Speed of EM & Mech Waves: Maxwell's Law Explained

[Barblorrane]

TL;DR Summary

Can mechanical waves be faster than electromagnetic waves?

Based on Maxwell's Law, the speed of light can be defined by:

$$c= \frac{1}{\sqrt{\epsilon_{0}\mu_{0}}}$$

Based on that, can we find a medium where a mechanical wave travels faster than a electromagnetic one? If so, how does that works?

 

[Ibix]

You've written an expression for the speed of light in vacuum. Materials are held together by electromagnetic forces, so changes in the material, such as mechanical waves, propagate via the electromagnetic interaction, so at or below (usually many orders of magnitude below) that speed.

Did you mean a material with a very high refractive index so that light travels very slowly in it? I don't think you can have mechanical waves traveling faster than electromagnetic waves in such a circumstance, for much the same reason as above.

Other things such as electrons may exceed the speed of light in the medium, although they rapidly slow down, emitting Cerenkov radiation as they do.