Do electromagnetic waves like light and gravitational waves (due to moon for instance) affect on mechanical waves like sound?
Can sound change the path of light?
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Any physical phenomenon is potentially capable to cause some change to any other phenomenon, more or less directly. If it was not the case, the physical world could be divided into completely independent realms; there would not be the one single world we call Nature.
Practically though, many if not most of the actually existing interactions between systems can be ignored, or just treated as perturbations in models taking into account only the most important ones. This is because interactions happen in a wide range of order of magnitudes. For example you would not usually include electromagnetic interactions between Moon and Earth when modelling their respective motion, although it certainly does play some part in the actual interplay of the two bodies (both having a magnetic field). If you do not ignore negligible effects, well even nocturnal urban lighting does play a part by sending photons to the Moon, pushing it away from Earth!
As a side note, the fact that some interactions are so much less intense than others is very useful: it allows us to use them as measuring devices. As shown in another answer, we can use Schlieren photography as a straightforward way to display air density because indeed the path of light is altered by compression waves, but only marginally so. If the dependence of electromagnetic waves on air density was more intense, it would be more complicated to decorrelate both effects.
I can answer half your question in that a sound can change the path of light.
A change in the density of the air produces a change in the refractive index of the air and so a Schlieren photograph can make this visible.
Here is a YouTube video to show a sound wave produced by clapping.
Yes, sound waves in a gas, liquid or solid can affect the light passing through it, as the motion of the atoms due to sound waves changes the atomic spacing, and this changes the index of refraction slightly. So the light would be diffracted and some amount of the light would experience a frequency shift up and a frequency shift down by the sound wave frequency.
The other possibility is that of electromagnetic waves creating sound waves directly. Here, the effect is much smaller: when radiation like light shines on a surface it exerts a pressure known as "radiation pressure" though again this is a very small effect.
In principle, though, if a wide-beam high powered laser were to operate in a repeating pulsed mode (with a power level low enough that it does not ionize or otherwise cause phase transitions like melting, etc) then the laser would cause a pulsed mechanical vibration in the surface due to the changing radiation pressure, thereby generating sound waves.
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