Why does FM sound better than AM?

FM sounds better than AM partly because frequency is more durable than amplitude, but it's not the whole story.

Frequency does not diminish with the inverse square law, as does the amplitude of a wave that is broadcast in all directions. This is because frequency is related to a count of events over time.

Frequency from a source light years away is intact; we can look at frequency bands from a radiating celestial body and know which chemical elements there are, and also tell exactly how fast it is moving away from us from the red shift in that spectral pattern.

Be all that as it may, AM should sound great when you are close to the radio tower, and have ideal reception with no multi-path reflections, and good signal/noise ratio.

It still doesn't sound good, and that simply because of the bandwidth allocated to it is low. Furthermore, AM Stereo is a retrofit and crams two channels into one via phase modulation.

AM stations are separated only by 10 kHz, as you can see on your AM tuner (which you likely have only in your car, if that). The bandwidth is directly related to the audio bandwidth because modulation produces side bands.

For instance, if we modulate the amplitude of a 650 kHz carrier with a 1 kHz audio tone, we get side bands of 651 kHz and 649 kHz. You see where this is going? We can only go up to 5 kHz before we bump into the next station, which also needs +/- 5 kHz for its side bands.

This 5 kHz limitation is why AM radio sounds like your speakers have a heavy woolen blanket over them. It's almost as bad as the bandwidth limitation as narrow band phone calls. Listening to AM music is almost as bad as listening to on-hold music over a narrow band codec like G.711.

The kicker is that only one side band is needed to reconstruct the signal, so in theory AM stations could have 10 kHz bandwith. Unfortunately, SSB was not deployed for broadcast AM, even though it was already known at the dawn of radio.

(https://en.wikipedia.org/wiki/Single-sideband_modulation has a note about why)

Can we use this fact to enable faster than light communication?

I think we had some fairly recent discussion on HN since I remember commenting.

As you're saying, it's about bandwidth and signal to noise. Not something inherent to modulation.

Not if measuring by relative speed.

The modulation is important. FM is more robust against external noise than AM.

It would also be harder to tune into a station that is SSB because there's no carrier to detect. If you're slightly too high or low, the audio will have a slightly higher or lower pitch. I'm just guessing but with modern radios that wouldn't be a problem, but when AM was still used a lot I think (analog) oscillators tended to drift a bit, and you would have to adjust your radio often to correct for the changing pitch.

Even though the frequency survives the long trip, any changes in that frequency are observed only after a delay corresponding to the speed of light.

Someone once pointed out that shadows (which aren't objects with a mass and position) can move fast than light, at a sufficiently large distance from their origin. That is, the location of the border between the shadowed and unshadowed region can be changing faster than light speed. But that fact can't be used to communicate faster than light, because the changes in the location of the shadow's edge still take a comparatively enormous amount of time to propagate from their source to their destination. If you're creating the shadow, you can know that one galaxy will observe the shadow long before another galaxy does, but you can't use that knowledge to signal something to one galaxy or the other without waiting for the light (or lack of light) to travel all the way to that galaxy.

This is a myth. There is no reason that channel spacing need limit the modulation bandwidth. The only downside is that listeners to adjacent stations will hear a slight "monkey chatter" from the overlapping sidebands. In reality stations are never allocated adjacent frequencies within the same coverage area so this usually doesn't happen.

Only while signals are strong. On weak signals however, AM has a considerable benefit in intelligibility over FM.

FM stays good as the signal weakens, and then kind of drops off a cliff almost.

Be that as it may, AM radio is obviously low-pass filtered. It might not be a brick wall at 5 kHz, but it sounds obviously muffled to someone who can't hear anywhere near up to 20 kHz. If I were to guess, based on years of experience of playing with EQs, I would say that it has next to no content beyond somewhere around 8 kHz.

AM receivers have to apply a band pass filter to select the station. The width of that filter will directly affect the audio bandwidth. The filter probably can't be anywhere near +/- 20 kHz based on the idea that nobody nowhere would put two stations close together in the same area. Mass produced AM radios have to work everywhere.