Propagation of axially symmetric elastic vibrations along a waveguide in an elastic medium

The scatter equation is derived for axially symmetric (longitudinal and torsional) normal vibrations of an infinitely long elastic cylindrical waveguide embedded in an elastic medium. The low-frequency vibrations are analyzed thoroughly. It is shown that low-frequency longitudinal vibrations follow either of two branches of the scatter curve. Recommendations are made concerning the use of waveguide methods for studying the physicomechanical properties of polymers.