Trying to control a 120vac single phase AC motor speed with varying the frequency is very dicey, at best.
Forget it if the motor has a separate start winding, start capacitor, or centrifugal switch.
If you did get it to work, it would probably derate the motor to half it's rated HP. Also there's air flow/cooling concerns at speeds lower than the motor is designed to run, which will in time, cook the windings.
For these reasons, I don't recommend it.