Electromagnetic waves are one family of transverse waves that need no medium
Definition
Electromagnetic wave
A transverse wave that transfers energy and can travel through a vacuum, moving at 3.0×108 m/s3.0 \times 10^8\ \text{m/s}3.0×108 m/s when there is no matter in its path.
- Every electromagnetic wave is transverse, so the vibrations are at right angles to the direction in which the wave travels.
- Sound is longitudinal, which is one reason it is not a member of this family.
- Like all waves they transfer energy from one place to another without carrying matter along with them.
- They need no medium, so they pass happily through a vacuum in which there are no particles at all.
- That is why light and infrared from the Sun cross about 1.5×1011 m1.5 \times 10^{11}\ \text{m}1.5×1011 m of empty space and still reach your skin, while a bang on the Sun could never be heard here.
Radio waves sit at one end of the family and gamma rays at the other
Definition
Electromagnetic spectrum
The continuous range of all electromagnetic waves, arranged in order of frequency or of wavelength, running from radio waves at one end to gamma rays at the other.
- In order of increasing frequency, the main regions are radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays.
- In order of increasing wavelength that same list runs backwards: gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves and radio waves.
- Radio waves have the longest wavelength and the lowest frequency of any electromagnetic wave.
- Gamma rays have the shortest wavelength and the highest frequency.
- Visible light is a narrow band near the middle, with red at its long-wavelength edge and violet at its short-wavelength edge, as the colours spread out by a prism already show.
- Infrared lies just beyond red and ultraviolet just beyond violet, which is exactly where the two names come from.
The wavelengths shrink from kilometres down to less than a million millionth of a metre
- Radio waves run from kilometres down to about 1 m1\ \text{m}1 m, and a long-wave broadcast has a wavelength near 1500 m1500\ \text{m}1500 m.
- Microwaves are a few centimetres across, typically about 3 cm3\ \text{cm}3 cm, which is 3×10−2 m3 \times 10^{-2}\ \text{m}3×10−2 m.
- Infrared is around 10−5 m10^{-5}\ \text{m}10−5 m, about a tenth of the width of a human hair.
- Visible light runs from roughly 700 nm700\ \text{nm}700 nm at the red end to roughly 400 nm400\ \text{nm}400 nm at the violet end.
- Written in metres, that band is 7×10−7 m7 \times 10^{-7}\ \text{m}7×10−7 m down to 4×10−7 m4 \times 10^{-7}\ \text{m}4×10−7 m.
- Ultraviolet is around 10−8 m10^{-8}\ \text{m}10−8 m and X-rays around 10−10 m10^{-10}\ \text{m}10−10 m, which is about the width of one atom.
- Gamma rays reach down to about 10−12 m10^{-12}\ \text{m}10−12 m and shorter still.
- From one end of the family to the other the wavelength therefore changes by a factor of about 101510^{15}1015, even though the speed never changes at all.
A fixed speed forces frequency and wavelength to trade off against each other
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All electromagnetic waves travel at the same high speed in a vacuum, whatever their frequency or wavelength.
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That speed has the value:
v=3.0×108 m/s v = 3.0 \times 10^8\ \text{m/s} v=3.0×108 m/s -
The speed in air is approximately the same, so you can safely use 3.0×108 m/s3.0 \times 10^8\ \text{m/s}3.0×108 m/s for a wave crossing the atmosphere.
- Light does slow down on entering glass or water, so that value belongs to a vacuum and to air only.
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The three quantities are tied together by the wave equation:
v=fλ v = f\lambda v=fλ -
Because vvv is pinned at 3.0×108 m/s3.0 \times 10^8\ \text{m/s}3.0×108 m/s, the frequency fff and the wavelength λ\lambdaλ are inversely proportional: multiply one by ten and the other divides by ten.
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Substituting a radio frequency of 1.0 MHz1.0\ \text{MHz}1.0 MHz gives λ=3.0×1081.0×106=300 m\lambda = \dfrac{3.0 \times 10^8}{1.0 \times 10^6} = 300\ \text{m}λ=1.0×1063.0×108=300 m, while an X-ray frequency of 1.0×1018 Hz1.0 \times 10^{18}\ \text{Hz}1.0×1018 Hz gives λ=3.0×10−10 m\lambda = 3.0 \times 10^{-10}\ \text{m}λ=3.0×10−10 m.
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A high frequency and a short wavelength always arrive together, and neither wave is moving any faster than the other.
The named regions are labels on a continuous scale, not seven separate kinds of wave
- The spectrum is continuous, with no gaps and no missing wavelengths anywhere between radio and gamma.
- The boundaries between the named regions are agreed conventions rather than physical walls in nature.
- A wave of wavelength about 10−9 m10^{-9}\ \text{m}10−9 m sits where ultraviolet meets X-rays, and either name can fairly be used for it.
- Neighbouring regions overlap in what they can do, so the shortest ultraviolet and the longest X-rays behave in much the same way.
- The same blurring happens at the long end, where the shortest radio waves and the longest microwaves are hard to tell apart.
- Moving from one region to the next tells you the frequency and wavelength have changed, not that you are now handling a different type of wave.
Common Mistake
- Do not imagine radio waves crawling along while gamma rays race ahead, because in a vacuum every region moves at 3.0×108 m/s3.0 \times 10^8\ \text{m/s}3.0×108 m/s.
- Never describe an electromagnetic wave as longitudinal, since every region of the spectrum is transverse.
- Do not treat the seven names as seven different kinds of wave, because they are one continuous family split up by convenient labels.
- Check which direction a question asks for before writing the list out, because the frequency order and the wavelength order are exact reverses of each other.
- Do not quote 3.0×108 m/s3.0 \times 10^8\ \text{m/s}3.0×108 m/s as the speed of light inside glass or water, where light travels more slowly.
Exam technique
- When a question says increasing frequency, begin at radio waves; when it says increasing wavelength, begin at gamma rays, and write all seven names in full rather than abbreviating them.
- Comparing two regions is worth the phrase same high speed in a vacuum, because a vague answer such as "both are very fast" scores nothing.
- Quote the speed with its unit attached as 3.0×108 m/s3.0 \times 10^8\ \text{m/s}3.0×108 m/s, since a bare 3.0×1083.0 \times 10^83.0×108 can cost you the mark.
- Convert MHz\text{MHz}MHz or GHz\text{GHz}GHz into Hz\text{Hz}Hz, and nm\text{nm}nm into m\text{m}m, before you substitute anything into v=fλv = f\lambdav=fλ.
- Asked why a higher frequency means a shorter wavelength, say that the speed is the same for all these waves and then quote v=fλv = f\lambdav=fλ, rather than only asserting that the two are inversely related.
Self review
- Which region has the longest wavelength, and which has the highest frequency?
- What is the speed of every electromagnetic wave in a vacuum, and how does that compare with its speed in air?
- A microwave has a wavelength of 3.0 cm3.0\ \text{cm}3.0 cm, so what is its frequency?
- Why does the order by frequency come out as the exact reverse of the order by wavelength?
- What does it mean to say the spectrum is continuous, and why can a wave near a boundary carry either name?
