Sound waves can cause vibration of the particles/objects that are scattering/reflecting/emitting the light. Since vibration is spatial displacement, it causes a phase shift by affecting the value of "$x$" from the light (electromagnetic wave) phase formula: $\phi = k x - \omega t$.
Is it true that the louder the sound, the larger the phase shift? Or is the magnitude of the shift independent of the volume of the sound?
This question could be rather tricky. In light of the answers I have received, let me put together the whole experiment.
First of all, we need a large enough source of electromagnetic waves, so large that there will always be a portion of the waves that can escape the scattering, diffusion, and other factors that destroy coherence and make it to its destination.
Second, we need a mirror that is large enough and smooth enough to produce enough reflected signal (e.g., reflected light) to be captured by a receiver that is insignificantly small relative to both the signal source and the mirror.
Finally, we need to have these receivers that are light enough, light enough to move because of the oscillations of the sound waves. When all three are put together, we will be able to modulate the position of the receiver through sound waves and thus indirectly modulate the phase of the reflected electromagnetic wave.
If these understandings are correct, then the phase shift will actually depend only on the frequency of the sound, not on the volume. Unless, that is, the sound is loud enough to destroy those sophisticated receivers.
My question is, does the understanding correct? If we want to have such an experiment, what settings should be paid attention to during the experiment?