Raghuram et al. (1977) have shown that a long-duration monochromatic wave generated by a high-power VLF transmitter may quench natural magnetospheric hiss emissions over a frequency range Δf of the order of 50--150 Hz below the transmitter frequency. We show that quasi-linear diffusion in an inhomogeneous medium (Ashour-Abdalla, 1972; Welti et al., 1973) cannot be invoked to explain these results. On the contrary, by using a formalism similar to the one introduced by Roux and Pellat (1976), i.e., nonlinear trapping and detrapping of natural particles, we are able to interpret the variation of Δf with both the field intensity and the transmitter frequency. The time constants for the establishment and disappearance of the quiet band are also qualitatively interpreted. Numerical agreement with experimental data is obtained if the field intensity induced by the Siple transmitter in the equatorial region at L=3.5 is of the order of 4 m&ggr; (1 m&ggr;=1 pT (picotesla)).