Unit 14: Waves, Sound, and Physical Optics

A wave carries energy, and superposition does the rest

Unit 14 looks like nine things to memorize. It is closer to two.

The first is the definition the CED opens with, in essential knowledge 14.1.A.1: waves transfer energy between two locations without transferring matter between those locations. Nothing travels along the rope except the disturbance, and wavelength, period, frequency, amplitude and speed are all properties of that disturbance rather than of the stuff it moves through.

The second is superposition, in 14.6.A.3: when two or more wave pulses or waves overlap, the resulting displacement can be determined by adding the individual displacements.

Topics 14.6 through 14.9 are that one sentence in four geometries. Two waves confined to a region and travelling in opposite directions add to a standing wave (14.6.B.1). Wavefronts from one narrow opening add to bright and dark bands (14.7.A.4.i). Wavefronts from two slits add to evenly spaced maxima (14.8.A.1.i). Light reflected off the front of a thin film adds to light reflected off the back (14.9.A.4.i). Learn those as four unrelated formula sets and you carry four times the load.

Everything before 14.6 puts the pieces in place: what a wave is (14.1), how to measure a repeating one (14.2), what a boundary does to it (14.3), that light is one of these things (14.4), and what relative motion does to the frequency you measure (14.5).

The unit opener sets the same trajectory, saying the unit will address diffraction and interference, polarization, the Doppler effect, and thin-film interference, and then pointing forward: 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.

What the CED says about Unit 14

The numbers, verified against the unit opener and the exam weighting table:

• Exam weighting: 12 to 15 percent of the multiple-choice section. Units 12, 13, 14 and 15 share that band; Units 9, 10 and 11 each carry 15 to 18 percent.
• Suggested pacing: about 14 to 23 class periods, on a schedule where the class meets five days a week for 45 minutes a day. Counting all seven AP Physics 2 units, that is the widest suggested span and the highest upper figure in the course: Unit 9 is about 10 to 16, Unit 10 about 14 to 21, Unit 11 about 12 to 20, Unit 12 about 10 to 14, Unit 13 about 8 to 12, Unit 15 about 14 to 22.
• Nine topics, ten learning objectives. Each topic has one objective except Topic 14.6, which has two: 14.6.A on interference and 14.6.B on standing waves.

Those two figures together are the useful part. Unit 14 has the same exam weighting as Unit 13 and roughly twice the suggested teaching time, so the content is broad rather than deep. That is why it reads as nine topics instead of four.

The opener hangs the unit on five essential questions: why an ambulance siren sounds different moving toward you than away, why a puddle of water with oil in it at a gas station looks like a rainbow, why two notes an octave apart sound the same, why you can hear a person around a corner but cannot see them, and what makes a sonic boom. Four map straight onto topics: the siren is 14.5, the oil is 14.9, the octave is 14.2, the corner is 14.7.

The science practices the opener flags are 2.A, 2.C, 2.D and 3.B: students will derive new expressions from familiar equations (2.A) and use them to compare quantities between scenarios (2.C), make claims (3.B), and predict values using functional dependence (2.D). The illustration the CED gives is the shape of a real question: students might be asked to determine the new distance between bright fringes of a diffraction pattern if the frequency of the light through the single slit is doubled.

One planning hint: of the six sample instructional activities printed for this unit, five are for Topic 14.6 and one is for Topic 14.8. The CED calls those activities optional, but that is where classroom time tends to land.

Topics 14.1 to 14.3: the disturbance, the repetition, and the boundary

[Topic 14.1, Properties of Wave Pulses and Waves](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-1-properties-of-wave-pulses-and-waves). Objective 14.1.A: describe the physical properties of waves and wave pulses. It draws the pulse and wave distinction (14.1.A.1.i, 14.1.A.1.ii), splits mechanical from electromagnetic by whether a medium is required (14.1.A.2), and puts wave speed where it belongs: the speed at which a wave or wave pulse propagates through a medium depends on the type of wave and the properties of the medium (14.1.A.3), with $c = 3.00 \times 10^8$ m/s for electromagnetic waves in a vacuum (14.1.A.3.i), the string equation (14.1.A.3.ii), and the rise of the speed of sound with the temperature of the medium (14.1.A.3.iii). Then transverse against longitudinal (14.1.A.4, 14.1.A.5), sound as a mechanical longitudinal wave with compressions and rarefactions (14.1.A.5.i, 14.1.A.5.ii), and amplitude (14.1.A.6). Suggested skills: 1.C, 2.C, 3.B, 3.C. No boundary statement.

