Power Noise Question

The speed of at which ac motor rotates is proportional to the frequency of the power supply, so if f reduces from 60 to 50, speed is down 83% of the original.

Now, the real question is how is noise related to fan speed. If it's linear then you just reduce 20dB by 83% (first convert db to power then reduce then convert back to dB), if it's nonlinear, then you have to look up reference.

There is a power supply build into the fan that drives the motor, it doesn't matter what power is feed into it.

In theory, If you use a crude fan at a country using 120V and 60 Hz and measure 20dB noise, then you carry the fan to another country that is using 120V and 50 Hz and it works, the noise intensity would be 83% assuming the fan speed to noise is linear.