In two‐dimensional linear acoustic theory Huygens' principle fails; the failure of Huygens' principle being manifested by the existence of a tail to the acoustic pulse. A two‐dimensional problem of importance is the radiation of acoustic pulses of various shapes by an infinitely long circular cylinder. The problem is attacked directly via the use of the Laplace transform. In the inversion of the Laplace transform, relatively new function called the NielsenW0function is encountered. Exponential, sine, and rectangular pulses are studied and their shape determined at various distances from the cylinder. Finally the passage to the steady state of a semi infinite sine wave train is outlined.