The propagation in sea water of an electromagnetic field in the form of a semi‐infinite wave train or a radar pulse generated by an electric dipole is investigated analytically for low frequencies. The frequency‐domain formula for the downward‐traveling field of a horizontal electric dipole excited by a sinusoidally modulated electric‐current pulse is Fourier transformed to obtain an explicit expression for the field at any distance in the time domain. Specific application is made to a wave packet of 25.5 cycles in a time duration of 1 s. The amplitude and phase velocity of the wave packet are determined together with the amplitudes of the initial and final transients. Graphs are displayed and discussed for a range of distances; these show that the amplitude of the wave packet decays more rapidly than the amplitudes of the transients. Possible application to remote sensing in the ocean is considered.