A couple methods that may work:

1) a transducer at the top-left of the screen sends a pulse towards the
right-top screen. Acoustic prisms across the top of the screen cause the
pulse to reflect down. An acoustic-pulse scanned raster is created. Where
your finger is, an echo is created and timed. I read about a monitor that
used this a while back.

2) Vibrate the the screen, and look for damping at the four transducers. The
gradient locates the source of damping (a finger).

3) Pulse the transducers & look for reduced amplitude pulses, or reflections.

Should make for hours of fun. Off hand, since cheap piezo's arn't much good
above a hundred KHz (there first mode is around 2 KHz) I would try the
gradient-damping technique first. A short enough pulse in glass would
probably be several MHz & need more expensive circuitry. I wonder how many &
types of patents a search would turn up?

>I was thinking in use the same piezo sound element to design a touch
>screen, I put 4 piezo, one in each corner, and read it, based in their
>relative voltage, I can determine the point.
>I don't really need high precision.
>
>Does anyone think this work?