# Changing AC amplitude and frequency

I'm working on a project for school to monitor a 6 and 15 VAC signal coming in at 11KHz for both. I'm trying to find a simple way of recreating that at home for running some tests on circuits I'm developing. I have a simple function generator but it only goes up to 5VAC and has a very low current limiter so that's not an option and I'm poor so I can't afford a lab grade function generator.

Ideally, I just want to breadboard a few components that I can repurpose later if I need to. Reading up on some other posts I found Changing the frequency of an AC supply and the common suggested answer was "a rectifier followed by an inverter".

I found DC-AC Inverter Circuit - Toshiba Semiconductor (PDF) which explained a bit but it's still muddy for be. I understand I need to rectify wall supply 110VAC to a DC voltage then use an inverter to convert it back to an AC voltage. What I'm unclear on is how:

do I convert to 6 and 15 DC OR do I convert to a 12 and 30 DC (because the AC will do half positive, half negative)?

then use an inverter to make it AC at 11KHz? would it be PFM?

Any help or examples would be appreciated because most of the circuit examples I've found in my research are for converting 12VDC battery to 220VAC or 110VAC, AC to DC (guess I could just use it backward) but with no mention of frequency modification, or AC to AC but again no mention of frequency modification.