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

Electromagnetic Spectrum – Cambridge A‑Level Physics (9702)

Learning Objective

State that all electromagnetic (EM) waves are transverse and that they travel in free space with the same speed c (≈ 3.00 × 10⁸ m s⁻¹).

Key Concepts

  • EM waves consist of mutually perpendicular electric (E) and magnetic (B) fields.

  • The fields oscillate perpendicular to the direction of propagation – therefore EM waves are transverse.

  • In a vacuum every EM wave propagates at the universal speed

    \[

    c=\frac{1}{\sqrt{\mu{0}\varepsilon{0}}}\approx3.00\times10^{8}\ \text{m s}^{-1},

    \]

    where \(\mu{0}=4\pi\times10^{-7}\ \text{H m}^{-1}\) and \(\varepsilon{0}=8.85\times10^{-12}\ \text{F m}^{-1}\).

  • The relationship between wavelength \(\lambda\) and frequency \(f\) is

    \[

    c=\lambda f .

    \]

Transverse Nature of an EM Wave (example)

For a wave travelling in the +x direction:

  • E oscillates in a plane perpendicular to x (e.g., the y‑direction).

  • B oscillates in a plane also perpendicular to x but orthogonal to E (e.g., the z‑direction).

  • The three vectors E, B and the direction of propagation form a right‑handed set.

Polarisation (Section 7.5 of the syllabus)

  • Because EM waves are transverse, the direction of the electric‑field vector can be fixed – this is called linear polarisation.

  • A polarising filter (the “polariser”) transmits only the component of the electric field that is parallel to its transmission axis.

  • If a second filter (the “analyser”) is placed after the polariser and its axis makes an angle \(\theta\) with the polariser, the transmitted intensity is given by Malus’s law

    \[

    I = I_{0}\cos^{2}\theta ,

    \]

    where \(I_{0}\) is the intensity after the first polariser.

  • Polarisation therefore provides a clear experimental confirmation that EM waves are transverse.

Electromagnetic Spectrum – Quick Reference

The table below lists the approximate wavelength and frequency ranges used in the Cambridge syllabus. The values are representative; actual limits can overlap between regions.

RegionWavelength \(\lambda\) (m)Frequency \(f\) (Hz)Typical Uses / Physical Relevance
Radio10⁻¹ – 10³10⁵ – 10⁹Broadcasting, radar, long‑distance communication
Microwave10⁻³ – 10⁻¹10⁹ – 10¹²Satellite links, cooking ovens, radar
Infrared10⁻⁶ – 10⁻³10¹¹ – 10¹⁴Thermal imaging, remote‑control signals, molecular vibration spectroscopy
Visible4 × 10⁻⁷ – 7 × 10⁻⁷4.3 × 10¹⁴ – 7.5 × 10¹⁴Human vision, illumination
Ultraviolet10⁻⁸ – 4 × 10⁻⁷7.5 × 10¹⁴ – 3 × 10¹⁶Sterilisation, fluorescence, ozone absorption
X‑ray10⁻¹¹ – 10⁻⁸3 × 10¹⁶ – 3 × 10¹⁹Medical imaging, crystallography, material analysis
Gamma‑ray< 10⁻¹¹> 3 × 10¹⁹Radioactive decay, astrophysical phenomena, cancer radiotherapy

*The ranges shown are typical/representative values used for teaching; the exact limits of each region are not sharply defined and may overlap.*

Summary

  1. All electromagnetic waves are transverse: the electric field E and magnetic field B are 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 spectrum spans many orders of magnitude in \(\lambda\) and \(f\), but the underlying wave properties (transverse nature, speed c, and the relation \(c=\lambda f\)) are identical for all regions.

  4. Polarisation is a direct consequence of the transverse character; Malus’s law (\(I = I_{0}\cos^{2}\theta\)) quantifies the intensity transmitted through two linear polarisers.

  5. The visible region (≈ 4 × 10⁻⁷ – 7 × 10⁻⁷ m) is the only part of the spectrum that can be perceived directly by the human eye.

Suggested diagram: a transverse EM wave showing E, B, and the direction of propagation, together with a bar chart of the spectrum regions.