Topic 14.4: Electromagnetic Waves

What Topic 14.4 requires

Topic 14.4 carries one learning objective, 14.4.A, describe the properties of an electromagnetic wave. Three essential knowledge statements sit under it, two of them with sub-statements, and the topic does print a boundary statement.

• 14.4.A.1 Electromagnetic waves consist of oscillating electric and magnetic fields that are mutually perpendicular. Sub-statements: 14.4.A.1.i (electromagnetic waves are transverse waves because the oscillations of the electric and magnetic fields are perpendicular to the direction of propagation) and 14.4.A.1.ii (electromagnetic waves are commonly assumed to be plane waves, which are characterized by planar wave fronts).
• 14.4.A.2 Electromagnetic waves do not need a medium through which to propagate.
• 14.4.A.3 Categories of electromagnetic waves are characterized by their wavelengths. Sub-statements: 14.4.A.3.i (the categories, in order of decreasing wavelength, spanning a range from kilometers to picometers), 14.4.A.3.ii (visible light broken into colors, in order of decreasing wavelength) and 14.4.A.3.iii (visible electromagnetic waves are also called light, and sometimes electromagnetic waves of all wavelengths are collectively referred to as light or electromagnetic radiation).

The boundary statement, in full: AP Physics 2 expects students to know the ordering of the electromagnetic spectrum (including visible light). However, students will not be expected to define exact wavelength ranges within the electromagnetic spectrum.

Both halves matter. The first makes the ordering examinable. The second takes the numbers off the table, and stopping the quotation after "including visible light" would leave you memorizing a table the exam has said it will not ask for.

The suggested skills are 1.A (create diagrams, tables, charts, or schematics to represent physical situations), 2.C (compare physical quantities between two or more scenarios or at different times and locations in a single scenario), 3.B (apply an appropriate law, definition, theoretical relationship, or model to make a claim) and 3.C (justify or support a claim using evidence from experimental data, physical representations, or physical principles or laws). The topic page and the Unit at a Glance table list the same four.

Read that list again for what is absent. No 2.A, no 2.B, no 2.D. Topic 14.4's skill row contains no computational skill at all. Everything it asks you to do is describe, represent, compare and justify.

Unit 14 is weighted at 12 to 15 percent of the multiple-choice section across a suggested 14 to 23 class periods.

Two fields at right angles, and why that makes the wave transverse

14.4.A.1 is the definition: electromagnetic waves consist of oscillating electric and magnetic fields that are mutually perpendicular.

Three things are packed into that one line.

• There are two fields, not one. An electromagnetic wave is not a wiggling electric field with a magnetic field along for the ride. Both oscillate, and neither is optional.
• The two oscillations are mutually perpendicular to each other.
• Nothing material is displaced. In a sound wave, air molecules move. Here the quantity that varies from place to place and moment to moment is field strength.

14.4.A.1.i then adds the third perpendicular: electromagnetic waves are transverse waves because the oscillations of the electric and magnetic fields are perpendicular to the direction of propagation.

That sentence gives a reason rather than just a label, and the reason is the definition of transverse from Topic 14.1: 14.1.A.4 says that in a transverse wave, the direction of the disturbance is perpendicular to the direction of propagation. Here the disturbance is the pair of fields, so the wave is transverse by the same test that classifies a wave on a string. Put the three constraints together and you get three mutually perpendicular axes: electric field along one, magnetic field along a second, propagation along the third.

What the CED does not give you is the handedness. There is no cross product anywhere in Topic 14.4 and no right-hand rule for the fields of a light wave. A question can ask which axis the magnetic field oscillates along, because perpendicularity settles that. It cannot fairly ask which of the two directions along that axis.

Being transverse has a consequence one topic earlier. 14.3.A.2.i says transverse waves can be polarized and oscillate in a single plane, and 14.3.A.2.ii says longitudinal waves cannot be polarized. Light can be polarized. Sound cannot. That traces straight back to 14.4.A.1.i, and Topic 14.3 is where the polarization statements live.

Plane waves. 14.4.A.1.ii is a modeling assumption rather than a fact about light: electromagnetic waves are commonly assumed to be plane waves, which are characterized by planar wave fronts. Read "commonly assumed" as the hedge it is. Light from a small source spreads in expanding spheres, and far from the source a small patch of one of those spheres is nearly flat.

A wave front joins points of the wave at the same stage of their oscillation. The CED uses the term without defining it, but pins the geometry down in 13.1.A.1: a light ray is a straight line that is perpendicular to the wavefront of a light wave and points in the direction of travel of the wave. If the fronts are flat planes, the rays are parallel straight lines and the ray model of Unit 13 becomes available. 13.1.A.1.ii says where it stops: rays are not sufficient to understand the spreading of light, because in interference and diffraction the wave nature of light is important.

No medium required, and what that costs your intuition

14.4.A.2 is five words of physics and one of the two ideas most likely to be tested from this topic: electromagnetic waves do not need a medium through which to propagate.

