A theoretical study was conducted on a slowing sound propagation structure consisting of discs in a cylindrical waveguide. The diameters of the discs gradually increase while the gaps between them decrease. For a certain law of diameter variation along the axis, it is possible to slow down the speed of sound propagation to zero over the finite length of the structure. Such a structure is called an acoustic black hole (ABH). The pressure field is described by simple power-law dependencies. Based on these dependencies, the acoustic field inside the ABH and the phase of the reflection coefficient from the ABH are analyzed.