When is it appropriate to use zero normal stress boundary conditions when solving the acoustic wave equation. That is when the pressure is equal to zero.
Strictly speaking: never. Outside the idealized models there are always at least a bit of radiation impedance so the pressure on the boundary is not truly zero.
But let's focus on idealized models. Usually the zero pressure boundary condition is used for open ends of the waveguides or for the free surfaces of solid bodies.
Typical illustrative example would be the loose end of the string: there is nothing (e.g. no bridge) which can provide a support for string stretching. Therefore the tension (analogy of pressure) must be zero and all the energy goes into displacement.