[Topic 14.2, Periodic Waves](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-2-periodic-waves). Objective 14.2.A: describe the physical properties of a periodic wave. Six sub-statements under 14.2.A.1 define period, frequency, the independence of amplitude from both, the rise of energy with frequency, the link between frequency and pitch, and wavelength as the distance between successive corresponding positions such as peaks or troughs. 14.2.A.2 gives two sinusoidal descriptions, one a function of time and one a function of position, and 14.2.A.3 states that the wavelength is proportional to the wave's speed and inversely proportional to its frequency. Suggested skills: 1.A, 2.C, 3.B, 3.C. No boundary statement.

[Topic 14.3, Boundary Behavior of Waves and Polarization](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-3-boundary-behavior-of-waves-and-polarization). Objective 14.3.A: describe the interaction between a wave and a boundary. A wave can be transmitted or reflected depending on the properties of the boundary separating the two media (14.3.A.1), and the CED's own case is a wave travelling between low-mass and high-mass strings (14.3.A.1.i). The inversion rule is stated in terms of speed, not density: a reflected wave is inverted if the transmitted wave travels into a medium in which the speed of the wave decreases (14.3.A.1.ii), and is not inverted if the speed increases (14.3.A.1.iii). 14.3.A.1.iv adds the invariant that holds the unit together: the frequency of a wave does not change when it travels from one medium to another. Polarization follows in 14.3.A.2 and 14.3.A.3, and it belongs here because reflection and refraction are two of the three things the CED says can polarize a transverse wave. Suggested skills: 1.A, 2.C, 3.B, 3.C. No boundary statement.

They interlock. 14.1 says speed belongs to the medium, 14.3 says frequency belongs to the source and survives a boundary, and 14.2 supplies the relation that forces wavelength to absorb the difference.

Topics 14.4 and 14.5: light as a wave, and relative motion

[Topic 14.4, Electromagnetic Waves](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-4-electromagnetic-waves). Objective 14.4.A: describe the properties of an electromagnetic wave. 14.4.A.1 says such waves consist of oscillating electric and magnetic fields that are mutually perpendicular, and 14.4.A.1.i classifies them from that: electromagnetic waves are transverse waves because the oscillations of the electric and magnetic fields are perpendicular to the direction of propagation. That one sentence is why light can be polarized and sound cannot, and why Topic 14.3's polarization statements are written for transverse waves only. 14.4.A.1.ii notes they are commonly assumed to be plane waves, characterized by planar wave fronts, and 14.4.A.2 restates that they need no medium. 14.4.A.3 sets up the spectrum, ordered by decreasing wavelength as radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays (14.4.A.3.i), with visible light broken down by decreasing wavelength as red, orange, yellow, green, blue, violet (14.4.A.3.ii). Suggested skills: 1.A, 2.C, 3.B, 3.C. This topic carries a boundary statement, quoted in full below.

Topic 14.4 is the hinge with the rest of the course. Unit 13 treats light as a ray and gets mirrors and lenses. Unit 14 treats the same light as a wave and gets diffraction, interference and thin films. Neither model is wrong; each has a domain, and Unit 13 says so explicitly.

[Topic 14.5, The Doppler Effect](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-5-the-doppler-effect). Objective 14.5.A: describe the properties of a wave based on the relative motion between the source of the wave and the observer of the wave. 14.5.A.1 defines the effect as the relationship between the rest frequency of a wave source, the observed frequency of the source, and the relative velocity of the source and the observer. 14.5.A.2 says a greater relative velocity results in a greater measured difference between the observed and rest frequencies, then gives three cases: matched velocities means observed equals rest frequency (14.5.A.2.i), a source moving toward an observer gives a greater observed frequency (14.5.A.2.ii), and a source moving away gives a lesser one (14.5.A.2.iii). Suggested skills: 1.A, 2.C, 3.B, 3.C.

