Attenuating resonance modes in the cylindrical waveguide, placed in an elastic medium

The interference attenuating waves propagating in the cylindrical elastic waveguide, placed in an elastic medium are considered. The group velocity of waves is intermediate between that of $P$-wave and that of $S$-wave, the phase velocity equal that $P$-wave. The frequency of wave is almost constant and determined by a requirement of the constructive inerference. The dispersion and attenuation of these waves are described.