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

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SUMMARY

The discussion centers on the relationship between electromagnetic (EM) waves and mechanical waves as defined by Maxwell's Law, specifically the equation for the speed of light, \(c= \frac{1}{\sqrt{\epsilon_{0}\mu_{0}}}\). It concludes that mechanical waves cannot travel faster than EM waves due to the fundamental electromagnetic interactions that govern material properties. The conversation also touches on the phenomenon of Cerenkov radiation, where particles like electrons can exceed the speed of light in a medium but subsequently decelerate.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with the concept of refractive index
  • Knowledge of wave propagation in different media
  • Basic principles of Cerenkov radiation
NEXT STEPS
  • Research the implications of Maxwell's equations on wave propagation
  • Explore the concept of refractive index in various materials
  • Study the mechanics of Cerenkov radiation and its applications
  • Investigate the speed of sound in different media compared to light speed
USEFUL FOR

Physicists, engineering students, and anyone interested in wave mechanics and electromagnetic theory will benefit from this discussion.

Barblorrane
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TL;DR
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?
 
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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.
 
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