How do I prevent harmonic resonance hum in PVC vent of newly installed hot water heater?
Couple options come to mind:


Change the fan.
Change the fan speed.
Change the fan connection to the vent.
Dampen the vent.
Change the size or length of the vent.


If you can't or don't want to change the fan, then try dampening the vent by clamping it somewhere to the building structure and possibly adding some padding or pipe insulation where it makes those connections. This changes the resonance length without changing the actual length of the pipe.

If dampening the vent doesn't work, then you can change the length of the vent. You mention that you can't make it shorter, but perhaps you can make it longer, or larger. Check the manufacturers requirements on the maximum length, number of elbows, minimum size, and required slope before making any changes like this.