Skip to content
Marlbridge
Free trial

Flashcards · AP® Physics 2: Algebra-Based · Unit 14

Unit 14: Waves, Sound, and Physical Optics flashcards

57 cards on topics 14.1 to 14.9. Pick a topic or study the whole unit.

Study mode needs JavaScript. Every card is listed below, so you can still cover the answers and test yourself.

All 57 cards

For a quick read-through or printing. Cover the right-hand side to test yourself.

14.1 Properties of Wave Pulses and Waves

What does a wave transfer?
Energy, from one place to another. Each part of the medium only oscillates about its equilibrium position; the medium does not travel with the wave.
What is the difference between transverse and longitudinal waves?
Transverse: the disturbance is perpendicular to the direction of travel. Longitudinal: parallel to it. Sound is longitudinal, with compressions (high pressure) and rarefactions (low pressure).
What is the speed of a pulse on a string?
v = √(F_T/μ), with F_T the tension in N and μ = m/ℓ the mass per length in kg/m. μ = 0.010 kg/m and F_T = 25 N give 50 m/s.
The tension in a string is made four times larger. What happens to the pulse speed?
It doubles, since v ∝ √F_T. Doubling the tension gives only √2 times the speed. Four times the mass per length halves it.
Does a larger amplitude make a wave travel faster?
No. Speed depends only on the medium. Larger amplitude means more energy and, for sound, louder sound.
Which waves need a medium?
Mechanical waves (strings, water, sound) need one, so sound cannot cross a vacuum. Electromagnetic waves (light, radio) do not.
How do you measure amplitude?
As the maximum displacement from equilibrium, not crest to trough. For sound it can be the largest pressure change from normal pressure.

14.2 Periodic Waves

How are wave speed, frequency and wavelength related?
v = fλ = λ/T, with T = 1/f. Sound at 550 Hz travelling at 330 m/s has λ = 0.60 m.
What do displacement–position and displacement–time graphs of a wave show?
Displacement–position (a snapshot): the repeat distance is λ. Displacement–time (one point): the repeat time is T. Do not read λ from a time axis.
A source's frequency is tripled in the same medium. What happens to the wavelength and speed?
The speed is set by the medium, so it stays the same, and λ = v/f becomes one third.
What sets pitch and loudness?
Pitch follows frequency; loudness follows amplitude. The energy a wave carries increases with both amplitude and frequency.
What equations describe a sinusoidal wave?
At one place: x(t) = A cos(2πft) = A cos(ωt), with ω = 2πf. At one instant: y(x) = A cos(2πx/λ). Use radians.
What common errors arise reading wave diagrams?
Crest to trough is λ/2, not λ. Peak-to-peak height is 2A, not A.

14.3 Boundary Behavior of Waves and Polarization

What happens to a wave at a boundary between two media?
It is partly reflected and partly transmitted, sharing the energy, so each has a smaller amplitude. The frequency is unchanged; wavelength changes in proportion to speed.
When is a reflected pulse inverted?
When the wave slows down in the new medium (such as light rope to heavy rope, or a fixed end). It is upright when the wave speeds up (or at a free end). The transmitted pulse is always upright.
A 10 Hz wave at 40 m/s enters a medium where it moves at 15 m/s. What are the two wavelengths?
λ = v/f: 40/10 = 4.0 m, then 15/10 = 1.5 m. The frequency stays at 10 Hz.
What is polarization, and which waves can be polarized?
A polarized transverse wave oscillates in one direction. Only transverse waves can be polarized; longitudinal waves such as sound cannot. Filters, reflection and refraction can polarize light.
What intensity passes an ideal polarizing filter?
Unpolarized light: half, I = I₀/2. Already polarized light: all passes if the filter is parallel, none if perpendicular. 120 W/m² unpolarized gives 60 W/m².
What is intensity?
The average power per unit area: I = P/A, in W/m².

14.4 Electromagnetic Waves

What is an electromagnetic wave?
Oscillating electric and magnetic fields, perpendicular to each other, in step, and both perpendicular to the direction of travel. So EM waves are transverse; the polarization direction is the direction of E.
How fast do electromagnetic waves travel?
In a vacuum all travel at c = 3.00 × 10⁸ m/s whatever their frequency, and very close to c in air. They need no medium.
What is the order of the electromagnetic spectrum?
By decreasing wavelength (increasing frequency): radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Visible runs from red (longest λ) to violet.
What is the frequency of an EM wave with a wavelength of 0.20 m?
f = c/λ = 3.00 × 10⁸ / 0.20 = 1.5 × 10⁹ Hz (a microwave).
A wave travels along +x with E oscillating along z. Along which axis does B oscillate?
y. E, B and the direction of travel are mutually perpendicular.
How do you find a distance from an EM echo time?
d = ct gives the round-trip distance, so halve it for the distance to the reflector.

14.5 The Doppler Effect

What is the Doppler effect?
The observed frequency differs from the source's rest frequency f₀ because of the relative velocity of source and observer. The source's own frequency does not change.
How does the observed frequency depend on relative motion?
Separation shrinking: f is higher than f₀ (shorter λ). Separation growing: f is lower than f₀ (longer λ). Constant separation: f = f₀. Larger relative speed gives a larger shift.
What do you hear as a siren passes at constant speed?
A steady pitch above f₀ while approaching (getting louder), a quick fall through f₀ as it passes, then a steady lower pitch while receding. The pitch does not rise during the approach.
Why does a moving source change the wavelength in the medium?
Wavefronts bunch up ahead and spread out behind. The wave speed is set by the medium and does not change.
What does a red shift in a galaxy's spectrum show?
Its lines are at longer wavelengths, so it is receding. A blue shift (shorter λ) means it is approaching. For light only relative velocity matters.
Why does an observer moving towards a stationary source hear a higher frequency?
The wavelength in the medium is unchanged, but the observer meets crests more often, so more wavefronts arrive each second.

