My theory on why one toilet is noisy after another one is flushed is that the water pressure changes.
When you flush one toilet, the water pressure drops a little, when that toilet is full and the internal float valve turns off the water, there is a slight momentary water pressure increase. This increase causes the weak valve on the other toilet to be overcome with pressure and it turns on briefly. If the valve is weak on that toilet you will get a slow whistle as the weak valve attempts to close. This would become worse if the float is poorly adjusted or too high, and/or if the toilet has a slight leak that tends to reduce the amount of water in the tank. This can also be caused by not having or having a bad pressure tank on top of the hot water heater. The purpose of that tank is to even out the water pressure surges.
So, basically, the only thing that connects the two toilets is the water line. The only thing that can change in the water line is pressure.
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