Waves, Sound, and Physical Optics

Nine topics on what a wave carries and what happens when two of them meet. Pulses that move energy while the medium stays put, periodic waves and the two graphs that look alike, boundaries that reflect, transmit and polarize, electromagnetic waves that need no medium at all, the Doppler effect as bunched wavefronts rather than faster sound, interference and standing waves, and the three settings where path difference decides everything: diffraction, double slits and gratings, and thin films.

AP exam 12-15%9 topics

Topics

14.1

Properties of Wave Pulses and Waves

Periodic Waves

Boundary Behavior of Waves and Polarization

Electromagnetic Waves

The Doppler Effect

Wave Interference and Standing Waves

Diffraction

Double-Slit Interference and Diffraction Gratings

Thin-Film Interference

Lesson

Diagnostic

after diagnostic

Key forms For every problem in this unit

What a wave moves

ENERGY. The medium oscillates about a fixed spot and goes nowhere

Transverse or longitudinal

decided by the direction ONE PARTICLE moves, not by the shape of the graph. Sound is longitudinal

Wave relation

v = fλ. The MEDIUM fixes v, the SOURCE fixes f, so λ is what adjusts

Speed on a string

v = √(F(T) / (m/L)). Nothing about how the wave was made appears in it

Two graphs

displacement vs POSITION: repeat length is λ. Displacement vs TIME: repeat interval is T. Read the axis label first

Amplitude and frequency

independent. Loudness tracks amplitude, pitch tracks frequency

Crossing a boundary

f is unchanged; v is set by the new medium; λ = v/f absorbs the change

Reflected pulse

INVERTED off a fixed end or a slower medium, UPRIGHT off a free end or a faster one. A transmitted pulse goes with it

Polarization

TRANSVERSE waves only. Sound cannot be polarized

Polarizer stack

first filter halves unpolarized light and sets the direction; each later one depends on the angle to the light NOW arriving. Crossed axes pass nothing

Electromagnetic waves

oscillating E and B fields, mutually perpendicular and perpendicular to travel. NO medium needed; c = 3.00 × 10⁸ m/s in vacuum

Spectrum, longest to shortest

radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Within visible: red, orange, yellow, green, blue, violet

Doppler effect

wavefronts BUNCH ahead of an approaching source and spread behind it. The wave speed does not change. Constant approach gives one constant raised pitch

Superposition

add SIGNED displacements point by point. The pulses pass through each other and emerge unchanged

Standing wave

the PATTERN does not travel: nodes are fixed. Get v from v = fλ of the traveling waves that build it

String, or pipe open both ends

λ = 2L/n, all integers n

Pipe closed at one end

λ = 4L/n, ODD n only. Node at the closed end, antinode at the open one

Beats

f(beat) = |f₁ − f₂|, the DIFFERENCE. The perceived pitch is near the average

What decides interference

ΔL compared with λ. Whole numbers of λ: constructive. Odd half-integers: destructive. Divide before deciding

Diffraction spreads when

the opening is comparable to λ. NARROW slit, WIDE pattern. Judge by the ratio λ/a, never by size alone

Single slit, width a

a sinθ = mλ gives the MINIMA, m = 1, 2, 3 (no m = 0). Wide central bright band between the first two

Double slit, separation d

d sinθ = mλ gives the MAXIMA. Central maximum is m = 0

Screen position

y = mλL/d only when θ < about 10°. Otherwise solve for θ first, then y = L tanθ

Which letter is which

d = centre-to-centre slit SEPARATION (micrometres). L = slit-to-screen distance (metres). Slit WIDTH sets the envelope

Grating

same d sinθ = mλ. More slits do not move the maxima: they make them NARROWER and brighter

Grating colour order

θ rises with λ, so RED is farthest out and violet nearest the centre. Opposite to a prism, and the centre stays white

Thin film path

2t, because the ray crosses the film TWICE

Thin film wavelength

λ(film) = λ(air)/n. Compare 2t with the wavelength INSIDE the film

Reflection phase shift

reflecting off a HIGHER index adds half a wavelength; off a lower index adds nothing. Count both surfaces BEFORE writing the condition

Antireflection coating

quarter-wave: 2t = λ(film)/2, which is t = λ(film)/4

Unit 14 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items drawn from across all 9 topics, with guaranteed misconception-code coverage. Identifies which misconceptions still bite when you cannot see which topic the question came from.

Begin assessment →

Check what stuck.

Units 9 through 14, drawn evenly so earlier units get the same share as this one. Twenty questions or a full 42-question section, your choice. Even coverage means this is a retention check rather than a score estimate.

20 or 42questions

38topics

140codes covered

Begin assessment →