In the numerical computation of hyperbolic equations it is not practical to use infinite domains. Instead, one truncates the domain with an artificial boundary. In this study we construct a sequence of radiating boundary conditions for wave‐like equations. We prove that as the artificial boundary is moved to infinity the solution approaches the solution of the infinite domain as O(r−m−1/2) for the m‐th boundary condition. Numerical experiments with problems in jet acoustics verify the practical nature and utility of the boundary conditions.