The number of jet and rocket noise studies has increased in recent years as researchers have sought to better understand aeroacoustic source and radiation characteristics using predominantly linear reconstruction techniques. While jet and rocket noise is often finite-amplitude in nature, little is known about the existence of shock formation and coalescence close to the source. A numerical experiment determines that significant shock coalescence can occur when finiteamplitude noise is propagated over short distances at amplitudes similar to those expected of jet and rocket noise. Additionally, the errors associated with using linear reconstruction techniques are shown to be large when significant shock coalescence occurs. The results of this experiment point out the need for additional studies targeting shock coalescence and its possible role in near field jet and rocket noise propagation.