Why does FM sound better than AM?

I don’t buy this explanation. The FM modulation uses a much higher bandwidth than AM. The distance between channels on FM radio is 200 kHz compared to only 9 kHz on AM. That’s more than 20x more bandwidth for FM. On AM, no matter how deeply you modulate the carrier, the bandwidth will not exceed twice the bandwidth of the input signal. On FM, the deeper you modulate it, the wider the output spectrum will be, and it can easily exceed the bandwidth of the input signal.

In addition to that, the whole FM band is much higher frequency, while I guess quite a lot of noise, especially burst noise caused by eg thunderstorms is relatively low frequency. So it’s not picked up because it’s out of band.

Any noise that falls inside the channel does get picked up by the receiver regardless of modulation. However because the available bandwidth is so much higher than the real bandwidth of the useful signal, there is actually way more information redundancy in FM encoding, so this allows to remove random noise as it will likely cancel out.

If I encoded the same signal onto 20 separate AM channels and then averaged the output from all of them (or better - use median filter) that would cancel most of random noise just as well.

Also another thing with modulation might be that if there is any narrow-band non-white noise happening to fall inside the channel (eg a distant sender on colliding frequency), on AM it will be translated as-is to the audible band and you’ll hear it as a single tone. On FM demodulation it will be spread across the whole output signal spectrum, so it will be perceived quieter and nicer by human ear, even if its total energy is the same. That’s why AM does those funny sounds when tuning, but FM does not.

The wider channels is the source of the available audio fidelity, but wider channels make you more exposed to noise, not less. A wider channel means listening to more noise sources, and having transmitter power stretched thinner for a much lower SNR.

In other words, the noise rejection of FM is what enabled the use of wider channels and therefore better audio quality. An analog answer before digital error correction.

In FM, the rejection is so strong that if you have two overlapping transmissions, you will only hear the stronger one assuming it is notably stronger. This in turn is why air traffic still use AM where you can hear both overlapping transmissions at once (possibly garbled if carrier wave was off), and react accordingly rather than being unaware that it happened.

Technology moved on from both plain AM and plain FM a long time ago, and modern “digital” modulation schemes have different approach to interference rejection.