The diffraction of elastic waves by a crack tip is investigated for the case that cohesive tractions on the crack faces in the immediate vicinity of the crack tip have not been completely released. In this paper it is assumed that such residual cohesive tractions are proportional to the local crack-opening displacement. This assumption is equivalent to a spring-constrained near-tip zone. The crack is subjected to normal incidence of a longitudinal wave. For the time interval before signals from the other crack tip arrive, approximate expressions have been obtained for the spring tractions and the elastodynamic scattering field. The results are valid for the case of small range of constraints and small spring constant. In this approximation, the spring tractions are reduced to a separable form of a time dependence multiplied by a space dependence. The space dependence is found first. The time dependence is then expressed in a form of perturbation series for small in terms of powers of, where is the nondimensional spring constant. The leading order term result is then obtained.