Investigation of the properties of viscous 1D plane and cylindrical waves in problems with various boundary conditions

Phase velocities and attenuation of viscous plane and cylindrical waves in free space and in gaps are investigated analytically and numerically under various boundary conditions. It is shown that boundary conditions in a gap determine the nature of spatial dispersion of a viscous wave. The influence of finite dimensions of the source and the size of the gap on the phase velocity gradient and on viscous wave attenuation is analyzed. The viscous waves being investigated are generated during operation of acoustic oscillating transducers in small volumes of viscous incompressible liquids used for technological purpose.