The light warming your face, the radio in the car, the X-ray of a broken wrist and the microwave reheating dinner are all the same kind of wave. They differ in one number only — their frequency. Every one of them crosses empty space at exactly the same colossal speed, and every one of them is built from two invisible fields taking turns to wobble.
📘 What you need to know
An EM wave is made by the combined oscillation of an electric field and a magnetic field
The two fields are perpendicular to each other and to the direction of energy transfer
EM waves are transverse, so they can travel through a vacuum — no medium needed
In a vacuum every EM wave travels at the speed of light, c = 3.00 × 108 m s−1
Use c = fλ to swap between frequency and wavelength
Shorter wavelength → higher frequency → more energy
The visible spectrum runs from about 400 nm (violet) to 700 nm (red)
What is an electromagnetic wave?
Sound needed air. A wave on a rope needed the rope. An electromagnetic wave needs nothing at all — because the thing doing the oscillating isn’t matter, it’s a pair of fields.
An oscillating charged particle creates a wobbling electric field. A changing electric field creates a changing magnetic field, which in turn regenerates the electric field a little further along. The two fields keep handing energy back and forth, and the whole package sails away from the source.
The electric field (red) oscillates in one plane, the magnetic field (blue) in a plane at 90° to it, and the wave travels at 90° to both. All three directions are mutually perpendicular.
Because the fields oscillate across the direction of travel, every electromagnetic wave is a transverse wave. And because nothing material has to move, an EM wave is perfectly happy crossing a vacuum.
Hold your thumb, first finger and middle finger at right angles like a little 3D axis. Thumb = electric field, finger = magnetic field, middle finger = the way the wave goes. That’s the picture the examiner wants when they ask you to describe an EM wave — two fields, mutually perpendicular, both perpendicular to the travel direction.
They all travel at the speed of light
Here is the remarkable part. A gamma ray and a radio wave look nothing alike, yet in a vacuum they travel at exactly the same speed:
The speed of light in a vacuumc = 3.00 × 108 m s−1c = fλ
This is just the wave equation v = fλ with the speed already known. So for EM waves, frequency and wavelength are locked together: fix one and the other follows instantly. That single fact answers most spectrum questions.
Wavelength λ metres
c = fλ
Frequency f hertz
higher f means
More energy per wave
The spectrum
EM waves form a continuous spectrum. We chop it into named regions purely for convenience — there is no sudden physical change at the boundaries. Ordered from shortest wavelength to longest:
Visible light is a startlingly thin slice of the whole spectrum — expanded here from violet (400 nm) to red (700 nm). Everything to its left carries more energy per wave.
Region
Typical wavelength
Where you meet it
Gamma rays
Below 10−12 m
Radioactive decay, cancer treatment
X-rays
10−12 – 10−8 m
Medical imaging, airport scanners
Ultraviolet
10−8 – 4 × 10−7 m
Sunburn, sterilising equipment
Visible light
4 × 10−7 – 7 × 10−7 m
Everything you can see
Infrared
7 × 10−7 – 10−3 m
Heat, TV remotes, thermal cameras
Microwaves
10−3 – 10−1 m
Ovens, mobile phones, Wi-Fi
Radio waves
Above 10−1 m
Broadcasting, radio astronomy
Ordering trick: from longest wavelength to shortest — Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma. “Rich Men In Vegas Use eXpensive Gadgets.” Energy climbs as you walk down that list.
You are not expected to memorise the wavelengths — the spectrum is printed in your data booklet. What you must know by heart is that every EM wave travels at c in a vacuum, and that shorter wavelength means higher frequency and more energy. Gamma rays are dangerous precisely because they sit at the energetic end.
Working with c = fλ
📏 Getting the units right
Nanometres to metres: divide by 109. So 550 nm = 550 × 10−9 = 5.5 × 10−7 m.
kHz, MHz, GHz to hertz: multiply by 103, 106, 109.
Then substitute into c = fλ, rearranging first if you need to.
Sanity-check the answer. Visible light should come out around 1014 Hz; radio around 108 Hz.
