The big idea: An electromagnetic (EM) wave is a wave of vibrating electric and magnetic fields — light is one example.
Every EM wave is transverse (the fields wobble at right angles to the direction it travels), and in a vacuum they all travel at the same speed, c = 3.00 × 10⁸ m s⁻¹.
The EM spectrum is the whole family, sorted by wavelength (and so by frequency).
New words: Wavelength λ — the length of one full wave (m). Frequency f — how many waves pass each second (hertz, Hz).
Transverse — the wave's vibration is across (perpendicular to) the way it travels. Vacuum — empty space, no air or material.
| Region | Wavelength | Frequency | Everyday use |
|---|---|---|---|
| Radio | longest | lowest | TV, radio, phone signals |
| Microwave | ↓ | ↑ | ovens, wifi, radar |
| Infrared (IR) | ↓ | ↑ | heat, remote controls, night vision |
| Visible | ≈ 400–700 nm | ↕ | the light your eyes see |
| Ultraviolet (UV) | ↓ | ↑ | suntan, sterilising |
| X-ray | ↓ | ↑ | seeing bones |
| Gamma (γ) | shortest | highest | from nuclei, cancer treatment |
Remember the order: Radio → Micro → Infrared → Visible → Ultraviolet → X-ray → Gamma.
Going that way: wavelength gets shorter, frequency gets higher, and energy gets higher. A handy phrase: Rock Music Is Very Useful for eXtra Groove.
For any wave, the speed equals the frequency times the wavelength. This is the wave equation, and it is given in the data booklet.
- wave speed (m s⁻¹) — for EM waves in vacuum this is c
- frequency (Hz) — waves passing each second
- wavelength (m) — length of one full wave
For EM waves the speed is c: In a vacuum every EM wave travels at the speed of light, c = 3.00 × 10⁸ m s⁻¹ (a given constant).
So for EM waves the wave equation becomes:
c = f λ
Rearrange it to find whichever one is missing.
- speed of light in vacuum = 3.00 × 10⁸ m s⁻¹ (a given constant)
- frequency (Hz)
- wavelength (m)
[Diagram: phys-formula-triangle] - Available in full study mode
Worked example — frequency of a wave from its wavelength
A microwave used by a phone mast has a wavelength of 0.15 m in air. Treating the speed as c = 3.00 × 10⁸ m s⁻¹, find its frequency.
Solution
- Start with the given wave equation for an EM wave:
- Rearrange to make f the subject:
- Put in the numbers (c = 3.00 × 10⁸, λ = 0.15):
- Work it out — keep the unit:
Final answer
frequency f = 2.0 × 10⁹ Hz (2.0 GHz) — a microwave, just as expected.
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How this is tested: EM-spectrum questions are quick identify / outline marks.
- Paper 1A: given a wavelength or frequency, name the region (e.g. λ ≈ one atom across → an X-ray); state that EM waves are transverse. - Paper 2: outline a difference between sound and EM waves — e.g. EM waves travel through a vacuum but sound needs a medium.
Classic trap: thinking different colours or regions travel at different speeds. In a vacuum they all travel at c.
Sound waves (mechanical)
- Longitudinal (vibrate along the travel direction)
- Need a medium — cannot cross a vacuum
- Speed ≈ 340 m s⁻¹ in air (much slower)
- It is the air particles that oscillate
EM waves (e.g. light)
- Transverse (vibrate across the travel direction)
- Travel through a vacuum — no medium needed
- Speed = c = 3.00 × 10⁸ m s⁻¹ in vacuum
- It is electric & magnetic fields that oscillate
Why f against 1/λ is a straight line: Since c = f λ, dividing by λ gives f = c × (1/λ) — the form y = (slope) x.
So a graph of f against 1/λ is a straight line through the origin whose slope is c, the same for every EM region.
IB-style question — identify the spectral region
A physicist studies an EM wave whose wavelength is about 1 × 10⁻¹⁰ m (roughly the diameter of a single atom). Using c = 3.00 × 10⁸ m s⁻¹, find the wave's frequency and state which region of the EM spectrum it belongs to.
Solution
- Use the given wave equation for an EM wave:
- Rearrange to make f the subject:
- Put in the numbers (c = 3.00 × 10⁸, λ = 1 × 10⁻¹⁰):
- Work it out — keep the unit:
- A wavelength near one atom across (≈ 10⁻¹⁰ m), so high a frequency — that is an X-ray.
Final answer
f ≈ 3 × 10¹⁸ Hz; the region is X-rays (atom-sized wavelength ⇒ very high frequency).