The weakening of one-dimensional transverse viscous waves, their phase velocities, the spatial and frequency dispersion in free space by analytical and numerical methods were researched. The dispersion of the phase velocity in a cylindrical wave in a free half-space is negative. The gradient of the phase velocity is greater when the source wave size is less. With the increase in its size dispersion vanishes in the limit and the phase velocity approaches the value of the plane wave phase velocity. The weakening both flat and cylindrical viscous waves in a gap, the magnitude of their phase velocities, the dispersion laws depend on the wave width of a gap and on the boundary conditions on the source opposite the wall.
43.20.-f General linear acoustics
43.35.Mr Acoustics of viscoelastic materials
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