Experimental studies are reported of oscillations and radiation that is spontaneously excited by an electron beam which is shot along a diverging magnetic field into a plasma from a hot cathode. In the present study we focus on oscillations below the electron gyrofrequency, where we find that whistler mode radiation appears in the form of bursts, or wave packets, each with typically 0.1--1 ¿s time duration, and which together cover typically a few percent of the full time. Wave packets are found in a broad frequency range of 7--40 MHz, while each individual wave packet is dominated by a single frequency. There is propagation along two routes: at the group velocity resonance cone angle, away from the central channel where the waves are excited, and in a channel along the magnetic field. Features of the whistler mode wave packets that are studied include (1) the statistics of amplitudes, frequencies, and time durations; (2) the propagation and decay of wave packets with different frequencies; (3) the group and phase velocities; and (4) how the wave packet production varies with the energy, and the current density, in the electron beam.