Problem: Linear Array of Emitters, Phonons

   Consider a linear array of N identical radiation sources, placed at positions . Each source emits radiation at frequency , wavenumber k, amplitude A and the sources are coherent with zero phase difference. We detect the radiation with intensity (defined as the time-averaged amplitude square) with a detector positioned along the line of the array, far away from the sources. Assume that N is large.

Introduce a time-dependent modulation to the position of the sources, described by . The detector is capable of analyzing the frequency of the incident radiation as well as the intensity. At what frequencies and wavenumbers will strong radiation be detected?