Unit 14 · Topic 14.4 · about 30 minutes · 7 parts · 10 scored checks, 2 of them multiple choice, plus 2 from earlier lessons

AP Physics 2: Algebra-Based 14.4: Electromagnetic Waves

Q: Which color of visible light has the highest frequency?

Violet. All colors travel at c in a vacuum, and violet has the shortest wavelength, so by f = c it has the highest frequency.

Built by Tanner Crow from College Board's course framework · Every answer key independently checked

Unit 14: 12 to 15% of the multiple-choice section

What you'll be able to do

Describe the properties of an electromagnetic wave: the fields that make it up, why it is transverse and needs no medium, and how its categories, the colors of light among them, are ordered by wavelength.

Key vocabulary

Term	What it means	The exam trap
Electric field	The electric force per unit charge at a point, a vector written $\vec{E}$ .	The field points the way the force on a positive charge points; the force on a negative charge points the opposite way.
Wave front	A surface along which a wave is at the same point in its cycle, such as a crest, at one instant.	A wave front is the crest itself, spread out across space, not the path one part of the wave follows.
Electromagnetic spectrum	The whole range of electromagnetic waves, arranged by wavelength.	The spectrum is far wider than the colors you can see; most of it is invisible to the eye.

Two sources of electromagnetic waves. On the left, an FM radio broadcast tower labeled 100 MHz. On the right, a microwave oven labeled 2.45 GHz. No waves are drawn. — The two sources compared in Watch it done.

Part 1 Think first What waves in a beam of light?

Commit to a guess first. Being wrong now makes the right idea stick better.

Predict first

Sound is air being squeezed and stretched. Sunlight reaches you from the Sun. What is it that oscillates as light travels?

In short. An electromagnetic wave is a pair of oscillating electric and magnetic fields, perpendicular to each other and to the direction the wave travels, that needs no medium.

Every electromagnetic wave travels at $c = 3.00 \times 10^{8}$ m/s in a vacuum; the categories differ in wavelength, and so in frequency, $f = \frac{c}{λ}$ .
From the longest wavelength to the shortest: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.
Visible light from the longest wavelength to the shortest: red, orange, yellow, green, blue, violet.

Part 2 Learn it Fields, the spectrum and color

4a. Two fields at right angles

An electromagnetic wave is made of an oscillating electric field and an oscillating magnetic field. The two fields are mutually perpendicular: at every point, the magnetic field is at right angles to the electric field.

Both fields also oscillate at right angles to the direction the wave travels, so electromagnetic waves are transverse. If a wave travels north with its electric field oscillating east and west, its magnetic field oscillates up and down, and neither field points north or south.

No material is shaken. The fields themselves are the disturbance, so electromagnetic waves do not need a medium. They cross a vacuum, where they all travel at $c = 3.00 \times 10^{8}$ m/s.

The surfaces where a wave is at a crest at one instant are its wave fronts. Far from the source they are very nearly flat, so electromagnetic waves are commonly modeled as plane waves: waves with planar wave fronts, all moving the same way.

Quick check · Multiple choice

An electromagnetic wave travels east. At one point, its electric field oscillates up and down. Along which line does its magnetic field oscillate at that point?

4b. The electromagnetic spectrum

All electromagnetic waves are the same kind of wave, and in a vacuum they all travel at $c$ . What sorts them into categories is their wavelength. In order of decreasing wavelength:

radio waves
microwaves
infrared
visible light
ultraviolet
X-rays
gamma rays

The whole range runs from wavelengths of kilometers, for long radio waves, down to picometers, for gamma rays. The edges between neighboring categories are not sharp, and the course framework says students are not expected to define exact wavelength ranges. Know the order.

Since every category travels at $c$ in a vacuum, $f = \frac{c}{λ}$ puts them in the reverse order by frequency: radio waves have the lowest frequencies and gamma rays the highest.

Quick check · Put it in order

Tap the categories of electromagnetic waves in order, from the longest wavelength to the shortest.

4c. Light and its colors

Visible electromagnetic waves are also called light. Within the visible range, the colors are themselves categories ordered by wavelength. From the longest to the shortest:

red, orange, yellow, green, blue, violet

Red light, at the long end, sits next to infrared, and violet light, at the short end, sits next to ultraviolet. The names come from that: infrared is beyond red, ultraviolet beyond violet. In a vacuum every color travels at $c$ , so violet light, with the shortest wavelength, has the highest frequency of the visible colors.

The word light is sometimes stretched to cover electromagnetic waves of every wavelength, and the whole family is also called electromagnetic radiation. When a question says light, check whether it means the visible part or the whole spectrum.

Quick check · Rank it

Four beams travel through a vacuum: red light, green light, violet light and an infrared beam. Rank them by frequency.

Highest frequency first

Give each one a place, 1 for first. Give two the same place if they are equal.

