of frequencies and streamwise wave numbers in an axisymmetric domain. The flow conditions chosen are from the low- enthalpy experiments performed at the Boeing/AFOSR Mach-6 Quiet Tunnel (BAM6QT) at Purdue University.1-3 In the present work, the newly developed version of the Linearized Compressible Navier-Stokes solver (LinCS)4-6 using generalized cylindrical coordinates is introduced. The derivation of the linearized equations is presented along with results which were generated using the Linearized Compressible Navier-Stokes solver (LinCS) and Direct Numerical Simulations (DNS) for the aforementioned conditions. This new version of LinCS was verified for the linear regime with the Parabolized Stability Equations (PSE) results presented in the literature2 and our low amplitude DNS calculations. In addition, our previous DNS results6 for a 5 deg straight cone in a high-enthalpy flow indicated that, in the linear regime, oscillations in the phase speed, growth rate, wave number and N- factor are observed as amplified second mode wave components synchronize with different boundary layer modes(i.e. entropy/vorticity and acoustic modes)7. Also, such oscillations cease before an amplified wave component slows down to the same phase speed as the vorticity/entropy waves. Our present simulations show that a similar phenomenon is also present in the case of a low-enthalpy flow on a flared cone.