Electromagnetic waves and the spectrum
Key idea: All electromagnetic waves are transverse and travel at the same speed in a vacuum. From radio waves to gamma rays, wavelength decreases and frequency increases.
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Guided lessons · coming soon
Guided lesson
Guided steps
- Compare the properties of electromagnetic waves.
- Find the travel time for sunlight.
- Find both probe signals’ travel times and compare arrival.
- Read the seven regions in order.
- Explain why shorter wavelength means higher frequency.
- Recall the seven regions and show increasing frequency.
- Convert and order the three wavelengths.
- Rearrange the wave equation and convert the units.
- Convert megahertz and find the wavelength.
- Convert nanometres and find the frequency.
- Predict the frequency change, then calculate both frequencies.
- Find the phone wavelength and compare the signals’ arrival.
- Find the frequency and compare the waves’ vacuum speeds.
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ContinueRadio, microwaves, light and X-rays seem to have little in common, yet they are all the same kind of wave, travelling at the same speed through empty space. They differ only in wavelength and frequency, which places each one in the electromagnetic spectrum. The calculations use wave speed = frequency × wavelength from General properties of waves.
What all electromagnetic waves have in common
Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays look like very different things. A radio signal passes through the walls of a house; an X-ray passes through your hand; light is the only one your eyes detect. Yet they are all the same kind of wave: an electromagnetic wave, made of changing electric and magnetic fields. Together they form the electromagnetic spectrum.
Every electromagnetic wave shares these properties:
- It is a transverse wave. The electric and magnetic fields oscillate at right angles to the direction the wave travels, just as the particles of a rope move up and down while a pulse travels along it. There is no longitudinal electromagnetic wave.
- It needs no material medium. A wave on a rope or a spring needs the rope or the spring. An electromagnetic wave can travel through a vacuum. Light and infrared from the Sun reach the Earth across about 150 million km of almost empty space.
- It travels at the same speed in a vacuum. Every region, from radio waves to gamma rays, travels at the same speed, c.
In air, electromagnetic waves travel very nearly this fast, so you can use the same value for a signal in air.
Worked example 1
How long does sunlight take to reach the Earth?
Problem
The Sun is 1.5 × 10¹¹ m from the Earth. Find the time light takes to arrive.
Show full solution
Choose the speed
Method
Use c = 3.0 × 10⁸ m/s.Reason
The wave crosses a vacuum, where all electromagnetic waves travel at c.Working
Answer
c = 3.0 × 10⁸ m/s
Find the time
Method
Divide distance by speed.Reason
The speed is constant over the whole journey.Working
Answer
time = (1.5 × 10¹¹)/(3.0 × 10⁸) = 500 s, about 8.3 minutes
Extend to other regions
Working
Answer
The infrared and ultraviolet the Sun emits at the same moment arrive at the same moment too: they have the same speed.
Check your understanding 1
A probe 3.6 × 10⁹ m from Earth emits a radio signal and a visible flash simultaneously towards Earth. Calculate each travel time through space. Which arrives first?
Show answer
Both are electromagnetic waves, so both travel at 3.0 × 10⁸ m/s through space: time = (3.6 × 10⁹)/(3.0 × 10⁸) = 12 s for each. They arrive together; their different frequencies and wavelengths do not change their speed.
The seven regions in order
The regions differ in wavelength and frequency. From radio waves to gamma rays, the wavelength gets shorter and the frequency gets higher.
| Order | Region | Wavelength | Frequency |
|---|---|---|---|
| 1 | radio waves | longest | lowest |
| 2 | microwaves | shorter | higher |
| 3 | infrared | shorter | higher |
| 4 | visible light | shorter | higher |
| 5 | ultraviolet | shorter | higher |
| 6 | X-rays | shorter | higher |
| 7 | gamma rays | shortest | highest |
Read down the table: each region has a shorter wavelength and a higher frequency than the region above it. The table shows order only. The regions do not have equal widths, and neighbouring regions overlap at their edges, so there is no single number at which one region ends and the next begins.
Two names help you place the middle of the spectrum. Within visible light, red has the longest wavelength and violet the shortest. Infrared lies just beyond red (longer wavelength, lower frequency); ultraviolet lies just beyond violet (shorter wavelength, higher frequency).
Why frequency rises as wavelength falls
A wave’s speed is frequency × wavelength. For electromagnetic waves in a vacuum,
Because c is the same for every region, f and λ cannot both be large. If one region has a wavelength ten times shorter than another, its frequency must be ten times higher so that fλ still equals c. So “shorter wavelength” and “higher frequency” describe the same end of the spectrum.
Check your understanding 2
Order the regions from memory. Cover the table. Write the seven regions starting with the longest wavelength. Then put an arrow under your list showing the direction in which frequency increases, and check against the table.
Show answer
radio waves → microwaves → infrared → visible light → ultraviolet → X-rays → gamma rays. Frequency increases in the same direction as your list (towards gamma rays), because wavelength decreases that way. If you mixed up the middle, start from visible light: infrared is on the red side (longer wavelength), ultraviolet on the violet side (shorter wavelength). A memory sentence such as “Raging Martians Invaded Venus Using X-ray Guns” gives the order from radio to gamma.
Placing measured waves in order
Worked example 2
Three signals
Problem
Three records contain one radio signal, one infrared signal and one visible-light signal. Record M has wavelength 20 μm, N has 0.50 μm and P has 2 m. Which is which?
