1. What determines the speed of electromagnetic waves?
Electromagnetic waves travel because changing electric and magnetic fields continuously create each other. The speed at which this disturbance moves depends on how electric and magnetic fields behave in space.
In vacuum, these fields interact in a way that results in a fixed speed for all electromagnetic waves, no matter what their wavelength or frequency is.
1.1. Same speed for all EM waves
Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays may look very different, but in vacuum they all travel at exactly the same speed:
\(c = 3 \times 10^8\, \text{m/s}\)
This is one of the most important constants in physics.
2. Maxwell’s explanation for the speed of EM waves
Maxwell combined the laws of electricity and magnetism and discovered that electromagnetic waves should travel with a speed determined by two fundamental properties of free space:
- Electric permittivity (\(\varepsilon_0\))
- Magnetic permeability (\(\mu_0\))
2.1. Mathematical expression
Maxwell derived that the speed of electromagnetic waves in vacuum must be:
\(c = \dfrac{1}{\sqrt{\mu_0\,\varepsilon_0}}\)
This was a remarkable discovery because the value obtained from this formula matched the measured speed of light.
2.2. Physical meaning
Permittivity and permeability describe how electric and magnetic fields interact with space. The stronger their interaction, the harder it is for the fields to influence each other quickly, resulting in a particular propagation speed.
3. Relation between speed, frequency, and wavelength
The speed of a wave is related to its frequency \(f\) and wavelength \(\lambda\) by a simple formula:
\(v = f \, \lambda\)
For electromagnetic waves in vacuum, \(v = c\), so:
\(c = f \, \lambda\)
3.1. What happens when frequency changes?
The speed in vacuum stays constant. If the frequency increases, the wavelength must decrease. If the frequency decreases, the wavelength increases. But the product \(f \lambda\) stays equal to \(c\).
3.2. Examples
- A radio wave with very low frequency has a huge wavelength, sometimes kilometers long.
- A gamma ray has extremely high frequency and a wavelength that can be smaller than an atom.
4. Why do EM waves slow down in materials?
Although electromagnetic waves travel at speed \(c\) in vacuum, they generally slow down when they pass through materials like glass, water, and air.
4.1. Interaction with atoms
Inside a material, the wave interacts with electrons and atoms. These interactions take a tiny amount of time, which causes the average speed of the wave to reduce.
4.2. Speed in a material
The speed of the wave in a material is:
\(v = \dfrac{c}{n}\)
where \(n\) is the refractive index of the medium. A larger \(n\) means a slower wave.
5. Light as an electromagnetic wave
Since electromagnetic waves travel at the universal speed \(c\), and light also travels at this speed, Maxwell concluded that light is an electromagnetic wave. This was one of the greatest unifications in physics.
5.1. Implication
Every property of light—reflection, refraction, diffraction, interference—can be understood using the wave nature of oscillating electric and magnetic fields.
6. Summary of the key idea
The speed of electromagnetic waves in vacuum is a universal constant:
\(c = 3 \times 10^8\,\text{m/s}\)
This speed comes from the properties of free space itself and does not depend on frequency, wavelength, or the type of electromagnetic wave.