It restates half of 14.1.A.2, which draws the line for the whole unit: mechanical waves or wave pulses require a medium in which to propagate, and electromagnetic waves or wave pulses do not require a medium in which to propagate.

So the unit splits waves into two families by exactly this test, and 14.4 is the topic for the family that travels through nothing.

Three consequences worth carrying into an exam.

• Sunlight reaches you across a vacuum. So does every radio signal from every spacecraft. Nothing is oscillating in the space between: the fields themselves are the wave.
• There is no sound in a vacuum. 14.1.A.5.i says sound waves are modeled as mechanical longitudinal waves, and mechanical waves need a medium. A scenario that puts a source in an evacuated chamber and asks which signals get out is testing 14.4.A.2 against 14.1.A.2, and it is skill 2.C.
• A medium is optional, not forbidden. Electromagnetic waves travel through air, water and glass perfectly well. They just travel slower there, which is the whole content of the index of refraction in Topic 13.3.

The intuition this breaks is the one built on strings and springs, where the wave is a pattern of displacement in stuff. Drop that and keep the definition that survives: 14.1.A.1 says waves transfer energy between two locations without transferring matter between those locations. Nothing in that sentence requires stuff to be present.

One speed in a vacuum, and where c comes from

Topic 14.4 does not print the speed of an electromagnetic wave. The statement you need is one topic back, in 14.1.A.3.i: the speed of all electromagnetic waves in a vacuum is a universal physical constant,

The words "all" and "universal" are doing real work. A gamma ray and a radio wave differ in wavelength by something like eighteen powers of ten, and in a vacuum they travel at exactly the same speed. Frequency does not change it. Amplitude does not change it.

That value is also printed in the Constants and Conversion Factors block of the AP Physics 2 equation sheet, listed as the speed of light, so you do not have to remember it.

Two relationships connect the constant to the rest of the unit, and both are on the sheet:

Together with $c$ they let you move between wavelength and frequency for any electromagnetic wave in a vacuum, since $v = c$ there. That routine belongs to the wave speed, frequency and wavelength guide rather than to this page.

The second row is the one students skip. Inside a material an electromagnetic wave slows to $v = c/n$, so $c$ is the vacuum speed and nothing else. A question that says "in glass" or "in water" has already told you the speed is not $c$.

One nearby constant is easy to misread. The sheet prints $hc = 1240 \text{ eV} \cdot \text{nm}$ in the same block. That is a Unit 15 quantity, used with photon energies in Topic 15.1, not a Topic 14.4 quantity. As the Unit 14 opener puts it, the end of Unit 14 leaves an open question of whether light should be considered a wave or a particle, which will be further studied in Unit 15.

The spectrum: the order is required, the wavelength ranges are not

14.4.A.3 says categories of electromagnetic waves are characterized by their wavelengths. 14.4.A.3.i then lists them, in order of decreasing wavelength, spanning a range from kilometers to picometers: radio waves, microwaves, infrared, visible, ultraviolet, X-rays, and gamma rays.

Seven categories. Reading left to right, wavelength falls. Since every one of them travels at $c$ in a vacuum and $\lambda = v/f$, frequency rises in the same direction, and by 14.2.A.1.iv, which says the energy of a wave increases with increasing frequency, so does the energy.

The middle rows are deliberately blank, and that is the boundary statement talking. It says students will not be expected to define exact wavelength ranges within the electromagnetic spectrum. There is no number you owe anyone for where microwaves stop and infrared starts.

What the CED does give you is the outer scale: kilometers to picometers. Both units are in the prefixes table on the equation sheet, kilo at $10^{3}$ and pico at $10^{-12}$, so the span is about fifteen orders of magnitude. Knowing that radio wavelengths run to kilometers and gamma-ray wavelengths down to picometers is a different claim from knowing a boundary to three significant figures, and only the first is required.

So a problem that wants a number will hand you the wavelength. It will not expect you to supply one from the name of the category. What it can expect is that you place the category correctly relative to the others, and convert an ordering by wavelength into an ordering by frequency or energy without hesitating.

Two ordering traps are worth naming.

• Frequency order is the reverse of wavelength order. The CED's list is written in decreasing wavelength, so it is in increasing frequency. Copying the list into an answer about frequency without reversing it is the easiest mistake here.
• Visible sits between infrared and ultraviolet, and it is narrow. "Infra" means below and "ultra" means beyond, both relative to visible: infrared has longer wavelengths than red, ultraviolet shorter than violet. The names encode the ordering, which beats a mnemonic.

Color order, and the three meanings of the word light

14.4.A.3.ii splits the visible band: visible electromagnetic waves are further broken into categories of color, including, in order of decreasing wavelength, red, orange, yellow, green, blue, and violet.

Six colors, and the CED's list is decreasing in wavelength, so red has the longest visible wavelength and violet the shortest. Reverse it and you have increasing frequency and, by 14.2.A.1.iv, increasing energy.

The word "including" there is a hedge worth reading: indigo is missing from the CED's list. The six named colors are the ones the CED puts in order, and the ordering is what the boundary statement makes examinable.

