Yap, but you need a special medium. Actually the two could never interact, but both can interact with the propagation medium. I've seen some similar material. Look for in on the Internet, is written By Prof. Glorieux Christ (“Photoacoustics” and “acousto-optics”: listening to light and
looking at sound);
Pls. try this link: https://lirias.kuleuven.be/bitstream/123456789/201255/1/artikel_cg_NAG_photoacoustics_utrecht_2005.pdf
Yes, it’s very possible to do what you describe. Electro-acoustical devices have been used for many years in radar systems (and many other places). In the radar application, a broad spectrum pulse can be compressed, or decompressed (depending on direction) to enhance radar performance. This technique is called “chirp” compression because the radar pulse is swept in frequency (not fixed) and (if you could hear it) would sound like a birds’ chirp. Similar applications are found in optics, where devices are said to be “opto-acoustical”.
It’s true that acoustical waves cannot directly interact with electromagnetic waves. But when they both share a common medium, and that medium has electrical properties that vary with mechanical strain, the two phenomena can interact. What we’re talking about are piezoelectric materials. The underlying molecular basis for the piezoelectric behavior varies with material, but the net result is variation in electrical/electronic/electromagnetic properties under mechanical deformation.
Of course, the reverse is also true. That is, a mechanical deformation can be caused by an electrical excitation. An interesting and important application of this is in atomic force microscopes (AFMs) and scanning tunneling microscopes (STMs). There, small changes in applied voltages to a piezoelectric rod can make the end move with sub-nanometer precision. Without such control, AFMs and STMs would not be possible.
In direct response to your question, one could imagine an etalon (or Fabry–Pérot interferometer, or resonant cavity) with the cavity filled with a piezoelectric material. Resonant standing waves (either electromagnetic or acoustical) will produce fixed patterns of electromagnetic or acoustic properties in the material that you might find interesting or useful. Of course, this is just speculation on my part.
Dr. Bisson gave you a very good answer. Electromagnetic Acoustic Conversion many years is widely used. For example, high-frequency electromagnetic field attenuates rapidly in metals. But in certain circumstances, on the metal surface electromagnetic wave is converted into acoustic wave that propagates in a metal without attenuation and "drags" electromagnetic wave.