I'm looking for a "physical" explanation (or as close to one as I can get) for the displayed spectrum of an FM signal on a spectrum analyzer. I'm using a sinusoidal carrier of 200 MHz, a sinusoidal modulating tone, and a deviation of 5 KHz for my question. Lets say I use a very slow rate for the modulating tone, like 1 Hz, the spectrum analyzer will display a waveform that moves across the screen side to side at a rate of 1 Hz. If I continue to increase the rate for the modulating tone until I get to, say 4 KHz, I will see a classic FM spectrum with sidebands every 4 KHz. What I am wondering about is why I see such a spectrum. The actual time domain signal is moving through various frequencies between the two extremes of carrier-5KHz and carrier+5KHz at a 4 KHz rate, yet the spectrum analyzer appears to show little power at certain frequencies. What I am looking for is a good "physical" way to connect what is happening in the time domain and what the spectrum analyzer displays. Its possible I need to think more about what happens inside the spectrum analyzer when it receives such a frequency varying signal, then about the FM signal itself. Ive looked at the equations and I understand them mathematically, but I'm having trouble "seeing" such a spectrum physically. Anyone have a good way to think about this?