Expressions are presented for the electric and magnetic fields due to a pulse of charge, which may be oscillating transversely while moving down an infinitely long highly conducting pipe of circular cross section. The expressions are evaluated at large distances from the pulse and the fields are shown to decrease algebraically in the distance behind the pulse. In the absence of transverse oscillations the longitudinal electric field varies as the inverse three-halves power of the distance; in the presence of oscillations the dominant field component is the transverse magnetic field, which decreases as the inverse one-half power. In the long-range limit the amplitude of the fields is proportional to the square root of the wall resistivity. The phase of the field associated with the oscillating pulse is shown to be the phase of the pulse at the time when it passed the point of observation.