How to change the frequency of AC supply?
Maybe consider a single-phase motor speed controller like this one. According to the spec it runs from 48Hz to 62Hz and can produce an output frequency of 0 to 120Hz with 0.1Hz resolution. Output power is about 1 h.p.

There will be many options and alternatives in this type of product - this was top of the list on google when searching for "single-phase motor speed controller".