The interaction of sound waves with a medium causes a change in the dielectric constant and thus the impermeability and refractive index as well, but the change is due to a strain field. The strain field changes the lattice structure of the material by stretching or deforming the bonds between atoms in the material. This is the same type of strain that occurs when you are talking about mechanical strain on a piece of metal undergoing a tensile strength test, for example. In the case of the strain field induced in a medium in this case, the interesting aspect is that it actually doesn’t matter what the material is; given the correct applied acoustic wave, almost any medium can become a periodically perturbed medium with a periodically changed index of refraction.
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