Flashcards · 9702 · AS Topic 8

Superposition (AS Level) flashcards

21 cards on AS Topic 8, subtopics 8.1 to 8.4. Pick a subtopic or study them all.

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How is a stationary wave formed?: Two waves of the same frequency (and amplitude) travelling in opposite directions superpose, usually a wave and its reflection.
Node and antinode: Node: a point of zero amplitude (destructive superposition). Antinode: a point of maximum amplitude.
Distance between adjacent nodes: λ ÷ 2 (half a wavelength), not λ. The same for adjacent antinodes.
Three differences between progressive and stationary waves: Progressive: transfers energy; same amplitude everywhere; phase varies continuously along the wave. Stationary: no energy transfer; amplitude varies from zero at nodes to a maximum at antinodes; points between adjacent nodes are in phase.
Fundamental frequency of a string fixed at both ends: A node at each end and one antinode in the middle: L = λ ÷ 2, so f = v ÷ 2L.
Fundamental of an air column closed at one end (end correction neglected): A node at the closed end and an antinode at the open end: L = λ ÷ 4. A pipe closed at one end supports only odd harmonics.

Diffraction: The spreading of a wave as it passes through a gap or around an obstacle.
When is diffraction most noticeable?: When the gap width is comparable to the wavelength. A gap much wider than the wavelength gives little spreading.
Why does sound diffract around a doorway but light does not noticeably?: Sound wavelengths (around a metre) are comparable to the doorway width; light wavelengths (400–700 nm) are far smaller.
How is diffraction shown in a ripple tank?: Straight wavefronts pass through a gap in a barrier. With a narrow gap (comparable to λ) they spread out into circular wavefronts; with a wide gap they barely spread. The wavelength is unchanged.

Principle of superposition: When two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements.
Coherence: Two sources are coherent if they have a constant phase difference (which needs the same frequency). It is needed for a stable interference pattern.
Path difference for constructive interference (sources in phase): nλ, a whole number of wavelengths.
Path difference for destructive interference (sources in phase): (n + ½)λ, an odd number of half-wavelengths.
Young’s double-slit equation: λ = ax ÷ D a: slit separation x: fringe spacing D: slit-to-screen distance
Why do two separate lamps of the same colour not give a stable interference pattern?: They are not coherent: there is no constant phase relationship between them, so any pattern shifts randomly. A single source split by two slits is used instead.

Diffraction grating equation: d sin θ = nλ, where d is the slit spacing (d = 1 ÷ number of lines per metre), θ the angle of the nth-order maximum from the straight-through direction.
How do you find the highest order a grating can produce?: Set sin θ = 1: n = d ÷ λ, then round down to a whole number.
A grating has 500 lines per mm and λ = 600 nm. How many orders can be seen on each side?: d = 1 ÷ 500 000 = 2.0 × 10⁻⁶ m. d ÷ λ = 3.3, so the highest order is 3.
Light of 589 nm falls on a grating of 600 lines per mm. Find the first-order angle.: d = 1.67 × 10⁻⁶ m. sin θ = 589 × 10⁻⁹ ÷ 1.67 × 10⁻⁶ = 0.353, so θ = 20.7°.
Why is a grating better than a double slit for measuring wavelength?: Many slits contribute, so the maxima are much sharper and narrower and their angles can be measured more precisely.