Can I make a one-speed AC motor variable-speed by modulating the power input?
Can I make a one-speed AC motor variable-speed by modulating the power input?


You can not modulate power. You may be able to control the voltage. The motor and the load working together will determine what current will be drawn and how much power will be taken from the source.

If you control the voltage to a box fan, it is likely that the speed can be controlled over a limited but useful range. This will work with a permanent-split-capacitor or a shaded pole type of induction motor driving a fan or centrifugal pump. It will not work with other types of induction motors or other types of loads. Even under the above conditions, there is a possibility that the motor will overheat eventually.

The device used to control the voltage needs to have appropriate voltage and current ratings. You must be able to trigger the voltage turn-on in mud cycle to get a waveform like this:




  The question is, is this safe and efficient?


Safety depends the design and implementation. Part of that would be determining if the specific motor and load work properly and that the motor does not overheat. To be completely safe, the motor probably needs a thermal fuse imbedded in the winding my the manufacturer.

This will probably not reduce the efficiency very much as compared with constant-speed operation. Reducing the fan speed will reduce air flow and require less energy than full-speed operation even if the motor is slightly less efficient.