Red light
Green light
Violet light
Infrared beam

Your ranking: none yet

Common mistakes

The mistake	Why it is wrong	Do this instead
Thinking electromagnetic waves need air or some other medium.	The disturbance is the electric and magnetic fields themselves, which exist in empty space.	Expect any electromagnetic wave to cross a vacuum, at $c$ .
Drawing the magnetic field parallel to the electric field, or along the direction of travel.	The two fields are mutually perpendicular, and both are perpendicular to the direction of travel.	Find the one line at right angles to both the electric field and the travel.
Thinking higher-frequency waves travel faster through a vacuum.	Every electromagnetic wave travels at $c$ in a vacuum; the categories differ only in wavelength and frequency.	Hold the speed at $c$ and compare wavelengths.
Reversing the colors, or putting ultraviolet next to red.	Red has the longest visible wavelength, next to infrared; violet has the shortest, next to ultraviolet.	Use the names: infrared is beyond red, ultraviolet beyond violet.

Part 3 Watch it done A radio station and a microwave oven

Predict first, then watch each step, then finish the problem yourself.

In the picture at the top of this lesson, an FM radio station broadcasts at 100 MHz and a microwave oven works at 2.45 GHz. Both send electromagnetic waves through air, where they travel at very nearly $c$ . How many times as long as the oven's wavelength is the radio station's?

Predict first

Before you open the first step, predict: about how many times as long as the oven's wavelength is the radio station's?

Step 1 · Find the radio wavelength
$λ_{radio} = \frac{c}{f} = \frac{3.00 \times 10^{8} m/s}{1.00 \times 10^{8} Hz} = 3.00$ m.
Step 2 · Find the oven's wavelength
$λ_{oven} = \frac{3.00 \times 10^{8} m/s}{2.45 \times 10^{9} Hz} = 0.122$ m, about 12 cm.
Why this step?
Why can one speed, $c$ , be used for both waves?
Radio waves and microwaves are both electromagnetic waves, and every electromagnetic wave travels at $c$ in a vacuum and very nearly that in air. The two differ only in wavelength and frequency.
Your step · Calculate

Finish it. An FM radio wave has a wavelength of 3.00 m, and a microwave oven's waves have a wavelength of 0.122 m. How many times as long as the oven's wavelength is the radio wavelength?

Your answer

Part 4 Try it Signals from the Sun and the stars

Predict first: a flare on the Sun gives off radio waves, light and X-rays at one instant. Do the X-rays arrive first, the radio waves first, or all of them together? Then decide a claim, and pick what is true of starlight.

Try it · Decide and justify

A flare on the Sun gives off radio waves, visible light and X-rays at the same instant. A student says that the X-rays reach Earth first because they carry the most energy. Is he right?

Which reason supports your answer?

Try it · Select all

Light from a distant star crosses space and enters a telescope on Earth. Which two statements about that light are true? Pick two.

Select 2 answers, then check.

Part 5 Explain it Talking to a rover on Mars

On the exam this is handwritten, so answer on paper first. Nothing you type here leaves this page. Then check your answer against the model and each scoring point.

Free response is 50% of the exam score. This one is shaped like Question 1, Mathematical Routines.

Free-response practice · Question 1 style

Engineers send a radio signal of frequency $f$ from Earth to a rover on Mars, a distance $d$ away. Treat the space between as a vacuum.

(a) On paper, draw the signal's electric and magnetic fields at one instant, along a short stretch of its path, and mark the direction it travels. Do this by hand before you open the model.

(b) Derive an expression for the number of wavelengths $N$ that fit between Earth and the rover, in terms of $d$ , $f$ and $c$ .

(c) On one day $d = 2.25 \times 10^{11}$ m and $f = 8.40 \times 10^{9}$ Hz. Calculate the time the signal takes to reach the rover and the value of $N$ .

(d) An engineer suggests switching to a signal of twice the frequency so that commands arrive sooner. Justify whether this would work, and explain what would change about the signal instead.

Your answer stays on this page. It is never sent or saved.

Model answer

(a) Compare your drawing with the model below. The electric field oscillates along one line, say up and down; the magnetic field oscillates along a line at right angles to it; and both are at right angles to the direction of travel.

(b) The wavelength is $λ = \frac{c}{f}$ , so $N = \frac{d}{λ} = \frac{d f}{c}$ .

(c) $t = \frac{d}{c} = \frac{2.25 \times 10^{11} m}{3.00 \times 10^{8} m/s} = 750$ s, or 12.5 minutes. $N = \frac{(2.25 \times 10^{11} m) (8.40 \times 10^{9} Hz)}{3.00 \times 10^{8} m/s} = 6.30 \times 10^{12}$ wavelengths.

(d) It would not work. Every electromagnetic wave travels at $c$ in a vacuum whatever its frequency, so the travel time $\frac{d}{c}$ stays 750 s. Doubling the frequency halves the wavelength, $λ = \frac{c}{f}$ , so twice as many wavelengths, $1.26 \times 10^{13}$ , fit between Earth and the rover.

A model drawing in three dimensions. The wave travels to the right along an axis marked direction of travel. The electric field, E, is drawn as a wave in the vertical plane, with short lines from the axis showing it pointing up and down. The magnetic field, B, is drawn as a wave in the horizontal plane, slanting toward and away from the viewer, at right angles to the electric field and to the direction of travel. The two fields reach their largest values at the same places. — One correct drawing. Yours needs the two fields at right angles to each other and to the direction of travel.

