The interaction between a coherent whistler mode signal and the energetic electron population near the equator at L=4 has been studied by using a computer simulation technique. Our results show that trapping of particles by the wave at locations removed from the equator can cause a distortion in the equatorial distribution in the equatorial distribution function and have an important influence on the subsequent growth or damping of broad band hiss. The size and form of the distortion depends on whether a positive or negative gradient is present in the incident electron flux with respect to parallel velocity. This gradient is defined between the parallel velocity limits of the interaction. In the positive gradient case there is an intensification of growth above the frequency of the coherent signal. Below the signal, frequency hiss is strongly damped over a range of frequencies, and we interpret this quenching as representing a simulated VLF quiet band. In this model the frequency width of the quiet band varies as the square root of the amplitude of the causative coherent signal.