When a submerged solid body is subjected to a translational velocity step, it radiates oscillatory, transient acoustic pressures, whose natural period is proportional to the travel time of a sound pulse around the accelerated solid. Transient velocities displaying more‐complicated distributions over the radiating surface give rise to acoustic‐wave harmonics that, with the exception of the breathing mode, are also oscillatory, and characterized by one or more “natural” frequencies proportional to the ratio of the sound velocity to the characteristic dimension of the radiator. These pressures are analogous to room reverberation attenuated by radiation damping but their phase velocities and attenuation are reminiscent of creeping waves. If the initial velocity impulse is modified by subsequent gradual accelerations (or decelerations) as embodied, for example, in an exponentially decaying or “pulsed CW” velocity, the “reverberant” oscillatory‐sound field is superimposed on an acoustic field whose time history is identical with that of the motion of the radiating surface. The phenomenon of oscillatory transients radiated by nonoscillatory motions of submerged bodies appears to be characteristic of any finite solid geometry. The effect of these reverberant transients on the radiation and radiation loading of spherical sources generating CW pulses is analyzed. Finally, the effect of these transients on the performance of large arrays is explored. It is shown that, at the beginning of a CW pulse, radiation impedance is uniform over the array, the difference with the CW impedance that fluctuates strongly over the array surface being accounted for by the transient. Consequently, arrays in which circuits of individual elements have been adjusted for fluctuations in CW radiation impedance will display a non‐uniform response at the beginning of the pulse, which may result in fatigue failures.