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

In summary, the conversation discusses the relationship between Maxwell's Law and the speed of light in vacuum, and whether there is a medium where mechanical waves can travel faster than electromagnetic waves. The conclusion is that materials are held together by electromagnetic forces, so any changes in the material, including mechanical waves, are limited by the speed of light. While other particles, such as electrons, may exceed the speed of light in a medium, they quickly slow down and emit Cerenkov radiation.
  • #1
Barblorrane
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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?
 
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  • #2
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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FAQ: Speed of EM & Mech Waves: Maxwell's Law Explained

What is the speed of electromagnetic waves?

The speed of electromagnetic waves, also known as the speed of light, is approximately 299,792,458 meters per second in a vacuum. This value is a fundamental constant in physics and is denoted by the symbol c.

How is the speed of electromagnetic waves determined?

The speed of electromagnetic waves is determined by Maxwell's equations, which describe the behavior of electric and magnetic fields. These equations were developed by James Clerk Maxwell in the 19th century and are considered one of the cornerstones of modern physics.

What is Maxwell's law?

Maxwell's law, also known as Maxwell's equations, is a set of four partial differential equations that describe the behavior of electric and magnetic fields. These equations explain how electric charges and currents create electric and magnetic fields, and how changing electric and magnetic fields can generate electromagnetic waves.

How are electromagnetic waves different from mechanical waves?

Electromagnetic waves do not require a medium to travel through, while mechanical waves, such as sound waves, require a medium such as air or water. Electromagnetic waves can travel through a vacuum, while mechanical waves cannot. Additionally, electromagnetic waves can travel at the speed of light, while mechanical waves have a much slower speed.

Can the speed of electromagnetic waves be changed?

The speed of electromagnetic waves is a fundamental constant and cannot be changed. However, the wavelength and frequency of the waves can be altered by passing through different materials, causing changes in their speed. This is known as refraction and is responsible for phenomena such as the bending of light in a prism.

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