The piezo pickup is classed as a type of microphone. The piezo is often called a 'crystal' but it's more accurate to call it crystalline silicone oxide, or... sand. That's the basic way of putting it.
This crystal has an amazing property. When the crystal is subjected to pressure it generates an electrical voltage. The piezo microphone is often found on acoustic guitars. It is placed under the bridge saddle. When a string is plucked (strummed, whatever) the string(s) vibrates. These vibrations travel through the saddle into the piezo crystal where the crystal converts those vibrations into an electronic signal. The electronic signal can travel to a device such as an amplifier where the signal is converted back to audio noise.
Piezo crystal instruments are high-impedence and generate high output levels. They are easily damaged and are subject to the effects of heat or humidity. Generally speaking piezo pick-ups have weak bass response and need some sort of buffering like a pre-amp. Some bass players love the piezo sound, others do not. The quality of the pick-up itself also determines sound quality.
As mentioned earlier the piezo pickups can work great in acoustic type instruments such as acoustic guitars or violins.
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