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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?

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    $\begingroup$ OK, we have to read a lot between the lines in your question: You have some experimental setup (?) where you have reflective particles (?) that you shine coherent light at (?) and observe the phase of the reflected light(?). Is that correct? Please describe your setup in your question (edit it, don't just comment!) more precisely. we have no idea what "x" is. This feels like you're trying to skip the part where you describe the experiment and want to have the result. That doesn't work – we're not inside your head and know not what you're looking at! $\endgroup$ Aug 4, 2022 at 10:50
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    $\begingroup$ The "fact" you state in your first paragraph is not correct in all circumstances, and perhaps not even in most. Could you please edit your question with a specific example of what you're talking about. Alternately, if you are drawing your first paragraph from some source, cite that source either with a link or a book citation. In addition, if it's a printed source, please find a reasonable-length (half a page or less) excerpt that makes your point and quote it in your question. $\endgroup$
    – TimWescott
    Aug 4, 2022 at 13:53
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    $\begingroup$ Your question is better, but still misleading. Please edit your question including the title to make it clear that you are talking about a specific case involving reflective surfaces that are moved by sound waves. Right now it sounds like you're talking about sound in general. Since you're talking about a specific case, please include a sketch of your proposed experimental apparatus, proposed device, or whatever it is that you are actually proposing to do. $\endgroup$
    – TimWescott
    Aug 5, 2022 at 17:58

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In most cases the answer will be "no". Talking about a "phase" of light implies a mono-chromatic coherent light wave. Most scattering, diffusion or reflecting processes will destroy the coherence and there is no way to define the phase of the reflected light. It doesn't matter if the reflecting/scattering particles are moving or not.

A potential exception would be a reflective (or diffractive) object that's large and smooth enough to create a specular reflection. In this case the coherence of the light is maintained and you can determine the phase of the reflected light.

What exactly happens in this case, will depend a lot on the specific setup, but you could construct a setup where a sound wave could modulate the position of a (very light weight) mirror to modulate the phase of a light wave.

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  • $\begingroup$ Hilmar is very accurate in their description and in fact what they describe is exactly what happens in interferometric measurement techniques of vibrations. The only difference here is that in these measurements the vibrating element (which could very well be vibrating due to sound waves if it is light enough) is altering the phase of one laser beam which is compared to another one considered as the reference. $\endgroup$
    – ZaellixA
    Sep 4, 2022 at 11:11

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