Know that all electromagnetic waves travel at the same high speed in a vacuum

Published by Patrick Mutisya · 14 days ago

Cambridge IGCSE Physics 0625 – 3.3 Electromagnetic Spectrum

Cambridge IGCSE Physics 0625 – Topic 3.3 Electromagnetic Spectrum

Learning Objective

Know that all electromagnetic waves travel at the same high speed in a vacuum.

Key Points

  • Electromagnetic (EM) waves are transverse waves consisting of oscillating electric and magnetic fields.

  • In a vacuum there is no medium to slow them down, so every type of EM wave moves at the same speed.

  • The speed of light in vacuum is denoted by \$c\$ and is a fundamental constant.

  • The relationship between speed, frequency (\$f\$) and wavelength (\$\lambda\$) is \$c = \lambda f\$.

  • Different regions of the EM spectrum are distinguished by their wavelength or frequency, not by speed.

Why Do All EM Waves Have the Same Speed?

James Clerk Maxwell showed that changing electric fields produce magnetic fields and vice‑versa. In empty space these fields propagate without loss, and the resulting wave speed depends only on two fundamental constants: the permittivity of free space (\$\varepsilon0\$) and the permeability of free space (\$\mu0\$). The speed is given by

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

Since \$\varepsilon0\$ and \$\mu0\$ are fixed, every electromagnetic wave, regardless of its wavelength or frequency, travels at the same speed \$c\$.

Speed of Light

The accepted value for the speed of light in vacuum is

\$c = 3.00 \times 10^{8}\ \text{m s}^{-1}\$

Relationship Between Speed, Frequency and Wavelength

For any electromagnetic wave

\$c = \lambda f\$

where

  • \$\lambda\$ = wavelength (metres)

  • \$f\$ = frequency (hertz)

  • \$c\$ = speed of light in vacuum (\$3.00 \times 10^{8}\ \text{m s}^{-1}\$)

Electromagnetic Spectrum

RegionWavelength \$\lambda\$ (m)Frequency \$f\$ (Hz)Typical Uses / Sources
Radio\$10^{3}\$ – \$10^{-1}\$\$10^{5}\$ – \$10^{9}\$Broadcasting, radar, communication
Microwave\$10^{-1}\$ – \$10^{-3}\$\$10^{9}\$ – \$10^{12}\$Cooking, satellite communication, radar
Infrared\$10^{-3}\$ – \$7 \times 10^{-7}\$\$10^{12}\$ – \$4 \times 10^{14}\$Thermal imaging, remote controls
Visible\$7 \times 10^{-7}\$ – \$4 \times 10^{-7}\$\$4 \times 10^{14}\$ – \$7.5 \times 10^{14}\$Human vision, illumination
Ultraviolet\$4 \times 10^{-7}\$ – \$10^{-9}\$\$7.5 \times 10^{14}\$ – \$3 \times 10^{16}\$Sterilisation, sunburn, fluorescence
X‑ray\$10^{-9}\$ – \$10^{-11}\$\$3 \times 10^{16}\$ – \$3 \times 10^{19}\$Medical imaging, security scanners
Gamma\$<10^{-11}\$\$>3 \times 10^{19}\$Radioactive decay, astrophysical phenomena

Sample Calculation

Find the frequency of green light with a wavelength of \$5.00 \times 10^{-7}\ \text{m}\$ (500 nm).

  1. Write the speed‑wavelength‑frequency relation: \$c = \lambda f\$.

  2. Rearrange for frequency: \$f = \dfrac{c}{\lambda}\$.

  3. Substitute the known values:

    \$f = \frac{3.00 \times 10^{8}\ \text{m s}^{-1}}{5.00 \times 10^{-7}\ \text{m}}\$

  4. Calculate:

    \$f = 6.0 \times 10^{14}\ \text{Hz}\$

  5. Interpretation: The green light oscillates \$6.0 \times 10^{14}\$ times each second, yet it still travels at \$c\$.

Suggested diagram: A horizontal bar showing the electromagnetic spectrum from radio waves to gamma rays, with wavelength and frequency scales marked.

Summary

  • All electromagnetic waves, irrespective of type, travel at the constant speed \$c = 3.00 \times 10^{8}\ \text{m s}^{-1}\$ in a vacuum.

  • The differences between regions of the spectrum lie in wavelength and frequency, not in speed.

  • Understanding \$c = \lambda f\$ allows conversion between wavelength and frequency for any EM wave.