The behavior of hydromagnetic waves in a cylindrical resonator of arbitrary cross section is examined. The conducting fluid inside the resonator is permeated with a steady uniform magnetic field parallel to the generators of the cylinder. The equation describing the eigenfrequency spectrum is derived for all possible modes and types of waves. It is shown that a TLA (transverse longitudinal acoustic) type wave when reflected from a rigid conducting termination generates an accompanying TLM (transverse longitudinal magnetohydrodynamic) type wave and vice versa. Energy losses due to the finite viscosity and electrical conductivity of the fluid as well as to the finite conductivity of the walls are then estimated for the case of T (purely transverse) type waves. AQfactor for T type waves is subsequently calculated.