Actually I don't intend to recreate the sound by any way. I'd prefer to analyze the sound, so in a first time be able to divide it into several packs of frequencies with an associated intensity. But I don't know (yet) if the Arduino can perform this kind of things...
Do a search for "Arduino Spectrum Analyzer".
And if you can get-away with only 7 frequency bands, the [u]MSGEQ7[/u] is a cool little chip that does the frequency filtering for you. (That makes your software a lot easier, and it frees-up processor time for other stuff.)
Note that the Arduino doesn't have a lot of processing power so the examples you find are more of a visual effect than an actual spectrum analyzer [u]instrument[/u] used for science & engineering.
If you want to do "serious" audio analysis a regular computer (with the appropriate software) is better, and you might need to learn how to use MATLAB (or a MATLAB clone).
What do you mean by "You can use analogRead to sample that waveform at ~10,000 sample rate at 10 bit resolution" ?
The [u]Audacity website[/u] has a nice-easy introduction to how digital audio works. CD audio is sampled at 44.1kHz (44,100 times per second) but the Arduino's ADC cannot accurately-sample that fast.
How to do that ?
You have to use the [u]micros()[/u] for the timing (or maybe there are a more-advanced ways of doing it with the chips internal timers & interrupts). The 10-bits come "automatically" from the Arduino's ADC.
Note that the Arduino can't read the negative-half of the audio cycle* so the analog input is usually [u]biased[/u] (2 equal-value resistors and a capacitor). With the piezo, you can use higher-value resistors (~1M Ohm) and you'll get a stronger signal. And, you can also leave-out the capacitor (since the piezo is electrically 'like' a capacitor already).
And, if the signal from the piezo is too weak you may need a preamp. Or, you can use a [u]microphone board[/u] that has a microphone, preamp, and bias circuit.
- The Arduino can actually be damaged by negative voltages, although the piezo probably doesn't put-enough current to do any damage.