Topic 14.5's boundary statement changes how you study it: only qualitative treatments of the Doppler effect are required for AP Physics 2. No Doppler equation is printed on the equation sheet and none appears in the framework. Learn the three cases and the reason behind them, and stop looking for a formula with plus and minus signs in it.

Topic 14.6: superposition, written down

[Topic 14.6, Wave Interference and Standing Waves](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-6-wave-interference-and-standing-waves) is the only topic in the unit with two learning objectives, and the one the last three topics lean on.

14.6.A, describe the net disturbance that occurs when two or more wave pulses or waves overlap. The statement that separates waves from objects is 14.6.A.2: when two or more pulses or waves interact with each other, they travel through each other and overlap rather than bouncing off each other. Then superposition itself (14.6.A.3), the constructive and destructive split by whether the superposed displacements are in the same direction or in opposite directions (14.6.A.4.i, 14.6.A.4.ii), and the note that interacting waves can produce amplitude variations in the resultant wave (14.6.A.4.iii). Beats arrive in 14.6.A.6, with the beat frequency equal to the difference in the frequencies of the two waves.

14.6.B, describe the properties of a standing wave. Standing waves can result from interference between two waves that are confined to a region and travelling in opposite directions (14.6.B.1). A node is a point where the amplitude is always zero, an antinode a point where it is always at maximum (14.6.B.1.i). Possible wavelengths are set by the size and boundary conditions of the region (14.6.B.1.ii), and the regions named are pipes with open or closed ends and strings with fixed or loose ends (14.6.B.1.iii).

14.6.B.2 names the harmonics, and its last clause is where marks go. The longest possible wavelength is the fundamental or first harmonic, the second-longest is typically called the second harmonic, the third-longest the third harmonic, and so on. However, for a standing wave with a node at one end and an antinode at the other end, only odd harmonics can be established.

Suggested skills for 14.6: 1.B, 1.C, 2.A, 2.D, 3.A, 3.B. Six, the longest list in the unit, and one of only two topics that list 3.A, create experimental procedures; Topic 14.8 is the other. Five of the unit's six sample activities sit on this topic. No boundary statement.

Standing waves are where AP Physics 2 rejoins oscillations in AP Physics 1: a point at an antinode is doing simple harmonic motion. If period and frequency feel shaky, the simple harmonic motion guide is a faster fix than rereading this topic.

Topics 14.7 to 14.9: one idea, three geometries

[Topic 14.7, Diffraction](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-7-diffraction). Diffraction is the spreading of a wave around the edges of an obstacle or through an opening (14.7.A.1), and it is most pronounced when the size of the opening is comparable to the wavelength of the wave (14.7.A.2). That answers the unit's own question about hearing someone around a corner: a doorway is comparable to the wavelength of speech and nothing like the wavelength of light. Diffraction of multiple wavefronts through a single opening leads to observable interference patterns (14.7.A.3), which is superposition again. The quantitative setup is monochromatic light of wavelength $\lambda$ on an opening of width $a$ a distance $L$ from a screen (14.7.A.4), with path length difference $\Delta D = a \sin\theta$ (14.7.A.4.iii) and, for $\theta < 10^\circ$, a relation to the $m$th order of minimum brightness (14.7.A.4.iv):

14.7.A.5 adds that the pattern depends on the shape of the opening. Suggested skills: 2.A, 2.B, 2.D. Three, the shortest list in the unit, and the only Unit 14 topic listing none of the practice 1 or practice 3 skills. No boundary statement.

