Connecting a series resistor or variac will reduce the applied voltage across the motor, but it will not change the applied frequency. The reduced voltage will increase the current flowing through the motor because motors draw a minimum current when the voltage and frequency are a fixed ratio. Changing either the frequency or the voltage while leaving the other unchanged can, depending on the motor design, rapidly increase the motor current. This increase in current can lead to motor damage due to the overheating of the winding in motors which do not have enough margin or thermal protection. This margin adds cost to the motor, so it often designed out as a cost savings measure.
Note that the reduced voltage will also result in a reduced torque, which will usually result in a lower speed. Thus a series resistor could achieve your desired goal of speed reduction, but at the potential cost of a reduced motor lifetime.
A triac circuit may or may not safely control the speed of a motor depending on how it is controlled:
- If the triac circuit is operated in a phase controlled manner like a light dimmer and only conducts for a portion of every line cycle, then it effectively behaves like a resistor and can result in the same motor damage as a series resistor. In this phase controlled operation, the fundamental voltage amplitude will change based on the firing angle while the frequency is unchanged.
- If the triac circuit is operated in a motor control mode where it conducts for full line cycles, but not every line cycle; then no motor damage will occur. When the motor is conducting current, its voltage and frequency are matched and the motor produces normal operating torque. When the triac doesn't fire, the motor doesn't conduct current and produces zero torque. The fan speed will depend on the average torque which is based on the ratio of conducting cycles (torque) to non-conducting cycles (zero torque). The inertia of the fan will keep it turning during the non-conducting cycles.
That's the background. In terms of your situation, your particular fan motor appears to have thermal protection and appears to be dual frequency rated. This suggests that your fan motor has extra margin and so it can handle a wider range of volts/Hz ratios. In addition, it has a protection circuit that should turn it off before damage would occur. Thus, you might be able to get away with using a series resistor or light dimmer to control the speed.
Getting a motor speed controller would be a better option since it won't damage the motor and you won't have the additional losses of the resistor/dimmer.
[Note: additional losses == a hotter room which seems counter-productive to the reason for the whole exercise of cooling your room!]
Alternate solutions:
you can mechanically control the flow as @rockmagnet suggests, but that isn't using electronics ( :) ) and it reduces the efficiency of the motor/fan (but probably not as much the resistor-motor-fan). Note that this could result in more noise depending on how the flow restriction is realized.
An alternative to flow restriction would be to have ducting that "recycles" outlet air back around to the inlet. This would allow the fan to operate at its normal unrestricted operating point, but you'll have a lower net flow into the room. Even more mechanically complicated, but...
you can get a full blown variable speed / frequency drive. This will likely be very expensive and is probably excessive overkill (but it would be tres cool ;) ).
Finally, I would personally just buy a multi-speed fan...
