FM Signal Generation
So yes, defining an RF signal's shape in software is a relatively new thing (it's called Software Defined Radio, and a lot of things do it under the hood these days).

I can't believe you didn't find anything via Google using "FM transmitter circuit", but assuming you found something but didn't understand it, I'll post a rough explanation here. I'll explicitly not post a schematic; it's really easy to find hundreds of those, and since you're undergrads, it's going to be relatively much fun for you finding the things described below.

What you'll need is something that is a Voltage-Controlled Oscillator (VCO). By applying a varying voltage (in the case of audio transmissions, the amplified voltage from the microphone) to the control input of that oscillator, you change the frequency of that oscillator. Done! Sometimes, you use second, non-changing oscillator and a mixer to convert that varying frequency up the channel frequency you need it at.

So, in a minimal FM transmitter circuit, you'd be looking for:


input amplifier &amp; filtering, if any
a VCO, typically consisting of one or two transistors in conjunction with caps and/or inductances that oscillate,
and output amplifying stage (typically, a couple transistors and filters)
an antenna