Waves, Sound, and Physical Optics

What this unit covers

The topics below follow the published Physics 2 course framework for Unit 6. This unit is worth 12–15% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Lessons in this unit

• Wave Properties & the Wave Equation12 min · 3 objectivesDistinguish transverse from longitudinal waves and define wave quantities · Relate wave speed, frequency, and wavelength through v = fλ · Predict how wavelength changes when frequency changes at constant speed
• Sound Waves & the Doppler Effect13 min · 3 objectivesDescribe sound as a longitudinal pressure wave and relate its properties to what we hear · Apply v = fλ to sound in air · Explain the Doppler effect for a source moving relative to an observer
• Superposition & Interference14 min · 3 objectivesApply the principle of superposition to overlapping waves · Use path difference to distinguish constructive from destructive interference · Relate the double-slit condition to bright and dark fringes
• Diffraction & the Wave Nature of Light13 min · 3 objectivesDescribe diffraction and the condition under which it is pronounced · Explain how diffraction gratings and single slits spread light · Identify interference and diffraction as evidence that light is a wave
• Standing Waves on Strings & in Pipes15 min · 3 objectivesDetermine the harmonic frequencies of a string fixed at both ends · Distinguish open-open from open-closed pipes and their harmonic series · Relate the number of nodes and antinodes to the harmonic number
• Double Slits & Diffraction Gratings15 min · 3 objectivesApply the double-slit condition for bright and dark fringes · Compute fringe spacing on a distant screen · Explain why a grating produces sharper maxima than two slits
• Thin Films & the Phase Shift on Reflection15 min · 3 objectivesDetermine whether a reflection introduces a half-wavelength phase shift · Compute the film thickness for constructive or destructive interference · Explain the colors of soap films and the purpose of anti-reflective coatings

Formulas in Unit 6

Every term in Unit 6

All 47 terms we publish for Waves, Sound, and Physical Optics, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Double-slit interference

Bright fringes at d sin θ = mλ, with screen spacing Δy = λL/d. Longer wavelength or closer slits spread the pattern out.

Wave equation

v = fλ. In a given medium the speed is fixed, so raising frequency shortens wavelength.

Transverse vs longitudinal waves

Transverse oscillate perpendicular to travel (light, string waves); longitudinal oscillate parallel (sound). Only transverse waves can be polarized.

Wave speed depends on the medium

Set by the medium's properties, not the source. Changing frequency does not change speed in a given medium.

Superposition and interference

Overlapping waves add displacement. Constructive interference occurs when a path difference is a whole number of wavelengths, destructive at half-integer multiples.

Standing waves on a string

Fixed at both ends, wavelengths are 2L/n. The fundamental has one antinode; harmonics are integer multiples of the fundamental frequency.

Standing waves in pipes

A pipe open at both ends supports all harmonics; a pipe closed at one end supports only odd harmonics, with its fundamental an octave lower for the same length.

Beats

Two close frequencies produce a beat frequency equal to their difference — the effect used to tune instruments.

Doppler effect

Motion between source and observer shifts observed frequency: higher when approaching, lower when receding. The source frequency itself is unchanged.

Intensity and the inverse square law

Intensity falls as 1/r² for a point source spreading in three dimensions, so doubling the distance quarters the intensity.

Single-slit diffraction

a sin θ = mλ locates the DARK fringes — the opposite convention to double-slit, which is a frequent source of error.

Diffraction and wavelength

Spreading is significant when the aperture is comparable to the wavelength, which is why sound diffracts around a doorway and light does not.

Thin film interference

Reflections from the two surfaces interfere. A phase inversion occurs on reflection from a higher-index medium, and it decides which thickness gives constructive interference.

Polarization

Restricting the oscillation of a transverse wave to one plane. Proves light is transverse, since sound cannot be polarized.

What changes when a wave enters a new medium

Speed and wavelength change; frequency does not, because it is set by the source.

Reflection and phase inversion

A wave on a string reflects inverted from a fixed end and upright from a free end. The same rule governs thin-film interference.

Resonance

Driving a system at a natural frequency builds large amplitude, which is how instruments amplify and how structures fail.

Harmonics on a string

f_n = nv/2L. The fundamental has the longest wavelength; overtones are integer multiples of it.

Why a closed pipe sounds an octave lower

It supports only odd harmonics and its fundamental wavelength is 4L rather than 2L, so its fundamental frequency is half that of an open pipe of the same length.

Path difference and interference

Constructive when the path difference is a whole number of wavelengths, destructive at half-integer multiples — provided neither wave is phase-inverted.

Coherence

Interference patterns require a constant phase relationship, which is why a laser or a single source split in two is used rather than two separate lamps.

Effect of slit separation on fringe spacing

Fringe spacing is λL/d, so wider separation gives narrower fringes and longer wavelength gives wider ones.

Diffraction grating vs double slit

A grating has many slits, producing much sharper and more widely separated maxima at the same angles given by d sin θ = mλ.

Thin film thickness for constructive reflection

Depends on whether a phase inversion occurs at each surface; with one inversion, 2t = (m + ½)λ/n gives constructive reflection.