Score your own answer. This is a self-check, not a grade. Tick each point your answer makes.

Draws the electric and magnetic fields oscillating at right angles to each other and to the marked direction of travel.
Writes $λ = \frac{c}{f}$ and derives $N = \frac{d f}{c}$ .
Calculates the travel time as $\frac{d}{c} = 750$ s and $N = 6.3 \times 10^{12}$ .
Justifies that the time does not change, because every electromagnetic wave travels at $c$ in a vacuum whatever its frequency.
Explains that doubling the frequency halves the wavelength and doubles $N$ .

Part 6 Check yourself A snapshot of a radio wave

Both case questions use the graph.

The graph is a snapshot of the electric field of a radio wave from a broadcast station, traveling along the x-axis through air, where it travels at very nearly $c$ . It shows the field against position at one instant, not against time. Up on the graph means the field points up; down means it points down.

A graph of the electric field of a radio wave, pointing up or down, against position x in meters from 0 to 8, at one instant. The horizontal axis is the zero line, and the vertical axis has no scale. The field's crests, its largest values pointing up, are at x = 1.0 m and 5.0 m; its troughs, pointing down, are at 3.0 m and 7.0 m.

Case question 1 · Calculate

Using the graph: what is the frequency of the radio wave? Use it to test a classmate's claim that its frequency is above 100 MHz.

Your answer MHz

Case question 2 · Multiple choice

Using the graph: the station switches to a frequency twice as high. In a snapshot of the new wave against position, how far apart are neighboring crests?

The rest stand on their own and do not use the case.

Check yourself · Spot the error

A student compares a red laser beam with a violet one. Tap the first line that goes wrong.

Check yourself · Fill the statement

Complete the statements about electromagnetic waves. Tap a blank, then an answer.

Far from its source, an electromagnetic wave's wave fronts are very nearly flat, so it is modeled as a wave. The visible part of the spectrum is called , a word sometimes stretched to cover electromagnetic of every wavelength.

Part 7 Keep it Bring back earlier ideas

What happens at a boundary and which waves need a medium, from this unit's first lessons, are still part of the course. Retrieving them now, between new ideas, is what makes them easy to find later.

From 14.3 Boundary Behavior of Waves and Polarization · Calculate

A wave on a string travels at 12 m/s with a wavelength of 0.30 m. It reaches a knot, beyond which a second string, at the same tension, carries waves at 6.0 m/s. What is the wavelength of the transmitted wave?

Your answer m

From 14.1 Properties of Wave Pulses and Waves · Sort it

Each card describes a wave or a pulse. Tap a card, then whether it needs a medium to travel.

Needs a medium

Needs no medium

In three lines

An electromagnetic wave is oscillating electric and magnetic fields, perpendicular to each other and to its travel, so it is transverse; it is usually modeled as a plane wave.
Electromagnetic waves need no medium and all travel at $c$ in a vacuum; the categories differ in wavelength.
Longest to shortest: radio, microwave, infrared, visible (red to violet), ultraviolet, X-ray, gamma.

Exam strategy for this topic

Section I, Multiple Choice: 42 questions in 85 minutes.
Section II, Free Response: 4 questions in 95 minutes.
This lesson's Explain it is shaped like free-response question 1, Mathematical Routines.
A four-function, scientific, or graphing calculator is allowed on both sections of the exam.

When a question asks you to compare electromagnetic waves in a vacuum, write $v = c$ for all of them before anything else. Every comparison then comes down to wavelength and frequency, and $f = \frac{c}{λ}$ turns one into the other.

Questions students ask

What is an electromagnetic wave made of?

Oscillating electric and magnetic fields, perpendicular to each other and to the direction the wave travels. The fields are the disturbance, so no medium is needed.

Why are electromagnetic waves transverse?

Both the electric and the magnetic field oscillate at right angles to the direction the wave travels.

What is the order of the electromagnetic spectrum?

From the longest wavelength to the shortest: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. By frequency the order is reversed.

Do I need to know the wavelength range of each kind of electromagnetic wave?

The course framework says students are expected to know the order of the spectrum, visible colors included, but not the exact wavelength range of each category.

Which color of visible light has the highest frequency?

Violet. All colors travel at $c$ in a vacuum, and violet has the shortest wavelength, so by $f = \frac{c}{λ}$ it has the highest frequency.

Course alignment, for teachers

AP Physics 2: Algebra-Based topic 14.4, Unit 14: Waves, Sound, and Physical Optics.

Skill 1.A: Create diagrams, tables, charts, or schematics to represent physical situations.
Skill 2.C: Compare physical quantities between two or more scenarios or at different times and locations in a single scenario.
Skill 3.B: Apply an appropriate law, definition, theoretical relationship, or model to make a claim.
Skill 3.C: Justify or support a claim using evidence from experimental data, physical representations, or physical principles or laws.

This lesson maps all 8 essential knowledge statements of the topic to the part that teaches each one: 8 are checked by a scored question. The map is in the lesson file.