IB Physics SLTopic C.2 — Modelling WavesPaper 1 & 2c = 3 × 10⁸ m s⁻¹~8 min read
The Electromagnetic Spectrum
Light, radio, X-rays and the warmth of the Sun are all the same kind of wave — an electromagnetic wave. They differ only in wavelength, they’re all transverse, they all cross empty space, and they all travel at one universal speed.
📘 What you need to know
An EM wave is a combined oscillation of an electric field and a magnetic field
The two fields oscillate perpendicular to each other and to the direction of travel
EM waves are transverse, so they can travel through a vacuum
In a vacuum they all travel at the speed of light, c = 3 × 10⁸ m s⁻¹, whatever their frequency
They form a continuous spectrum: radio → microwave → infrared → visible → ultraviolet → X-ray → gamma
Shorter wavelength (higher frequency) means higher energy
What an Electromagnetic Wave Is
Unlike sound, an EM wave carries no vibrating particles — it’s a self-sustaining ripple of fields. A changing electric field creates a changing magnetic field, which recreates the electric field, and so on, leapfrogging through space. The two fields oscillate at right angles to each other, and both are at right angles to the direction the wave travels.
The electric field E (red) and magnetic field B (blue) oscillate in planes at right angles to each other, and both are perpendicular to the direction of travel.
Because they’re transverse and made of fields rather than matter, EM waves need no medium — they travel happily through the vacuum of space. And no matter their frequency, in a vacuum they all move at the same speed:
Speed of light in a vacuumc = 3.00 × 10⁸ m s⁻¹ (andc = fλ)
The Spectrum, End to End
Line the EM waves up by wavelength and you get a continuous spectrum. At one end sit gamma rays with tiny wavelengths and huge energy; at the other end sit radio waves with wavelengths that can be metres or kilometres long. The narrow band our eyes can detect — the visible spectrum — is just a sliver in the middle, running from about 400 nm (violet) to 700 nm (red).
The full EM spectrum. Wavelength grows to the right; frequency and energy grow to the left. The visible band (400–700 nm) is only a thin slice in the middle.
You don’t have to memorise the exact wavelengths — they’re in your data booklet — but you do need the order, and you must remember that every one of them travels at c in a vacuum. Their frequencies come straight from the wave equation, c = fλ.
Mechanical vs Electromagnetic Waves
It’s worth keeping the two big wave families straight, because exam questions love to compare them.
Mechanical waves
Need a medium (solid, liquid or gas) and cannot cross a vacuum
Can be transverse or longitudinal
Made by particles of the medium oscillating
Travel far slower than light; examples: sound, water and seismic waves
Electromagnetic waves
No medium needed — they can travel through a vacuum
Are only transverse
Made by oscillating charged particles (changing electric and magnetic fields)
All travel at the speed of light; examples: radio, UV, X-rays
Quick recap: EM waves are transverse field oscillations that cross a vacuum at c = 3 × 10⁸ m s⁻¹; shorter wavelength means higher frequency and energy, from radio (long) up to gamma (short).
WE 1
Blue light has wavelengths between 450 nm and 490 nm. The speed of light is 3.00 × 10⁸ m s⁻¹.
Determine the range of frequencies of blue light.
Set up
Convert: 450 nm = 4.5 × 10⁻⁷ m, 490 nm = 4.9 × 10⁻⁷ m. Use f = c/λ
Lowest frequency (longest λ)f = (3.00 × 10⁸) ÷ (4.9 × 10⁻⁷)f ≈ 6.1 × 10¹⁴ HzHighest frequency (shortest λ)f = (3.00 × 10⁸) ÷ (4.5 × 10⁻⁷)f ≈ 6.7 × 10¹⁴ HzSo blue light spans roughly 6.1 × 10¹⁴ to 6.7 × 10¹⁴ Hz — shorter wavelength, higher frequency.
WE 2
A radio station broadcasts at a frequency of 100 MHz.
Calculate the wavelength of the radio waves in air (take the speed as 3.00 × 10⁸ m s⁻¹).
Use the wave equation
Rearrange c = fλ to λ = c/f, with f = 100 MHz = 1.0 × 10⁸ Hz
λ = (3.00 × 10⁸) ÷ (1.0 × 10⁸)λ = 3.0 mMetres long — exactly what you’d expect from the radio end of the spectrum.
💡 Top tips
Learn the order of the spectrum (radio → gamma), not the exact wavelengths — those are in the data booklet
Every EM wave travels at c = 3 × 10⁸ m s⁻¹ in a vacuum — a reliable mark-earner
Shorter wavelength ⇒ higher frequency ⇒ higher energy (gamma is the extreme)
Visible light is just 400–700 nm — a tiny part of the whole spectrum
Convert nm to m (× 10⁻⁹) before using c = fλ
⚠ Common mistakes
Thinking different EM waves travel at different speeds — in a vacuum they’re all c
Assuming EM waves need a medium; they don’t, which is how sunlight reaches us
Believing all mechanical waves are longitudinal — water and seismic waves can be transverse
Getting the energy trend backwards; short wavelength means high energy, not low
Forgetting the nm → m conversion in frequency calculations
That completes the Wave Model — you can now describe any wave, tell transverse from longitudinal, and place sound and light in their families. Next we’ll see what happens when waves meet obstacles and each other, in Wave Phenomena.
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