Boundary conditions choose the frequencies

A fixed end must be a node; an open end must be an antinode. Which frequencies fit follows entirely from that.

String fixed at both ends

f_n = nv/2L for all n. Fundamental wavelength is 2L, NOT L — using L makes every harmonic wrong by two.

Pipe open at both ends

f_n = nv/2L, all harmonics — the same series as a string.

Pipe closed at one end

f_n = nv/4L with n ODD only. Fundamental is a quarter wavelength, so it sounds an octave below an open pipe of equal length.

Why a closed pipe skips even harmonics

It needs a node at one end and an antinode at the other. Adding a half wavelength each time gives 4L, 4L/3, 4L/5 — odd multiples only.

What changes every harmonic

Anything that changes v. On a string that is tension and linear density — how tuning works. In a pipe it is the speed of sound, which rises with temperature.

Path difference decides interference

Whole number of wavelengths → in phase → bright. Half-integer → out of phase → dark. Every interference formula is a path-difference statement.

Double slit

Bright: d sin θ = mλ. Fringe spacing Δy = λL/d, so CLOSER slits spread the pattern OUT.

Single slit is reversed

a sin θ = mλ gives the DARK fringes for one slit, the reverse of the double-slit convention. The central maximum is twice as wide as the others.

Why a grating is sharper

The condition d sin θ = mλ is identical, but thousands of slits make cancellation between maxima nearly complete — narrow bright lines usable for spectroscopy.

Gratings are specified in lines per mm

So d is the reciprocal of that figure. Forgetting to invert it is a standard error.

The phase shift rule

Reflection from LOW index into HIGH index gives a half-wavelength shift. High into low gives none. This single rule selects the thin-film condition.

Thin film: count the shifts

ONE net shift → constructive at 2t = (m + ½)λ_film. ZERO or TWO shifts → constructive at 2t = mλ_film. Two shifts cancel each other.

Use the wavelength IN the film

λ_film = λ_vacuum/n. The light traverses the film, so the film wavelength must fit — the second most common thin-film error.

Why the thinnest soap film looks black

With 2t ≈ 0 and one phase shift, every wavelength cancels in reflection. Visible just before the film bursts.

Anti-reflective coatings

Chosen with index between air and glass so BOTH reflections shift and cancel. Thinnest working thickness is a quarter wavelength in the film.

Doppler effect direction

Approaching source raises the observed frequency, receding lowers it. Depends on relative motion, not on which one is moving.

Beat frequency

The absolute difference between two frequencies. 440 Hz against 444 Hz gives 4 beats per second — the basis of tuning by ear.

Transverse versus longitudinal

Transverse oscillates perpendicular to travel — light, waves on a string. Longitudinal oscillates along it — sound. Only transverse waves can be polarized.

The wave equation

v = fλ. Frequency is set by the source and does not change between media; the speed and wavelength do.

What determines wave speed

The MEDIUM, not the source. Amplitude and frequency do not affect the speed of a wave in a given medium.

Why sound needs a medium and light does not

Sound is a mechanical compression wave requiring particles; light is an electromagnetic wave that propagates through vacuum.

Intensity and distance

For a point source, intensity falls as 1/r² because the same power spreads over a sphere of growing area.

What examiners penalize here

• When a wave passes from one medium to another, its *frequency stays the same* (set by the source), while its speed and wavelength both change. This fact underlies refraction: light slows in glass, so its wavelength shortens while its color (frequency) is unchanged.
• Doppler shorthand: approaching → higher pitch (compressed waves), receding → lower pitch (stretched waves). The dramatic drop you hear as a vehicle passes is the switch from approaching to receding at the instant it goes by.
• Convert everything to meters before using d sinθ = mλ: millimeters are 10⁻³ and nanometers are 10⁻⁹. A power-of-ten error here is the most common way to lose the double-slit point.
• Sort the evidence: interference and diffraction demonstrate light’s *wave* nature; the photoelectric effect and Compton scattering demonstrate its *particle* nature. Light is both — the exam expects you to name which experiment reveals which side.
• Sketch the standing-wave pattern before computing. Marking the nodes and antinodes fixes the wavelength geometrically, which is more reliable than recalling which formula has 2L and which has 4L.
• Check whether the question is about a single slit or a double slit before writing the condition. The same equation d sin θ = mλ gives bright fringes for two slits and dark fringes for one, and using the wrong one inverts the entire pattern.
• Write the phase-shift count explicitly — "top: shift; bottom: no shift; one net shift, so constructive is 2t = (m + ½)λ_film". That line is often its own rubric point and it prevents the inverted answer that otherwise looks fully worked.

Practice Physics 2

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

Questions about this unit

All 7 units of AP Physics 2: Algebra-Based

1. Unit 1 · Thermodynamics
2. Unit 2 · Electric Force, Field, and Potential
3. Unit 3 · Electric Circuits
4. Unit 4 · Magnetism and Electromagnetism
5. Unit 5 · Geometric Optics
6. Unit 6 · Waves, Sound, and Physical Optics
7. Unit 7 · Modern Physics