We theoretically, numerically and experimentally demonstrate the acoustic isolator effect in a one-dimensional waveguide with direction-dependent controlled boundary conditions. A theoretical model is used to explain the principle of nonreciprocal propagation in boundary-controlled waveguides. Numerical simulations are preformed on a reduced model to show the nonreciprocity as well as the passivity of the system through the computation of the scattering matrix and the power delivered by the system. Finally, an experimental implementation validates the potential of programmable boundary conditions for nonreciprocal propagation.