Frequency spectrum — UPSC Physics Optional CSE 1996 Paper II

Derive the expression for the frequency spectrum of a carrier wave of frequency f_c which is amplitude modulated by a frequency f_m. A certain transmitted radiates 9\text{ kW} of power when the carrier wave is unmodulated and 10.12\text{ kW} power when the carrier wave is sinusoidally modulated. Calculate the modulation index.