7.4 - The electromagnetic spectrum

7.4 - The electromagnetic spectrum

Recognise electromagnetic waves as one transverse-wave family with a common speed in free space. Learn the approximate wavelength ranges of its principal regions, use frequency and wavelength to identify clear examples, and recall the visible range of 400–700 nm.

One wave family and one vacuum speed

If a radio pulse and a visible flash cross the same vacuum distance after leaving together, which arrives first? Neither wins. Different electromagnetic frequencies have the same propagation speed in free space.

Electromagnetic waves are transverse waves. Their electric and magnetic field variations are perpendicular to their propagation direction; they are not oscillations of air or another material medium. They can transfer energy across a vacuum, unlike sound in air.

All electromagnetic waves travel in free space at speed cc. The examination data sheet gives c=3.00×108 m s−1c=3.00\times10^{8}\,\mathrm{m\,s^{-1}}. Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays share that speed. Their frequencies and wavelengths differ, rather than their vacuum speeds.

Electromagnetic wavelength and frequency

c=fλc=f\lambda

Here cc is the speed in free space in m s−1\mathrm{m\,s^{-1}}, ff is frequency in Hz\mathrm{Hz}, and λ\lambda is wavelength in free space in m\mathrm{m}. Higher frequency means shorter wavelength when cc is fixed.

The value of cc is on the data sheet. The wave equation is not on the data sheet: learn it.

Worked example 1: a radio wavelength

Question. An electromagnetic signal has frequency 100 MHz100\,\mathrm{MHz}. Calculate its wavelength in free space, using c=3.00×108 m s−1c=3.00\times10^{8}\,\mathrm{m\,s^{-1}}.

Plan. Convert megahertz to hertz and rearrange the wave equation.

λ=cf=3.00×108100×106 m=3.00 m\lambda=\frac{c}{f} =\frac{3.00\times10^{8}}{100\times10^{6}}\,\mathrm{m} =3.00\,\mathrm{m}

Answer. 3.00 m3.00\,\mathrm{m}.

Check. One hundred million wavelengths of three metres pass each second, consistent with the free-space speed.

For comparison, radiation of wavelength 2.0 μm2.0\,\mathrm{\mu m} has frequency c/λ=1.5×1014 Hzc/\lambda=1.5\times10^{14}\,\mathrm{Hz}. Its much greater frequency does not give it a greater vacuum speed.

Model limit

The common-speed statement is for free space. Electromagnetic waves can travel more slowly in a material, and their speed there can depend on frequency. Do not substitute a material wavelength into a free-space classification without considering that difference.

Approximate wavelength ranges

The electromagnetic spectrum is continuous. Its named regions are useful divisions of that spectrum, rather than seven different propagation mechanisms. Learn the sequence and the approximate length scales together.

From long to short wavelength, the order is radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Frequency increases in the opposite direction. Do not reverse the frequency order simply because a diagram's wavelength axis runs the other way.

Principal regionApproximate free-space wavelength rangeA clear example
Radioroughly 10−1 m10^{-1}\,\mathrm{m} to 106 m10^{6}\,\mathrm{m} and longer100 m100\,\mathrm{m}
Microwaveroughly 10−3 m10^{-3}\,\mathrm{m} to 10−1 m10^{-1}\,\mathrm{m}10−2 m10^{-2}\,\mathrm{m}
Infraredabout 7×10−7 m7\times10^{-7}\,\mathrm{m} to 10−3 m10^{-3}\,\mathrm{m}10−5 m10^{-5}\,\mathrm{m}
Visible4×10−7 m4\times10^{-7}\,\mathrm{m} to 7×10−7 m7\times10^{-7}\,\mathrm{m}5×10−7 m5\times10^{-7}\,\mathrm{m}
Ultravioletroughly 10−8 m10^{-8}\,\mathrm{m} to 4×10−7 m4\times10^{-7}\,\mathrm{m}10−7 m10^{-7}\,\mathrm{m}
X-rayroughly 10−13 m10^{-13}\,\mathrm{m} to 10−8 m10^{-8}\,\mathrm{m}10−10 m10^{-10}\,\mathrm{m}
Gamma raytypically below about 10−10 m10^{-10}\,\mathrm{m}, extending far shorter10−14 m10^{-14}\,\mathrm{m}

The ranges are approximate and conventional; X-ray and gamma wavelengths overlap. Their names can also reflect how the radiation is generated. Do not treat an arbitrary boundary as a sudden physical change, or assume an overlapping wavelength alone always distinguishes an X-ray from a gamma ray.

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