Electromagnetic Waves
Light, radio, X-rays, the heat from the sun β they are all the same thing travelling at the same speed. This lesson takes you from what a wave is all the way to the full spectrum, with things you can drag, slide, and test yourself on.
Use β β arrow keys to move between sections. Your progress saves automatically on this computer.
What is a wave?
A wave is a disturbance that carries energy from one place to another β without carrying the material along with it. Drop a stone in a puddle: the ripple travels outward, but the water itself just bobs up and down.
Mechanical Waves
They need a medium β solid, liquid, or gas β to travel.
- Sound waves (need air)
- Water waves
- Waves on a guitar string
- Earthquake waves
Electromagnetic Waves
They need no medium at all. They travel through empty space.
- Radio, microwaves, infrared
- Visible light
- UV, X-rays, gamma rays
- Sunlight crossing 150 million km of vacuum
Remember
In space, no one can hear you scream β but they can see you. Sound is mechanical and dies in a vacuum. Light is electromagnetic and sails right through. That is the single biggest difference between them.
Try it: the parts of a wave
Move the sliders and watch the wave change. Notice what happens to the number of waves on screen when you shorten the wavelength.
Crest
The highest point of the wave.
Trough
The lowest point of the wave.
Wavelength
Crest to crest, in metres.
Amplitude
Rest line to crest β the energy carried.
How an EM wave is made
Shake an electric charge back and forth. The moving charge makes a changing electric field. A changing electric field creates a changing magnetic field β which creates another electric field, and so on. The two fields keep regenerating each other and the whole package flies off through space.
Perpendicular
The electric field (red) and magnetic field (blue) are at right angles to each other and to the direction of travel.
Transverse
The vibration is sideways to the travel direction. Every EM wave is transverse β never longitudinal like sound.
Always 3 Γ 10βΈ m/s
In a vacuum, every EM wave moves at the speed of light. Radio is not slower than gamma β only its wavelength is longer.
The people who figured it out
| Year | Scientist | Contribution |
|---|---|---|
| 1666 | Isaac Newton | Split white light into ROYGBIV using a prism. |
| 1800 | William Herschel | Found infrared β the first invisible light ever detected. |
| 1801 | Johann Ritter | Found ultraviolet, just past the violet end. |
| 1865 | James Clerk Maxwell | Predicted mathematically that electric and magnetic fields travel together as waves β at the speed of light. |
| 1887 | Heinrich Hertz | Produced and detected radio waves, proving Maxwell right. |
| 1895 | Wilhelm RΓΆntgen | Discovered X-rays and imaged the bones of his wife's hand. |
Wave properties & the formula
Three numbers describe any wave: how long it is, how often it repeats, and how tall it is. One equation ties the first two to the speed of light.
Wavelength
Symbol Ξ» (lambda). Measured in metres (m). Crest to crest.
Frequency
Symbol f. Measured in hertz (Hz). Waves per second.
Amplitude
Height of the crest. Sets brightness or loudness, not colour.
speed of light = frequency Γ wavelength Β· c = 3 Γ 10βΈ m/s
Remember β the seesaw rule
Because c never changes, frequency and wavelength sit on a seesaw. Long wavelength β low frequency β low energy. Short wavelength β high frequency β high energy. That single sentence explains why gamma rays are dangerous and radio waves are not.
Try it: the c = fΞ» calculator
Pick what you want to find, type the numbers you know, and check your work.
Worked example
Problem: A radio station broadcasts at 92.3 MHz. What is the wavelength of its signal?
Given: f = 92.3 MHz = 92.3 Γ 10βΆ Hz = 9.23 Γ 10β· Hz
c = 3 Γ 10βΈ m/s
Find: Ξ»
Formula: Ξ» = c Γ· f
Solve: Ξ» = (3 Γ 10βΈ) Γ· (9.23 Γ 10β·)
Ξ» = 3.25 m
Answer: about 3.25 metres β roughly the height of a basketball ring. That is one single wave of the song you are hearing.
The electromagnetic spectrum
The electromagnetic spectrum is the complete range of EM waves, arranged by wavelength and frequency. Click any band below to open it.
Memory trick
Roman Men Invented
Very Unusual X-ray
Gadgets
= Radio Β· Microwave Β· Infrared Β· Visible Β· Ultraviolet Β· X-ray Β· Gamma
The wavelength runs from longest to shortest.
All seven, side by side
| Band | Wavelength | Frequency | Main use |
|---|
Photon energy: E = hƒ
The spectrum you just met is ordered by wavelength. Now for the question that actually matters: why is one end of it harmless and the other end dangerous? The answer is a single formula, and it says that light arrives in packets whose energy depends only on the frequency.
Light comes in packets
An EM wave is not a smooth stream you can pour out in any amount. It arrives in indivisible packets called photons. You can send more photons or fewer photons, but you cannot send half a photon β and the energy of each one is fixed by its frequency alone. Brightness changes how many; frequency changes how hard each one hits.
Speed of light
c = 3.00 × 108 m/s in a vacuum. Every EM wave travels at exactly this speed, from radio to gamma. It never changes.
Planck's constant
h = 6.626 × 10−34 J·s. The conversion rate between a wave's frequency and a photon's energy. Named for Max Planck, 1900.
The electronvolt
1 eV = 1.602 × 10−19 J. A joule is enormous for a single photon, so physicists use this smaller unit instead.
