A Colpitts oscillator uses a combination of inductors and capacitors to produce an oscillation at the resonant frequency of LC circuit.

To see that in action, I built one on a protoboard and it delivers an almost perfect 22.9kHz .. compared to the theoretical 22.5kHz.

As always, all notes, schematics and code are in the Little Arduino Projects repo on GitHub.

Here's a trace of the output signal on CH1, and the mid-point of the capacitor pair on CH2: