Uniform approximations for the combined permanent and transient start-up waves produced by the impulsive motion of a body in a density-stratified fluid are calculated. These new approximations to the wave field remove the unphysically diverging fluid velocities and phase shifts near the boundary of the causality envelope associated with previous non-uniform approximations. The calculated wave field is compared to experimental measurements of the wave field generated by towing a spherical body through a linearly stratified fluid. Synthetic schlieren, a technique previously used only to analyse two-dimensional or axisymmetric flow, is developed further to allow comparison with this fully three-dimensional wave field. In particular, breadth averaging across the tank is employed. Good agreement is found between the theoretical and experimental results in the far field.