14.6 Wave Interference and Standing Waves

What is the principle of superposition?
Where waves or pulses overlap, the net displacement is the sum of the individual displacements, with signs. The waves pass through each other unchanged.
What are beats?
Two waves of slightly different frequency drift in and out of phase, so the loudness rises and falls. f_beat = |f₁ − f₂|: 440 Hz and 437 Hz give 3 Hz.
What are nodes and antinodes in a standing wave?
Nodes never move; antinodes have the largest amplitude. Neighbouring nodes are λ/2 apart; a node and the next antinode are λ/4 apart.
What are the standing-wave frequencies for a string fixed at both ends or an open–open pipe?
λₙ = 2L/n and fₙ = nv/(2L), with n = 1, 2, 3, … The fundamental has λ = 2L.
What are the resonant frequencies of a pipe closed at one end?
λₙ = 4L/n and fₙ = nv/(4L), odd n only. A 0.17 m pipe with v = 340 m/s gives 500 Hz and 1500 Hz.
What boundary conditions apply to standing waves?
A fixed string end or closed pipe end is a node. A loose string end or open pipe end is an antinode.
An upward 3 cm pulse meets a downward 1 cm pulse. What is the displacement where they overlap fully?
+2 cm: add signed displacements (+3 − 1), not sizes.

14.7 Diffraction

What is diffraction, and when is it strongest?
A wave spreading as it passes through an opening or around an edge. It is strongest when the opening width is comparable to λ; a much wider gap gives a sharp shadow. v, f and λ are unchanged.
Where are the dark fringes in single-slit diffraction?
Where a sin θ = mλ, m = ±1, ±2, … (a = slit width). This marks dark fringes, not bright ones; the centre is the brightest point.
How wide is the central band in single-slit diffraction?
2λL/a, twice the width of each side band (λL/a), for small angles. 500 nm through 0.10 mm onto a screen 2.0 m away gives 20 mm.
The slit width is doubled. What happens to the diffraction pattern?
The central band halves in width: pattern width ∝ λL/a. A narrower slit gives a wider pattern.
Why does sound spread through a doorway much more than light?
Sound wavelengths are comparable to the doorway width; light wavelengths are about a million times smaller, so light barely diffracts.
What is the path difference between waves from the two edges of a slit?
ΔL = a sin θ. Where it equals a nonzero whole number of wavelengths (λ, 2λ, …), the point is dark.

14.8 Double-Slit Interference and Diffraction Gratings

Where are the bright fringes in double-slit interference?
Where the path difference d sin θ = mλ, m = 0, ±1, …, with d the slit separation. Dark fringes are at d sin θ = (m + ½)λ.
What is the fringe spacing in a double-slit pattern?
λL/d, for small angles. 600 nm, d = 0.30 mm and L = 2.0 m give 4.0 mm. A larger slit separation gives narrower spacing.
Why was Young's double-slit experiment evidence that light is a wave?
Dark fringes show that light from two slits can cancel, which particles cannot do.
How is a diffraction grating different from a double slit?
It has many evenly spaced slits, with d = 1/N (N in lines per metre). The maxima are at the same angles, d sin θ = mλ, but much sharper and brighter.
What does white light look like through a grating?
The central maximum is white (zero path difference for every wavelength). Each order is a spectrum with violet nearest the centre and red farthest out.
A grating has 500 lines/mm. For 450 nm light, what is the highest visible order?
d = 2.0 × 10⁻⁶ m, so d/λ = 4.44. Since sin θ cannot exceed 1, the highest order is m = 4.
Why are some double-slit fringes missing?
Real slits have width, so the fringes sit inside the single-slit diffraction envelope. A fringe that falls where the envelope is zero does not appear.

14.9 Thin-Film Interference

How does thin-film interference arise?
Light reflects from both the top and bottom surfaces of the film, and the two reflected waves interfere. It shows when the thickness is comparable to the wavelength.
When does reflected light undergo a phase change?
Reflection from a higher-n medium gives a 180° phase change; from a lower n, none. Refraction never changes the phase.
What are the thin-film conditions at normal incidence?
Extra path 2t in the film, using λ/n_film. With 0 or 2 phase changes: bright for 2nt = mλ, dark for 2nt = (m + ½)λ. With 1 phase change the conditions swap.
What is the minimum thickness of an antireflection coating?
t_min = λ/(4n_coating), with the coating index between air and the lens. A coating of n = 1.25 for 600 nm needs 120 nm.
Why does a soap film look black just before it bursts?
It is much thinner than λ, and there is one phase change, so the two reflections cancel for every colour.
What is the wavelength of light inside a film?
λ_film = λ/n_film; the frequency is unchanged. 520 nm light in a film with n = 1.30 has λ = 400 nm.

Study Unit 14 further

AP® and Advanced Placement® are trademarks registered by the College Board, which is not affiliated with, and does not endorse, this website. Marlbridge is an independent tuition provider. It is not an authorized AP course provider, an AP school or an exam centre, and these resources are not official College Board materials. Reading them or doing simulations does not meet the laboratory requirement of an AP science course.