Two radio station broadcast their programmes at the same amplitude A and at slightly different frequency ${\omega _1}$ and ${\omega _2}$ respectively where ${\omega _2} - {\omega _1} = {10^3}\,\,{\rm{Hz}}$. A detector is receiving signals from the two stations simultaneously. It can only detect signals of intensity $ > 2{A^2}$. The time interval between successive maxima of the intensity of the signal received by the detector is