Frequency and Function Generators

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Hello, I am new to electronics in general. I have a specific project in mind involving resonant energy transfer. I'm wondering about a function generator as a necessary component of my primary coil. The cheapest "kit" I've found is around $35 (of course they're out of stock) and this would be an internal component that theoretically I would not need to adjust because once the correct frequency is set there would be no need. My question is, Can I instead build a cheap "frequency converter" that could be set to convert the AC from say, a standard 12V AC wall wart to a specific, square-wave frequency? If so, how can I calculate the output frequency? Even if someone could just point me in the right direction in terms of information I would appreciate it. Also, I read that the standard AC frequency from a 125V outlet is 50-60Hz. Is this true? Thank you for your time.