AP® Physics 2: Algebra-Based review sheet from Aim for Five (aimforfive.com/physics-2/units/14/14-4)
Unit 14 · Topic 14.4
14.4 Electromagnetic Waves
An electromagnetic wave is made of an electric field and a magnetic field that oscillate at right angles to each other and to the direction the wave moves. It needs no medium and travels at c = 3.00 × 10⁸ m/s in a vacuum. The electromagnetic spectrum runs from long radio waves to tiny gamma rays, and you need to know its order, including the colors of visible light.
Key terms
- electromagnetic wave
- speed of light
- electromagnetic spectrum
- visible light
- transverse wave
What an electromagnetic wave is
An electromagnetic (EM) wave is a traveling pattern of changing electric and magnetic fields. A changing magnetic field creates an electric field (Faraday's law, from 12.4), and a changing electric field creates a magnetic field, so each keeps the other going as the wave moves.
The electric field, the magnetic field and the direction of travel are all perpendicular to one another. If the wave moves along x and the electric field oscillates along y, the magnetic field oscillates along z. Because both fields oscillate perpendicular to the direction of travel, EM waves are transverse, which is why light can be polarized.
EM waves are usually modeled as plane waves: their wavefronts are flat planes, like sheets moving through space, rather than expanding spheres. That's a good model far from the source.
No medium needed
Unlike sound, an EM wave isn't a disturbance of any material. It travels through empty space, which is how light from the Sun and distant stars reaches us.
Every EM wave in a vacuum travels at the same speed, c = 3.00 × 10⁸ m/s, whatever its wavelength. In a material it moves more slowly, at . For all EM waves, c = fλ in a vacuum.
The electromagnetic spectrum
EM waves are grouped by wavelength. In order of decreasing wavelength (and increasing frequency):
- Radio waves (longest, up to kilometers): radio, TV
- Microwaves: microwave ovens, Wi-Fi, radar
- Infrared: heat lamps, remote controls, thermal cameras
- Visible light: the narrow band our eyes detect
- Ultraviolet: causes sunburn
- X-rays: medical imaging
- Gamma rays (shortest, down to picometers): from nuclear decay
Visible light and the word "light"
Within visible light, the colors in order of decreasing wavelength are red, orange, yellow, green, blue and violet. Red has the longest wavelength and lowest frequency; violet has the shortest wavelength and highest frequency.
\"Light\" usually means visible EM waves, but physicists often call any EM wave light or electromagnetic radiation.
You need the order of the spectrum, not exact wavelength ranges. It's still handy to know visible light is roughly 400 to 700 nm, because it helps you check whether an answer is reasonable.
A useful memory hook for the full spectrum: wavelength gets shorter and frequency gets higher as you go from radio to gamma. In Unit 15 you'll see that higher frequency also means more energy per photon, which is why UV, X-rays and gamma rays can damage cells.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Wavelengths from frequencies
An FM radio station broadcasts at 100 MHz, and a microwave oven works at 2.45 GHz. Find each wavelength.
Show the solutionHide the solution
- Step 1: FM: m.
- Step 2: Microwave: m, about 12 cm.
- Step 3: That fits the spectrum: radio waves are longer than microwaves.
Answer: Radio: 3.00 m. Microwave: 0.122 m (about 12 cm).
- Example 2
Directions of the fields
An EM wave travels in the +x direction. At one instant its electric field points in the +y direction. Along which axis does its magnetic field point? If the wave's frequency is doubled, what happens to its speed and wavelength in a vacuum?
Show the solutionHide the solution
- Step 1: The magnetic field must be perpendicular to both the electric field (y) and the direction of travel (x). The only axis left is z, so the magnetic field points along the z-axis.
- Step 2: All EM waves travel at c in a vacuum, so the speed doesn't change.
- Step 3: With c fixed, , so doubling f halves the wavelength.
Answer: Along the z-axis; the speed stays c and the wavelength halves.
- Example 3
Ranking by frequency
Rank these from lowest to highest frequency: green light, X-rays, microwaves, infrared, red light.
Show the solutionHide the solution
- Step 1: Lower frequency means longer wavelength. Use the spectrum order from longest to shortest wavelength: radio, microwave, infrared, visible (red to violet), ultraviolet, X-ray, gamma.
- Step 2: So: microwaves, then infrared, then red light, then green light, then X-rays.
Answer: Microwaves < infrared < red light < green light < X-rays
Common mistakes
- Saying radio waves are sound waves. Radio waves are electromagnetic; a radio turns them into sound.
- Thinking higher-frequency EM waves travel faster in a vacuum. All EM waves travel at c.
- Reversing the color order. Red has the longest wavelength and lowest frequency in visible light; violet has the shortest wavelength.
- Drawing the electric and magnetic fields parallel to each other. They're perpendicular to each other and to the direction of travel.
On the exam
- Ranking questions are common: order parts of the spectrum or visible colors by wavelength, frequency or (connecting to Unit 15) photon energy.
- Short calculations with c = fλ show up often. Watch the prefixes: MHz is 10⁶ Hz, GHz is 10⁹ Hz and nm is 10⁻⁹ m.
Connected topics
Videos
Check yourself
4 questions on 14.4 Electromagnetic Waves. Pick an answer to see if you got it, and why.
An FM radio station broadcasts at 100 MHz (1.00 × 10⁸ Hz). What is the wavelength of these radio waves in air?
Green light has a wavelength of 500 nm in a vacuum. What is its frequency?
Which list puts these electromagnetic waves in order from lowest frequency to highest frequency?
A beam of light travels straight east. At some point in the beam, the electric field oscillates up and down (vertically). Along which direction does the magnetic field oscillate at that point?
0 of 4 answered