Two formulas, or really one
You already know c = ƒλ, so ƒ = c ÷ λ. Substitute that in and you get the same law written in terms of wavelength:
Remember β the seesaw again
Energy sits on the same side of the seesaw as frequency and the opposite side to wavelength. Short wavelength → high frequency → high energy. That single chain is why gamma rays hurt you and radio waves do not, and it is worth three marks on its own.
Try it: the photon solver
Because c and h never change, any one of wavelength, frequency and energy fixes the other two. Tap whichever one the problem gives you. The marker on the strip shows where that photon sits on the spectrum, drawn on a true logarithmic scale β which is why visible light is the sliver it really is.
Tap the one quantity the problem gives you.
Worked example: green light
Problem: Green light has a wavelength of 550 nm. Find its frequency and the energy of one photon.
STEP 1 - Convert to SI
550 nm = 550 x 10^-9 m = 5.50 x 10^-7 m
STEP 2 - Frequency, from c = fl
f = c / l = (3.00 x 10^8) / (5.50 x 10^-7)
= 5.45 x 10^14 Hz
STEP 3 - Energy, from E = hf
E = (6.626 x 10^-34) x (5.45 x 10^14)
= 3.61 x 10^-19 J
STEP 4 - In electronvolts
E = (3.61 x 10^-19) / (1.602 x 10^-19)
= 2.26 eV
CHECK: f x l = 5.45e14 x 5.50e-7 = 3.00 x 10^8 m/s = c. Correct.
2.26 eV is below the ~10 eV ionising threshold, which is why
visible light is safe to look at and ultraviolet is not.
Watch the units. Almost every wrong answer in this topic is a nanometre that never became a metre. Convert first, calculate second, convert back last.
The 10 eV line
Around 10 eV a photon carries enough energy to tear an electron off an atom. That is called ionising radiation, and it is the real dividing line on the spectrum β not brightness, not heat.
| Photon | Wavelength | Energy | Ionising? |
|---|---|---|---|
| FM radio (92.3 MHz) | 3.25 m | 3.8 × 10−7 eV | No β nowhere near |
| Microwave oven | 12.2 cm | 1.0 × 10−5 eV | No β it heats, that is all |
| Red light | 700 nm | 1.77 eV | No |
| Violet light | 400 nm | 3.10 eV | No β but the highest visible |
| UV-B (sunburn) | 300 nm | 4.13 eV | Borderline β damages skin DNA |
| Medical X-ray | 0.1 nm | 12 400 eV | Yes β hence the lead apron |
| Gamma ray | 0.001 nm | 1 240 000 eV | Yes β the most energetic of all |
The mistake this page exists to kill
"A brighter light is more dangerous." No. Brightness is the number of photons; danger is the energy of each one, and that depends only on frequency. A blazing red lamp will never give you sunburn, while UV you cannot even see will β because each UV photon clears the ionising bar and no red photon ever does.
Uses vs dangers
Every EM wave is a tool and a hazard at the same time β it depends on how much energy it carries and how long you are exposed. Sort each item into the right bin.
Radio β Visible light
Not enough energy to knock electrons off atoms. It can still heat you (microwave, infrared) but it does not directly break DNA.
UV β Gamma rays
Enough energy to strip electrons and damage DNA. This is the half of the spectrum that needs sunblock, lead aprons, and concrete shielding.
Safety in real life
- Wear sunblock and use a payong between 10 AM and 4 PM β the PH UV index is high all year.
- Never look directly at a welding arc without a proper shield.
- Wear the lead apron at the dental or X-ray clinic. It is not optional.
- Do not run a microwave oven with a damaged or open door.
EM waves around you
You have been swimming in the electromagnetic spectrum all day. Tap each scene to reveal which band is doing the work.
Remember
Your phone is a spectrum machine: radio waves for the cell signal and Wi-Fi, infrared for the face-unlock dot projector, and visible light coming off the screen β all at once, all at 3 Γ 10βΈ m/s.
Flashcard review
Twelve terms you need before the quiz. Tap a card to flip it. Cover the answers and say the definition out loud first β that is what makes it stick.
Practice quiz
Twelve questions. You get an explanation after every answer β read it even when you get it right.
The questions shuffle
Every attempt reorders the items, so you cannot memorise the sequence β only the science.
Explain it out loud
Before tapping an answer, say why in one sentence. If you cannot, you are guessing β go back to that section.
Aim for 10 / 12
Below that, revisit the spectrum and the flashcards, then try again.
The whole lesson on one page
If you remember nothing else, remember these. Hit the printer icon at the top to save this page as a reviewer.
Same speed, different sizes
Every EM wave travels at c = 3 Γ 10βΈ m/s in a vacuum. What separates radio from gamma is only wavelength and frequency.
No medium needed
EM waves are made of vibrating electric and magnetic fields, perpendicular to each other. That is why sunlight crosses empty space but sound cannot.
The seesaw
c = fΞ». Frequency up β wavelength down. And energy follows frequency (E = hf), so short waves hit hardest.
Ionizing vs non-ionizing
The line sits just past visible light. UV, X-rays and gamma carry enough energy to damage DNA. Everything below only heats.
One-page cheat sheet
| Band | Remember it by | Watch out for |
|---|
Before you close this
Say the mnemonic out loud once: Roman Men Invented Very Unusual X-ray Gadgets. Then write c = fΞ» and c = 3 Γ 10βΈ m/s on the top of your scratch paper on exam day. Half the items fall out of those two lines.