You know how a tuning fork always produces a very specific note? That’s because the shape of the tuning fork is precisely adjusted to vibrate at the frequency corresponding to that note.
Quartz is a piezoelectric material. That means it generates electricity when you bend it, and bends when you apply electricity to it.
Now put those things together: by [cutting a small chunk of quartz into a tuning fork shape](https://en.m.wikipedia.org/wiki/Quartz_clock#/media/File%3AInside_QuartzCrystal-Tuningfork.jpg), you get something that vibrates at a specific frequency. By passing an electrical current through the tuning fork, the piezoelectric effect keeps it vibrating “forever”. When you initially put the battery in, a little burst of electricity from the circuit closing gives the initial kick that starts the quartz vibrating.
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