Recent experiments reveals how dynamic fracture is characterized by the interplay of crack front with microscopic material heterogeneities. Heterogeneous dynamic fracture remains a current challenge both for numerical modeling and experiments because of the associated fine time and length scales. In this work, we rely on a spectral boundary integral formulation of the elastodynamic wave equations. The numerical discretization focuses along the interface bounding two semi-infinite body and allows a very fine description of the fracture process which is modeled following a cohesive approach. This work study the perturbation of dynamic crack front in presence of a tougher inclusion along the rupture plane. We show numerically how shock waves are radiated from cusp emerging after large distortion of the crack front. We detail how these short-lived bursts persist far from the heterogeneity site and impact the overall rupture dynamics. Since any material presents heterogeneities at a certain scale, we further investigate how the heterogeneous interface properties (heterogeneity size, toughness contrast, crack speed) control the transition from quasi-homogeneous to heterogeneous dynamics. We finally measure the size of the fracture process zone and discuss the role of this critical length scale for heterogeneous dynamic fracture.