[Topic 14.8, Double-Slit Interference and Diffraction Gratings](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-8-double-slit-interference-and-diffraction-gratings). Same geometry, two openings. The pattern from monochromatic light on two slits a distance $d$ apart is caused by a combination of wave diffraction and wave interference (14.8.A.1), and considering interference alone, a double slit creates a pattern of uniformly spaced maxima (14.8.A.1.i). Path length difference is $\Delta D = d \sin\theta$ (14.8.A.1.iv), and the small-angle relation locates the $m$th order of maximum brightness (14.8.A.1.v):

14.8.A.1.vi puts the pair back together: considering both effects, a double slit creates an interference pattern of maxima and minima superimposed within the envelope created by single-slit diffraction. 14.8.A.2 supplies the history, that interference patterns from a double slit indicate light has wave properties, with Young's double-slit experiment as the source of the discovery. A diffraction grating is a collection of evenly spaced parallel slits producing an interference pattern that combines numerous diffraction patterns superimposed on each other (14.8.A.4), and under white light the center maximum is white while the higher orders disperse it into a rainbow, red farthest out (14.8.A.5). Suggested skills: 1.B, 2.A, 2.B, 2.D, 3.A. No boundary statement.

[Topic 14.9, Thin-Film Interference](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-9-thin-film-interference). Two reflections instead of two slits. The phase change of a reflected ray depends on the relative indices of refraction of the materials the ray interacts with (14.9.A.2): 180 degrees when a light ray is reflected from a medium with a greater index of refraction than the medium through which the ray is traveling (14.9.A.2.i), none when it reflects from a medium with a lower index (14.9.A.2.ii). 14.9.A.3 adds that the phase of a wave does not change when it is refracted. Thin-film interference occurs when light interacts with a medium whose thickness is comparable to the light's wavelength (14.9.A.4), and the two reflected waves add (14.9.A.4.i). The examples named are soap bubbles, oil films and antireflection coatings (14.9.A.5). Suggested skills: 1.A, 2.B, 2.C, 3.B. This topic carries the unit's third boundary statement.

Notice the pattern. In 14.7 the two contributions come from different parts of one opening, in 14.8 from different openings, in 14.9 from different surfaces. The arithmetic differs; the physics is 14.6.A.3 every time. The index of refraction in 14.9 is the same $n$ defined in Topic 13.3, so read that first if the phase-change rule feels arbitrary.

The Unit 14 equations, counted against the sheet

The AP Physics 2 equation sheet prints 129 equations across seven groups. Waves live in the Waves, Sound, and Optics group, which holds 15. Ten of those 15 are cited inside Unit 14:

Four of the remaining five belong to Unit 13: $n = c/v$, Snell's law, the image equation and the magnification equation. The fifteenth is $\Delta D = m\lambda$, printed on the sheet but attached to no Unit 14 essential knowledge statement. It is the condition that turns a path length difference into a maximum, and you are expected to combine it with $\Delta D = a\sin\theta$ or $\Delta D = d\sin\theta$ yourself.

Three things students expect on this sheet and will not find:

• No Doppler equation. The framework prints none for Topic 14.5, and that topic's boundary statement says only qualitative treatments are required.
• No intensity equation. Topic 14.3 defines intensity as a measure of the amount of power transferred per unit area (14.3.A.3.i) and as the average power per unit area over one period of the wave (14.3.A.3.ii). Neither is labeled a relevant equation, and no expression for intensity appears anywhere among the 129. Nothing resembling a polarizer intensity law appears in the framework either.
• No thin-film thickness equation. 14.9.A.5.iii states the quarter-wavelength result in words, not as a formula.

Two entries from elsewhere on the sheet do real work here: $c = 3.00 \times 10^8$ m/s in the Constants group, cited by 14.1.A.3.i, and $\lambda = c/f$ in the Modern Physics group, the light-specific twin of $\lambda = v/f$. If the arithmetic is the sticking point rather than the AP framing, the wave speed, frequency and wavelength guide is the place for it. Note the form the sheet prints: $\lambda = v/f$, not $v = f\lambda$.

