Re: Frequency comparator
Is your uncle wanting to listen to short wave radio?
Certain types of broadcasts use single-side-band. They sound garbled on low-end receivers.
A BFO (per mister_rf, preceding post) is needed to hear them properly. The oscillator has to be in the radio receiver circuitry.
A deluxe short wave radio will have a BFO. It's adjusted by a knob on the front (mine is, anyway).
LC oscillators implies coils and capacitors. Sine wave.
Never heard of a synchronous generator that does what your uncle describes. Maybe your uncle means 'sinewave generator'?
Look up Colpitts, Clapp, Hartley, etc. These use one transistor.
It will take some work to obtain (or fabricate) the right coils. Nowadays there are easier ways to make a sine-wave oscillator.