Propagation of acoustic wave along a hollow cylinder immersed in a liquid

The problem of the propagation of an nonabsorbed, continuous, progressive and axially-symmetric acoustic wave along an infinite homogeneous and isotropic cylinder filled with air and immersed in an ideal liquid has been considered. The wave equations of displacement potentials have been solved. The characteristic equation has been derived for the preset boundary conditions and solved numerically for the selected data characteristic for the conditions of the biopsy performed in an ultrasonic field. It has been shown that a wave guided along a needle immersed in a liquid can propagate with the velocity only slightly smaller than the wave velocity of the surrounding liquid. The distributions of displacement, stresses and acoustic pressure of the propagating wave have been determined.