The unit's three boundary statements, in full

A boundary statement is the CED saying where a topic stops. Unit 14 prints exactly three, and not on the topics students expect. Do not assume a topic has one: Topics 14.1, 14.2, 14.3, 14.6, 14.7 and 14.8 print none at all.

Topic 14.4, Electromagnetic Waves. 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.

Read the second sentence as carefully as the first. You need the order, not the nanometer figures.

Topic 14.5, The Doppler Effect. Only qualitative treatments of the Doppler effect are required for AP Physics 2.

This one saves the most study time in the unit. The three cases in 14.5.A.2 are the whole content: same velocity, same frequency; approaching, higher; receding, lower; larger relative velocity, larger shift.

Topic 14.9, Thin-Film Interference. Quantitative analysis of thin-film interference is limited to waves that are normal to the incident surface.

The restriction is on calculation only. 14.9.A.4.ii lists the angle at which the incident light strikes the film among the things the amount of interference depends on, so angle stays part of the qualitative picture. The same limit is repeated inside 14.9.A.5.iii, which ends by saying its quarter-wavelength result assumes incident light is normal to the surface.

How Unit 14 is tested, and an order to learn it in

The AP Physics 2 exam is 3 hours long. Section I is 42 multiple-choice questions in 85 minutes for 50 percent of the score. Section II is 4 free-response questions in 95 minutes for the other 50 percent: Question 1 Mathematical Routines, Question 2 Translation Between Representations, Question 3 Experimental Design and Analysis, Question 4 Qualitative/Quantitative Translation. A four-function, scientific, or graphing calculator is allowed on both sections. The 12 to 15 percent figure is the multiple-choice weighting, so roughly 5 to 6 of the 42 questions.

Line the science-practice weightings up against the unit's skill lists. Practice 3.B, apply an appropriate law, definition, theoretical relationship, or model to make a claim, is 20 to 25 percent of the multiple-choice section and is listed on seven of the nine topics, every one except 14.7 and 14.8. Practice 2.B, calculate an unknown quantity, is also 20 to 25 percent but is listed on only three: 14.7, 14.8 and 14.9. Practices 1.A, 1.B, 1.C and 3.A are not assessed on the multiple-choice section at all. Most of this unit is tested by asking you to state or apply a relationship, and the calculating happens at the diffraction end.

A workable order:

1. [14.1](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-1-properties-of-wave-pulses-and-waves) and [14.2](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-2-periodic-waves) together. One topic split in two: what a disturbance is, and how you measure it when it repeats.
2. Then [14.3](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-3-boundary-behavior-of-waves-and-polarization). The inversion rule and the frequency invariant are two of the most quotable facts in the unit, and both return in 14.9.
3. Then [14.4](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-4-electromagnetic-waves) and [14.5](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-5-the-doppler-effect). The lightest pair, both trimmed further by a boundary statement.
4. Then [14.6](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-6-wave-interference-and-standing-waves), slowly. This is where the teaching time goes and it is the prerequisite for the last three topics. Do not move on until you can say what happens when two pulses meet without using the word bounce.
5. Then [14.7](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-7-diffraction) and [14.8](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-8-double-slit-interference-and-diffraction-gratings) side by side. Their small-angle equations differ by one letter and by which fringe they locate, and learning them apart is what makes students swap minima for maxima under time pressure.
6. Finish with [14.9](/ap-physics-2/unit-14-waves-sound-and-physical-optics/14-9-thin-film-interference). It needs the phase-change rule, which needs index of refraction from Unit 13, and it needs superposition from 14.6.

Two habits pay off throughout. Draw the wave first, because 14.6.A.5, 14.6.B.3, 14.7.A.6 and 14.8.A.3 each say in their own words that visual representations are useful for the thing being asked. And when a question changes one quantity and asks what happens to another, answer as a ratio rather than recomputing both cases: that is what practice 2.D tests, and it is how the unit opener's own example is phrased.

Unit 14 sits in the wider AP Physics 2 course between the ray optics of Unit 13 and the photons of Unit 15. It is the middle term of an argument about what light is, and reading it that way makes the last three topics feel like evidence rather than formulas.