WE 1
Green light has a wavelength of 550 nm. Calculate its frequency, taking c = 3.00 × 108 m s⁻¹.
Step 1 — convert nanometres to metres
λ = 550 nm = 5.5 × 10⁻⁷ m
Step 2 — rearrange c = fλ for f
f = c / λ
Step 3 — substitutef = (3.00 × 10⁸) / (5.5 × 10⁻⁷)f = 5.5 × 10¹⁴ HzRight in the middle of the 10¹⁴ Hz band, exactly where visible light belongs. Good sign.
WE 2
An FM radio station broadcasts at 100 MHz. Calculate the wavelength of the wave it transmits.
Step 1 — convert megahertz to hertz
f = 100 MHz = 1.00 × 10⁸ Hz
Step 2 — rearrange c = fλ for λ
λ = c / f
Step 3 — substituteλ = (3.00 × 10⁸) / (1.00 × 10⁸)λ = 3.0 mA radio wave metres long — about ten million times longer than green light, from the very same equation.
WE 3
The Sun is 1.5 × 1011 m from the Earth. Calculate how long its light takes to reach us, and state whether an X-ray from the Sun would arrive sooner.
Step 1 — light crosses a vacuum, so it travels at c
t = d / c
Step 2 — substitutet = (1.5 × 10¹¹) / (3.00 × 10⁸) = 500 st = 500 s ≈ 8.3 minutesStep 3 — the X-ray
All EM waves travel at c in a vacuum, so it arrives at the same time.
Higher energy does not mean higher speed. Sunlight you see now left the Sun over eight minutes ago.
Mechanical waves vs electromagnetic waves
With sound and light both behind us, the whole wave model can be split cleanly in two:
Feature
Mechanical waves
Electromagnetic waves
Need a medium?
Yes — a solid, liquid or gas
No
Travel through a vacuum?
No
Yes
Type
Transverse or longitudinal
Always transverse
Produced by
Oscillating particles of a medium
Oscillating charged particles
Speed
Far slower than light; depends on the medium
Always c in a vacuum
Examples
Sound, water waves, seismic waves
Radio, visible light, UV, X-rays
Careful: mechanical does not mean longitudinal. Sound is a longitudinal mechanical wave, but water waves and seismic S-waves are transverse mechanical waves. Only the electromagnetic family is transverse without exception.
💡 Top tips
c = fλ is the wave equation with the speed handed to you — learn it as a rearrangement drill.
Convert nm → m and MHz → Hzbefore substituting. This is where most marks are lost.
Describe an EM wave with three perpendicular directions: E field, B field, direction of travel.
The spectrum order and wavelengths are in the data booklet — but c and the energy trend are not.
Check your answer’s order of magnitude against the region you expect.
⚠ Common mistakes
Thinking gamma rays travel faster than radio waves — in a vacuum, all EM waves travel at c
Saying EM waves are longitudinal — they are always transverse
Believing EM waves need a medium — the fields are the wave, so a vacuum is fine
Forgetting the nanometre conversion, giving answers 109 times too big or small
Assuming bigger amplitude means more energetic radiation — for EM waves, energy per wave is set by frequency
Placing the visible band at the low-frequency end — it sits between UV and infrared
Quick recap: An EM wave is an electric field and a magnetic field oscillating perpendicular to each other and to the direction of travel, so it is transverse and needs no medium. In a vacuum every EM wave travels at c = 3.00 × 108 m s−1, linking frequency and wavelength through c = fλ. Shorter λ means higher f and more energy, running from radio at one end to gamma at the other, with visible light (400–700 nm) as a thin slice in between.
That completes the wave model: you can now describe any wave, sort it into transverse or longitudinal, and handle both sound and light. Next comes the fun part — what waves actually do. What happens when a wave hits a boundary, bends into a new material, squeezes through a gap, or meets another wave head-on? That’s wave behaviour, and it starts on the next page.
Ready to master waves properly?
Book a free meeting and we’ll drill c = fλ, the spectrum and past-paper wave questions until they’re second nature.
