The radiation‐loading distribution over a large, rigid, circular piston embodies fluctuations associated with Freznel zone interference patterns. These fluctuations do not vanish as thekaof the piston tends to infinity, thus leading to the paradoxical conclusion that an infinite, rigid, plane piston does not radiate plane waves. It is shown that plane‐wave radiation and a uniform, ρcimpedance can be predicted by accounting for the transients occurring at the beginning of a CW pulse. These transients produce a ρcimpedance in regions of the piston not yet reached by a diffraction wave that starts from the piston edge at the beginning of the pulse. By allowing the piston diameter and, hence, the envelopment time to become arbitrarily large, the plane‐wave radiation loading prevails over an arbitrarily large region of the piston.