Thinking in stage
Because the shape of the acrylic sheet is rather random when heated, it is difficult to accurately replicate the water wave formations formed by the sound vibrations.
There are two approaches that I've come up with so far, one is to use the water directly as a lens to capture real-time images. The other is to use modelling and 3D printing to replicate the water waves created by the sound vibrations to create a solid-state lens. I preferred to use water as a lens, which is more direct.
But I had a few problems to solve: many of the water waves produced by insufficiently strong sound vibrations were too small, making the distortion of the pattern less pronounced. Moreover, a sound will continue to produce different water waves, and the shape of one moment may not be representative.
The solution I have come up with so far is to find some sound that has a fixed frequency and simulate that frequency to get a static image that shows this sound.