Both direct-drive and indirect-drive inertial confinement fusion targets use temporally shaped drive pulses to optimize the target performance. The timing of multiple shock waves is crucial to the performance of inertial confinement fusion ignition targets. This paper reports an experimental study on the shock wave characteristics of laser-irradiated targets. The shock wave velocity profiles are measured using the velocity interferometer system for any reflector (VISAR). Presented are measurements of velocities from shock waves in quartz targets driven by single 120 ps pulse, two 120 ps pulses separated by 1.1 ns and a special shaped pulse. These pulses drive two shock waves that coalesce in the target, and the coalescence times and transit times are observed by VISAR.