I get that. What I was always trying to wrap my head around was the concept of how the sidebands would contain the two component parts of speech or music, which are made up of many different frequencies that are spread out across the bandwidth, along with their individual levels. Does that make sense? I'm thinking more in terms of the theory, as opposed to the practical.The power is determined by the carrier. At 100% modulation the PEP will be 4x carrier power. You can achieve 100% PEP with a single tone but it won't use the entire available audio bandwidth that the modulator is set for.
You need to think in terms of looking at this on an oscilloscope, not what you see on a waterfall or frequency spectrum display.
Consider what you'd have in each sideband if you were to modulate the carrier with a white noise signal, where each frequency in the white noise was at the same power level. That's what I've been unable to conceptualize until I really started looking at the waterfall spectral display on my receiver. It got me thinking about it tonight, after having it pointed out to me about my error in saying that the loudness, or amplitude of the modulating signal determined the bandwidth. I started thinking about the spectral display on my radio, and I think I finally saw what I had been missing for so long about all this. I finally saw in the spectral display what I couldn't see in my head for so long! And, it really should have been obvious to me knowing that, if a modulating signal of a single frequency can produce sidebands of a single frequency, that that same modulating signal made up of many different frequencies will produce sidebands with corresponding frequencies, each individual frequency spread across the bandwidth of the sidebands that the modulating signal creates that, when the two sides are added together, comprise the entire bandwidth of the AM signal. Does that make sense?
I think my brain just cramped with that one!