state that all electromagnetic waves are transverse waves that travel with the same speed c in free space

Electromagnetic Spectrum

Learning Objective

State that all electromagnetic waves are transverse waves that travel with the same speed c in free space.

Key Concepts

• Electromagnetic (EM) waves consist of mutually perpendicular electric and magnetic fields.
• The fields oscillate perpendicular to the direction of propagation – i.e., EM waves are transverse.
• In a vacuum every EM wave propagates at the universal speed c ≈ \$3.00\times10^{8}\ \text{m s}^{-1}\$.

Why All EM Waves Travel at the Same Speed

The speed of an EM wave in free space is given by the relationship between the electric constant \$\varepsilon0\$ and the magnetic constant \$\mu0\$:

\$c = \frac{1}{\sqrt{\mu0 \varepsilon0}}\$

Since \$\mu0\$ and \$\varepsilon0\$ are universal constants, the value of \$c\$ is the same for every frequency or wavelength of electromagnetic radiation.

Transverse Nature of EM Waves

For any EM wave travelling in the \$+x\$ direction:

• The electric field \$\mathbf{E}\$ oscillates in a plane perpendicular to \$x\$ (e.g., the \$y\$‑direction).
• The magnetic field \$\mathbf{B}\$ oscillates in a plane also perpendicular to \$x\$ but orthogonal to \$\mathbf{E}\$ (e.g., the \$z\$‑direction).
• The three vectors \$\mathbf{E}\$, \$\mathbf{B}\$, and the direction of propagation form a right‑handed set.

Overview of the Electromagnetic Spectrum

The spectrum is usually divided into regions according to wavelength (\$\lambda\$) or frequency (\$f\$). All regions share the same transverse nature and propagation speed.

Summary

1. All electromagnetic waves are transverse; the electric and magnetic fields oscillate perpendicular to each other and to the direction of travel.
2. In free space every EM wave propagates at the same speed \$c = 3.00\times10^{8}\ \text{m s}^{-1}\$, regardless of its wavelength or frequency.
3. The electromagnetic spectrum spans many orders of magnitude in wavelength and frequency, but the underlying wave properties remain identical.