Title: InkPhysics / Waves
On every note of this deck, unless a note says otherwise:
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Front: DEFINITION
Define: Longitudinal wave.
Back: A wave whose oscillations are parallel to the direction of energy transfer, as compressions and rarefactions.

Front: CHECK YOURSELF
A wave on a rope has a period of 0.020 s and a wavelength of 8.0 m. Find (a) its frequency and (b) its speed.
Show a hint
Which equation links frequency to period? Use its answer in the second equation.
Back: (a) f = 1/T = 1 / 0.020 = 50 Hz.
(b) c = fλ = 50 × 8.0 = 400 m s^−1.
The rope itself never travels at 400 m s^−1. That is the speed of the pattern, and of the energy it carries; each piece of rope just oscillates fifty times a second about the place it started.

Front: CHECK YOURSELF
Ultrasound is used to image a fetus, and light is used to read a barcode. One of these waves could in principle be polarised. Which one, and why?
Show a hint
Classify each wave first. Which way does each one oscillate compared with its direction of travel?
Back: The light. Light is an electromagnetic wave, so it is transverse, and its oscillations are perpendicular to the ray. A filter can select one oscillation direction, which is what polarisation is.
Ultrasound is sound: a longitudinal wave. Its particles oscillate along the direction of travel, so there are no perpendicular oscillation directions to select between, and no filter orientation can polarise it.

Front: DEFINITION
Define: Diffraction.
Back: The spreading of a wave as it passes through a gap or past an edge, greatest when the gap is comparable to the wavelength.

Front: DEFINITION
Define: Node.
Back: A point on a stationary wave where the displacement is always zero.

Front: DEFINITION
Define: Path difference.
Back: The difference in the distances from two sources to a point, often expressed in wavelengths.

Front: EQUATION — NOT ON THE DATA SHEET
Grating spacing from N lines per metre:
d = ?
Back: d = 1N

Front: DEFINITION
Define: Polarised wave.
Back: A transverse wave whose oscillations are confined to a single plane containing the direction of travel.

Front: EQUATION — NOT ON THE DATA SHEET
Constructive interference condition:
constructive: path difference = ?
Back: constructive: path difference = nλ

Front: DEFINITION
Define: Stationary wave.
Back: The superposition of two progressive waves of the same frequency travelling in opposite directions, storing energy rather than transferring it.

Front: DEFINITION
Define: Critical angle.
Back: The angle of incidence in the denser medium for which the angle of refraction is 90°; beyond it total internal reflection occurs.

Front: CHECK YOURSELF
A red laser and a blue laser shine in turn through the same narrow slit. Which produces the wider central maximum, and why?
Show a hint
Which colour has the longer wavelength?
Back: The red laser. Red light has a longer wavelength than blue, so the slit width is closer to λ for red light, and the diffraction is stronger.
Stronger diffraction means the light spreads through a larger angle beyond the slit, so every feature of the pattern, including the central maximum, is wider for red than for blue.

Front: CHECK YOURSELF
In a double-slit experiment, light of wavelength 630 nm falls on slits 0.45 mm apart, and the screen is 2.0 m away. Calculate the fringe spacing.
Show a hint
Put every length into metres before you substitute.
Back: λ = 630 × 10^− 9 m, s = 0.45 × 10^− 3 m, D = 2.0 m.
w = λD / s = (630 × 10^− 9 × 2.0) / (0.45 × 10^− 3) = 2.8 × 10^− 3 m, so the bright fringes sit 2.8 mm apart.

Front: DEFINITION
Define: Transverse wave.
Back: A wave whose oscillations are perpendicular to the direction of energy transfer.

Front: DEFINITION
Define: Refractive index.
Back: The ratio of the speed of light in a vacuum to its speed in the material: n = c/v.

Front: DEFINITION
Define: Antinode.
Back: A point on a stationary wave where the amplitude of oscillation is maximum.

Front: DEFINITION
Define: Superposition.
Back: When two waves meet, the resultant displacement is the vector sum of the individual displacements.

Front: CHECK YOURSELF
A glass block has a refractive index of 1.50. Calculate the critical angle for light travelling from this glass into air.
Show a hint
Which refractive index belongs on top of the fraction?
Back: Going from glass (n_1 = 1.50) into air (n_2 = 1.00), the condition n_1 > n_2 holds, so a critical angle exists.
sin θ_c = n_2/n_1 = 1.00 / 1.50 = 0.667, so θ_c = sin^−1(0.667) = 41.8°.
Any ray inside this glass that meets the surface at more than 41.8° to the normal cannot get out; it is totally internally reflected as if the surface were a mirror.

Front: CHECK YOURSELF
A string 1.20 m long is fixed at both ends and vibrates in its third harmonic. (a) What is the wavelength? (b) At the same tension, how does its frequency compare with the first harmonic?
Show a hint
How many half-wavelengths fit into the 1.20 m?
Back: (a) The third harmonic has three loops. Each loop is half a wavelength, so L = 3λ/2, which gives λ = 2L/3 = 2 × 1.20 / 3 = 0.80 m.
(b) The wave speed depends only on the tension and the mass per unit length, so it has not changed. In the first harmonic the wavelength is 2L = 2.40 m. The wavelength has fallen by a factor of three, so by v = fλ the frequency has risen by the same factor: the third harmonic is three times the frequency of the first.
Notice what decided the answer. The fixed ends select the wavelengths that can exist, and the fixed wave speed then turns each wavelength into a frequency. The oscillator driving the string does not choose the frequencies; the string does.

Front: DEFINITION
Define: Frequency.
Back: The number of complete oscillations per second, in hertz; equivalently the number of complete waves passing a point per second.

Front: DEFINITION
Define: Wavelength.
Back: The distance between two adjacent points on a wave oscillating in phase, such as crest to crest.

Front: DEFINITION
Define: Amplitude.
Back: The maximum displacement of a particle from its equilibrium position.

Front: DEFINITION
Define: Diffraction grating.
Back: A plate ruled with a very large number of equally spaced slits, typically hundreds per millimetre.

Front: EQUATION — NOT ON THE DATA SHEET
Harmonic wavelengths on a string of length L:
λ_n = ?
Back: λ_n = 2Ln

Front: EQUATION — NOT ON THE DATA SHEET
Phase difference from path difference d:
phase difference = ?
Back: phase difference = 2πdλ

Front: EQUATION — NOT ON THE DATA SHEET
Destructive interference condition:
destructive: path difference = ?
Back: destructive: path difference = (n + 12)λ

Front: DEFINITION
Define: Step-index optical fibre.
Back: A thin glass core carrying light by total internal reflection, wrapped in cladding of slightly lower refractive index.

Front: DEFINITION
Define: Coherent sources.
Back: Sources with the same frequency and a constant phase difference.

Front: CHECK YOURSELF
Light of wavelength 550 nm falls on a grating with 300 lines per mm. Find (a) the angle of the first-order maximum and (b) the highest order that can be seen.
Show a hint
Find d first, and remember that sin θ can never pass 1.
Back: (a) d = 1/N = (1.0 × 10^− 3) / 300 = 3.33 × 10^− 6 m. Then sin θ = λ/d = (550 × 10^− 9) / (3.33 × 10^− 6) = 0.165, so θ = 9.5°.
(b) d/λ = 6.06, so the highest whole n with sin θ ≤ 1 is n = 6, and that sixth order sits out at 81.9°.

Front: DEFINITION
Define: Phase difference.
Back: The fraction of a cycle by which one oscillation leads or lags another, in radians or degrees.