Know that the speed of electromagnetic waves in a vacuum is 3.0 × 10^8 m/s and is approximately the same in air

3.3 Electromagnetic Spectrum

Learning Objective (AO1)

State that electromagnetic (EM) waves travel at a speed of c = 3.0 × 10⁸ m s⁻¹ in vacuum and that the speed in ordinary air is ≈ 2.999 × 10⁸ m s⁻¹ (0.9997 c). The difference is <0.03 % and is therefore negligible for IGCSE calculations.

Key Concepts

  • EM waves do not need a material medium; they can propagate through vacuum.

  • All EM waves obey the universal relationship c = λ f (or v = λ f in any medium), where

    • λ = wavelength (m)

    • f = frequency (Hz)

    • c or v = speed of the wave in the medium.

  • In air the refractive index is n ≈ 1.0003. Using v = c/n gives

    \[

    v = \frac{3.0\times10^{8}}{1.0003}\approx2.999\times10^{8}\;\text{m s}^{-1}=0.9997c

    \]

    For all IGCSE work we may simply use c = 3.0 × 10⁸ m s⁻¹.

  • The spectrum is ordered increasing frequency / decreasing wavelength: radio → microwave → infrared → visible → ultraviolet → X‑ray → γ‑ray.

  • Each region has characteristic applications and, for some, health hazards. The table below follows the exact ordering and wording of the Cambridge syllabus.

Electromagnetic Spectrum Overview

RegionTypical λ (m)Typical f (Hz)Common Uses / Applications (syllabus wording)Health Hazard (syllabus wording)
Radio10⁻¹ – 10³10⁶ – 10⁹Radio & TV broadcasting, RFID tags, mobile‑phone base‑station links, satellite communication (UHF/VHF)Non‑ionising – no known health risk
Microwave10⁻³ – 10⁻¹10⁹ – 10¹²Microwave ovens, radar, satellite phones, Wi‑Fi, mobile‑phone cellular networks (≈ 2.4 GHz & 5 GHz)Non‑ionising – internal heating of body cells; high‑power exposure can cause burns
Infrared (IR)10⁻⁶ – 10⁻³10¹² – 10¹⁴Remote controls, thermal‑imaging cameras, fibre‑optic communication (near‑IR), heating panelsNon‑ionising – skin burns at very high intensity
Visible4 × 10⁻⁷ – 7 × 10⁻⁷4.3 × 10¹⁴ – 7.5 × 10¹⁴Photography, illumination, displays, optical fibres (glass), laser pointersNon‑ionising – bright light can damage eyes; lasers are hazardous
Ultraviolet (UV)10⁻⁸ – 4 × 10⁻⁷7.5 × 10¹⁴ – 3 × 10¹⁶Sterilisation, fluorescent lamps, sun‑burn protection (sunscreen), UV curing, satellite TVPartly ionising – skin‑cancer & eye damage (photokeratitis)
X‑ray10⁻¹¹ – 10⁻⁸3 × 10¹⁶ – 3 × 10¹⁹Medical imaging, security scanners, crystallographyIonising – DNA damage, mutation; requires shielding and limited exposure
Gamma‑ray (γ‑ray)< 10⁻¹¹> 3 × 10¹⁹Cancer radiotherapy, food sterilisation, astrophysical observationsHighly ionising – severe health risk; used only under strict safety controls

Deriving and Using the Relationship c = λ f (AO1)

All EM waves travel the same distance in a given time when they are in the same medium. By definition:

  • Speed = distance ÷ time.

  • One complete wave cycle travels one wavelength (λ) in one period (T).

  • Frequency f = 1/T.

Hence:

\[

c = \frac{\lambda}{T} = \lambda\,f

\]

This relationship holds for every region of the spectrum, from radio waves to γ‑rays.

Worked Example 1 – Frequency from Wavelength

Find the frequency of a radio wave with λ = 0.5 m (air).

\[

f = \frac{c}{\lambda}

= \frac{3.0 \times 10^{8}\ \text{m s}^{-1}}{0.5\ \text{m}}

= 6.0 \times 10^{8}\ \text{Hz}

\]

Worked Example 2 – Wavelength from Frequency

A mobile‑phone signal has f = 2.4 GHz. Determine λ in air.

\[

\lambda = \frac{c}{f}

= \frac{3.0 \times 10^{8}\ \text{m s}^{-1}}{2.4 \times 10^{9}\ \text{Hz}}

= 0.125\ \text{m}\;(12.5\ \text{cm})

\]

Syllabus Note (AO2 – handling information): Digital vs. Analogue Signals

  • Analogue – amplitude and/or frequency varies continuously (e.g., traditional AM/FM radio, analogue TV).

  • Digital – information is represented by discrete values (0 or 1) and transmitted as pulses of EM waves (e.g., digital TV, mobile data, Wi‑Fi).

  • Both travel at the same speed c; the difference lies only in the encoding of information.

Exam‑style question: “Identify whether the signal shown in the diagram is digital or analogue and state one advantage of the chosen type.”

Optical Fibre – A Practical Use of the Visible & Near‑IR Spectrum (AO2)

  • Glass or plastic fibres guide light (λ ≈ 0.85 µm – 1.55 µm) by total internal reflection.

  • Because the light is confined, loss is very low, allowing high‑speed data transmission over long distances.

  • Relevant syllabus point: “use of optical fibres for telecommunications”.

Common Exam‑Style Questions (AO1 & AO2)

  1. State the speed of light in vacuum and in ordinary air (to 3 s.f.).

  2. Calculate the wavelength of a microwave used for a satellite link with frequency = 12 GHz.

  3. Identify the part of the spectrum used for:

    • TV broadcasting

    • Microwave ovens

    • Medical X‑ray imaging

  4. Explain why the speed of EM waves in air can be taken as 3.0 × 10⁸ m s⁻¹ for most IGCSE calculations.

  5. List two health hazards associated with UV radiation and two with X‑rays.

  6. State whether the signal shown below is digital or analogue and give one advantage of the type you chose.

Summary (AO1)

  • Speed of EM waves in vacuum: c = 3.0 × 10⁸ m s⁻¹**.

  • In ordinary air: ≈ 2.999 × 10⁸ m s⁻¹ (0.9997 c); the 0.03 % difference is negligible for exam work.

  • The universal relationship c = λ f applies to all regions of the spectrum.

  • Ordering of the spectrum is increasing frequency / decreasing wavelength from radio to γ‑ray.

  • Applications range from radio/TV broadcasting to optical‑fibre telecommunications; health hazards are non‑ionising for radio‑microwave‑IR‑visible, partially ionising for UV, and ionising for X‑rays/γ‑rays.

  • Digital and analogue signals both travel at c; the distinction lies in how information is encoded.