When is amplitude modulation equal to frequency modulation?

Amplitude modulation and frequency modulation are two different types of modulation techniques used in electronic communication systems. Amplitude modulation (AM) varies the amplitude of a carrier wave in accordance with the modulating signal, while frequency modulation (FM) varies the frequency of the carrier wave in accordance with the modulating signal.

In general, amplitude modulation and frequency modulation are not equal. However, there is one special case where they are equal. This occurs when the modulating signal is a sine wave with a frequency that is equal to the carrier frequency. In this case, the amplitude modulation index is equal to the frequency modulation index, and the two modulation techniques produce identical waveforms.