The nonlinear interaction of electromagnetic waves propagating in a cold plasma across a magnetic field is investigated. The amplitude of the generated wave is evaluated, and numerical computations are given for two cases of interest: (a) the interaction of an extraordinary wave with an ordinary wave leading to the generation of an ordinary wave; (b) the interaction of two ordinary waves leading to the generation of an extraordinary wave. The results show that under appropriate conditions the detection of generated wave is feasible and the scheme should provide a diagnostic method for measuring the local density and its fluctuations in magnetized plasmas.