That ordering shows up again in Topic 14.8, where 14.8.A.5 says that when white light hits a diffraction grating, the higher-order maxima disperse white light into a rainbow of colors, with the longest-wavelength light (red) appearing farthest from the central maximum. Knowing red is the long-wavelength end lets you predict which side of the pattern it lands on rather than memorizing the result.

14.4.A.3.iii then handles vocabulary: visible electromagnetic waves are also called light, and sometimes electromagnetic waves of all wavelengths are collectively referred to as light or electromagnetic radiation.

So the CED sanctions two readings of the word, and both appear in this course.

• Narrow: light means the visible band. This is the reading in Unit 13, where a light ray is drawn, reflected and refracted.
• Broad: light or electromagnetic radiation means the whole spectrum. This is the reading in Topic 15.5, where 15.5.A.1 describes the photoelectric effect as the emission of electrons when electromagnetic radiation is incident upon a photoactive material, with no restriction to visible wavelengths.

Notice this and a question saying "the light is replaced by ultraviolet" stops looking like a contradiction. It is the narrow reading followed by the broad one, and the CED has told you both are in use.

What the equation sheet gives you for this topic

The AP Physics 2 equation sheet prints 129 entries across seven groups. Counting the Waves, Sound, and Optics group gives 15 equations. Not one of them is a Topic 14.4 equation.

That is the honest answer, and it is not a gap. Topic 14.4 has no equation of its own anywhere in the CED: no relevant equation, no derived equation, nothing printed beside any of its three essential knowledge statements. It is a describe-and-compare topic, which is exactly what its four suggested skills say.

What the sheet does give you, and what you will use on 14.4 questions:

• $c = 3.00 \times 10^8 \text{ m/s}$, in the Constants and Conversion Factors block.
• $\lambda = \dfrac{v}{f}$, the first line of the Waves, Sound, and Optics group, cited at 14.2.A.3.
• $n = \dfrac{c}{v}$, the second line, cited at 13.3.A.3, for when the wave is inside a material.
• The prefixes table, which is where kilo and pico come from.

What is not printed anywhere on the sheet:

• Any diagram or table of the electromagnetic spectrum, in any order.
• Any wavelength or frequency boundary between categories. The boundary statement says you will not be asked for these, and the sheet agrees by not supplying them.
• Any relationship between the electric field magnitude and the magnetic field magnitude in an electromagnetic wave.
• Any expression for the speed of light in terms of $\varepsilon_0$ and $\mu_0$. Both constants are printed, $\varepsilon_0 = 8.85 \times 10^{-12}$ and $\mu_0 = 4\pi \times 10^{-7}$, but they are there for Topic 10.1 and Topic 12.3, and this CED never connects them to $c$.

The sheet's variable list defines $v$ as speed and $\lambda$ as wavelength and stops there. It does not define $c$, $E$ or $B$ for this context, so when a Topic 14.4 question names a field direction, the question itself has to establish the axes.

How Topic 14.4 is tested, and what sits in neighbouring topics

The AP Physics 2 exam runs 3 hours: 42 multiple-choice questions in 85 minutes for half the score, and 4 free-response questions in 95 minutes for the other half. A four-function, scientific or graphing calculator is allowed on both sections. Unit 14's 12 to 15 percent weighting applies to the multiple-choice section.

The four suggested skills map onto four recognizable shapes.

• 1.A, create diagrams: sketch the two field oscillations and the propagation direction on perpendicular axes, or sketch planar wave fronts with rays perpendicular to them.
• 2.C, compare across scenarios: two electromagnetic waves of different wavelength, or the same wave in a vacuum and then in glass, with a question about which quantity changed.
• 3.B, make a claim: apply 14.4.A.2 to decide whether a signal crosses a vacuum, or the ordering in 14.4.A.3.i to rank frequencies.
• 3.C, justify a claim: give the reasoning, not just the verdict. This is where "because electromagnetic waves do not need a medium" has to actually appear in your answer.

Skill 1.A is a free-response skill only. The CED's exam-weighting table lists no multiple-choice weighting for 1.A, 1.B or 1.C, and notes that Science Practice 1 will not be assessed in the multiple-choice section. So the diagram work from this topic surfaces in Section II.

Four things regularly attached to electromagnetic waves belong to other topics.

• Polarization is Topic 14.3. Every polarization statement sits in 14.3.A.2 and 14.3.A.3.
• Reflection and refraction of light are Unit 13. Topic 14.4 tells you what light is. Unit 13 tells you what it does at a surface.
• The Doppler effect for light is not separated out. Topic 14.5 is written for a wave source and an observer in general and never singles out electromagnetic waves.
• Photons are Unit 15. Nothing in 14.4 mentions energy quantization, photon energy, or the photoelectric effect. The wave-versus-particle question is what Unit 14 hands to Unit 15.

This page is built on the CED effective Fall 2024, and the 14.4 boundary statement shows why that matters: material written for the older course routinely drills exact spectrum wavelength ranges that this CED says you will not be asked to define.