Show full solution
Convert to one unit
Method
Write each wavelength in metres.Reason
Wavelengths can only be compared in the same unit.Working
Answer
M: 2.0 × 10⁻⁵ m; N: 5.0 × 10⁻⁷ m; P: 2 m
Order them
Method
Arrange from longest to shortest wavelength.Reason
Frequency increases as wavelength decreases.Working
Answer
Wavelength decreases in the order P, M, N, so frequency increases in that order.
Name the regions
Method
Match the order to the spectrum.Reason
Radio waves have the longest wavelength and visible light the shortest of these three regions.Working
Answer
P is radio, M is infrared and N is visible light.
Check what made this possible
Working
Answer
The statement that there is one signal from each region is what lets you name them. Three measurements alone give their order, not their regions.
Calculating frequency and wavelength
Use c = fλ with c = 3.0 × 10⁸ m/s for any electromagnetic wave in a vacuum (or in air). Rearranged, λ = c/f and f = c/λ. Convert to hertz and metres before you substitute:
| Given in | Convert with | Example |
|---|---|---|
| kHz, MHz, GHz | 1 kHz = 10³ Hz, 1 MHz = 10⁶ Hz, 1 GHz = 10⁹ Hz | 100 MHz = 1.00 × 10⁸ Hz |
| μm, nm | 1 μm = 10⁻⁶ m, 1 nm = 10⁻⁹ m | 500 nm = 5.0 × 10⁻⁷ m |
Worked example 3
From a radio frequency to a wavelength
Problem
A radio station broadcasts at 100 MHz. Find the wavelength of its waves.
Show full solution
Convert the frequency
Method
Change megahertz to hertz.Reason
The wave equation needs hertz to give metres.Working
Answer
f = 100 MHz = 1.00 × 10⁸ Hz
Find the wavelength
Method
Rearrange c = fλ.Reason
All electromagnetic waves travel at c in air, very nearly.Working
Answer
λ = c/f = (3.0 × 10⁸)/(1.00 × 10⁸) = 3.0 m
Check
Working
Answer
Radio waves have the longest wavelengths in the spectrum, so a wavelength of metres is sensible.
Worked example 4
From a light wavelength to a frequency
Problem
Green light has a wavelength of 500 nm. Find its frequency.
Show full solution
Convert the wavelength
Method
Change nanometres to metres.Reason
The wave equation needs metres to give hertz.Working
Answer
λ = 500 nm = 5.0 × 10⁻⁷ m
Find the frequency
Method
Rearrange c = fλ.Reason
Light travels at c.Working
Answer
f = c/λ = (3.0 × 10⁸)/(5.0 × 10⁻⁷) = 6.0 × 10¹⁴ Hz
Check
Working
Answer
This frequency is about six million times the radio station’s 1.00 × 10⁸ Hz, and the wavelength is six million times shorter. Their product is 3.0 × 10⁸ m/s in both cases.
Check your understanding 3 Predict, then compare wavelength and frequency
Predict how frequency changes when wavelength decreases in a vacuum. Then calculate the frequencies of waves with wavelengths 300 m and 500 nm, using c = 3.0 × 10⁸ m/s.
Show the steps Optional working
You can compare the wavelength and frequency readouts in the EM Spectrum Explorer after making your prediction.
Show answer
Shorter wavelength goes with higher frequency, because the product fλ stays 3.0 × 10⁸ m/s in a vacuum. For the two given wavelengths, 300 m gives 1.0 × 10⁶ Hz, while 500 nm = 5.0 × 10⁻⁷ m gives 6.0 × 10¹⁴ Hz. In both comparisons, a fixed vacuum speed requires frequency and wavelength to change inversely.
If the frequency of a wave doubles, twice as many waves pass each second, so each must be half as long: the wavelength halves and the speed stays the same.
Check your understanding 4
A phone signal has frequency 2.0 GHz. Calculate its wavelength in air using c = 3.0 × 10⁸ m/s. A higher-frequency signal is emitted simultaneously along the same path. Which arrives first?
Show the steps Optional working
Show answer
f = 2.0 × 10⁹ Hz, so λ = (3.0 × 10⁸)/(2.0 × 10⁹) = 0.15 m. They arrive together: both signals travel at 3.0 × 10⁸ m/s. A higher frequency means more waves each second, each with a shorter wavelength, not a faster wave.
Check your understanding 5
A wave in a vacuum has wavelength 0.060 m. Calculate its frequency. Does its shorter wavelength make it travel faster than a longer-wavelength wave?
Show answer
f = c/λ = (3.0 × 10⁸)/0.060 = 5.0 × 10⁹ Hz. A shorter wavelength goes with a higher frequency, so that fλ still equals c. The speed does not change.
Common mistakes
- Saying a higher frequency means a faster wave in a vacuum. Every region travels at the same speed c; frequency and wavelength change together.
- Saying gamma rays have the longest wavelength. Radio waves have the longest; gamma rays have the shortest wavelength and the highest frequency.
- Calling radio waves sound waves. Radio waves are electromagnetic and can cross a vacuum; the radio’s loudspeaker makes the sound.
- Saying electromagnetic waves need air to travel. Light and infrared reach us from the Sun through space.
- Saying some electromagnetic waves are longitudinal. Every electromagnetic wave is transverse.
- Substituting MHz or nm straight into c = fλ. Convert first: 1 MHz = 10⁶ Hz and 1 nm = 10⁻⁹ m.
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Syllabus and review details
- SEC G2 Science Physics component 2027 · 2027
Physics section, PDF pages 8–23
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